Bayesian statistical inference
Bruno De Finetti
2017-04-01
Full Text Available This work was translated into English and published in the volume: Bruno De Finetti, Induction and Probability, Biblioteca di Statistica, eds. P. Monari, D. Cocchi, Clueb, Bologna, 1993.Bayesian statistical Inference is one of the last fundamental philosophical papers in which we can find the essential De Finetti's approach to the statistical inference.
Inference in hybrid Bayesian networks
Lanseth, Helge; Nielsen, Thomas Dyhre; Rumí, Rafael
2009-01-01
Since the 1980s, Bayesian Networks (BNs) have become increasingly popular for building statistical models of complex systems. This is particularly true for boolean systems, where BNs often prove to be a more efficient modelling framework than traditional reliability-techniques (like fault trees...... decade's research on inference in hybrid Bayesian networks. The discussions are linked to an example model for estimating human reliability....
Bayesian inference with ecological applications
Link, William A
2009-01-01
This text is written to provide a mathematically sound but accessible and engaging introduction to Bayesian inference specifically for environmental scientists, ecologists and wildlife biologists. It emphasizes the power and usefulness of Bayesian methods in an ecological context. The advent of fast personal computers and easily available software has simplified the use of Bayesian and hierarchical models . One obstacle remains for ecologists and wildlife biologists, namely the near absence of Bayesian texts written specifically for them. The book includes many relevant examples, is supported by software and examples on a companion website and will become an essential grounding in this approach for students and research ecologists. Engagingly written text specifically designed to demystify a complex subject Examples drawn from ecology and wildlife research An essential grounding for graduate and research ecologists in the increasingly prevalent Bayesian approach to inference Companion website with analyt...
Interactive Instruction in Bayesian Inference
Khan, Azam; Breslav, Simon; Hornbæk, Kasper
2018-01-01
An instructional approach is presented to improve human performance in solving Bayesian inference problems. Starting from the original text of the classic Mammography Problem, the textual expression is modified and visualizations are added according to Mayer’s principles of instruction. These pri......An instructional approach is presented to improve human performance in solving Bayesian inference problems. Starting from the original text of the classic Mammography Problem, the textual expression is modified and visualizations are added according to Mayer’s principles of instruction....... These principles concern coherence, personalization, signaling, segmenting, multimedia, spatial contiguity, and pretraining. Principles of self-explanation and interactivity are also applied. Four experiments on the Mammography Problem showed that these principles help participants answer the questions...... that an instructional approach to improving human performance in Bayesian inference is a promising direction....
Bailer-Jones, Coryn A. L.
2017-04-01
Preface; 1. Probability basics; 2. Estimation and uncertainty; 3. Statistical models and inference; 4. Linear models, least squares, and maximum likelihood; 5. Parameter estimation: single parameter; 6. Parameter estimation: multiple parameters; 7. Approximating distributions; 8. Monte Carlo methods for inference; 9. Parameter estimation: Markov chain Monte Carlo; 10. Frequentist hypothesis testing; 11. Model comparison; 12. Dealing with more complicated problems; References; Index.
Probability biases as Bayesian inference
Andre; C. R. Martins
2006-11-01
Full Text Available In this article, I will show how several observed biases in human probabilistic reasoning can be partially explained as good heuristics for making inferences in an environment where probabilities have uncertainties associated to them. Previous results show that the weight functions and the observed violations of coalescing and stochastic dominance can be understood from a Bayesian point of view. We will review those results and see that Bayesian methods should also be used as part of the explanation behind other known biases. That means that, although the observed errors are still errors under the be understood as adaptations to the solution of real life problems. Heuristics that allow fast evaluations and mimic a Bayesian inference would be an evolutionary advantage, since they would give us an efficient way of making decisions. %XX In that sense, it should be no surprise that humans reason with % probability as it has been observed.
Inference in hybrid Bayesian networks
Langseth, Helge; Nielsen, Thomas D.; Rumi, Rafael; Salmeron, Antonio
2009-01-01
Since the 1980s, Bayesian networks (BNs) have become increasingly popular for building statistical models of complex systems. This is particularly true for boolean systems, where BNs often prove to be a more efficient modelling framework than traditional reliability techniques (like fault trees and reliability block diagrams). However, limitations in the BNs' calculation engine have prevented BNs from becoming equally popular for domains containing mixtures of both discrete and continuous variables (the so-called hybrid domains). In this paper we focus on these difficulties, and summarize some of the last decade's research on inference in hybrid Bayesian networks. The discussions are linked to an example model for estimating human reliability.
Bayesian inference on proportional elections.
Gabriel Hideki Vatanabe Brunello
Full Text Available Polls for majoritarian voting systems usually show estimates of the percentage of votes for each candidate. However, proportional vote systems do not necessarily guarantee the candidate with the most percentage of votes will be elected. Thus, traditional methods used in majoritarian elections cannot be applied on proportional elections. In this context, the purpose of this paper was to perform a Bayesian inference on proportional elections considering the Brazilian system of seats distribution. More specifically, a methodology to answer the probability that a given party will have representation on the chamber of deputies was developed. Inferences were made on a Bayesian scenario using the Monte Carlo simulation technique, and the developed methodology was applied on data from the Brazilian elections for Members of the Legislative Assembly and Federal Chamber of Deputies in 2010. A performance rate was also presented to evaluate the efficiency of the methodology. Calculations and simulations were carried out using the free R statistical software.
Bayesian methods for hackers probabilistic programming and Bayesian inference
Davidson-Pilon, Cameron
2016-01-01
Bayesian methods of inference are deeply natural and extremely powerful. However, most discussions of Bayesian inference rely on intensely complex mathematical analyses and artificial examples, making it inaccessible to anyone without a strong mathematical background. Now, though, Cameron Davidson-Pilon introduces Bayesian inference from a computational perspective, bridging theory to practice–freeing you to get results using computing power. Bayesian Methods for Hackers illuminates Bayesian inference through probabilistic programming with the powerful PyMC language and the closely related Python tools NumPy, SciPy, and Matplotlib. Using this approach, you can reach effective solutions in small increments, without extensive mathematical intervention. Davidson-Pilon begins by introducing the concepts underlying Bayesian inference, comparing it with other techniques and guiding you through building and training your first Bayesian model. Next, he introduces PyMC through a series of detailed examples a...
Bayesian inference for Hawkes processes
Rasmussen, Jakob Gulddahl
The Hawkes process is a practically and theoretically important class of point processes, but parameter-estimation for such a process can pose various problems. In this paper we explore and compare two approaches to Bayesian inference. The first approach is based on the so-called conditional...... intensity function, while the second approach is based on an underlying clustering and branching structure in the Hawkes process. For practical use, MCMC (Markov chain Monte Carlo) methods are employed. The two approaches are compared numerically using three examples of the Hawkes process....
Bayesian inference for Hawkes processes
Rasmussen, Jakob Gulddahl
2013-01-01
The Hawkes process is a practically and theoretically important class of point processes, but parameter-estimation for such a process can pose various problems. In this paper we explore and compare two approaches to Bayesian inference. The first approach is based on the so-called conditional...... intensity function, while the second approach is based on an underlying clustering and branching structure in the Hawkes process. For practical use, MCMC (Markov chain Monte Carlo) methods are employed. The two approaches are compared numerically using three examples of the Hawkes process....
Nonparametric Bayesian inference in biostatistics
Müller, Peter
2015-01-01
As chapters in this book demonstrate, BNP has important uses in clinical sciences and inference for issues like unknown partitions in genomics. Nonparametric Bayesian approaches (BNP) play an ever expanding role in biostatistical inference from use in proteomics to clinical trials. Many research problems involve an abundance of data and require flexible and complex probability models beyond the traditional parametric approaches. As this book's expert contributors show, BNP approaches can be the answer. Survival Analysis, in particular survival regression, has traditionally used BNP, but BNP's potential is now very broad. This applies to important tasks like arrangement of patients into clinically meaningful subpopulations and segmenting the genome into functionally distinct regions. This book is designed to both review and introduce application areas for BNP. While existing books provide theoretical foundations, this book connects theory to practice through engaging examples and research questions. Chapters c...
Variations on Bayesian Prediction and Inference
2016-05-09
inference 2.2.1 Background There are a number of statistical inference problems that are not generally formulated via a full probability model...problem of inference about an unknown parameter, the Bayesian approach requires a full probability 1. REPORT DATE (DD-MM-YYYY) 4. TITLE AND...the problem of inference about an unknown parameter, the Bayesian approach requires a full probability model/likelihood which can be an obstacle
Compiling Relational Bayesian Networks for Exact Inference
Jaeger, Manfred; Darwiche, Adnan; Chavira, Mark
2006-01-01
We describe in this paper a system for exact inference with relational Bayesian networks as defined in the publicly available PRIMULA tool. The system is based on compiling propositional instances of relational Bayesian networks into arithmetic circuits and then performing online inference...
Compiling Relational Bayesian Networks for Exact Inference
Jaeger, Manfred; Chavira, Mark; Darwiche, Adnan
2004-01-01
We describe a system for exact inference with relational Bayesian networks as defined in the publicly available \\primula\\ tool. The system is based on compiling propositional instances of relational Bayesian networks into arithmetic circuits and then performing online inference by evaluating...
Bayesian Inference Methods for Sparse Channel Estimation
Pedersen, Niels Lovmand
2013-01-01
This thesis deals with sparse Bayesian learning (SBL) with application to radio channel estimation. As opposed to the classical approach for sparse signal representation, we focus on the problem of inferring complex signals. Our investigations within SBL constitute the basis for the development...... of Bayesian inference algorithms for sparse channel estimation. Sparse inference methods aim at finding the sparse representation of a signal given in some overcomplete dictionary of basis vectors. Within this context, one of our main contributions to the field of SBL is a hierarchical representation...... analysis of the complex prior representation, where we show that the ability to induce sparse estimates of a given prior heavily depends on the inference method used and, interestingly, whether real or complex variables are inferred. We also show that the Bayesian estimators derived from the proposed...
Bayesian Inference on Gravitational Waves
Asad Ali
2015-12-01
Full Text Available The Bayesian approach is increasingly becoming popular among the astrophysics data analysis communities. However, the Pakistan statistics communities are unaware of this fertile interaction between the two disciplines. Bayesian methods have been in use to address astronomical problems since the very birth of the Bayes probability in eighteenth century. Today the Bayesian methods for the detection and parameter estimation of gravitational waves have solid theoretical grounds with a strong promise for the realistic applications. This article aims to introduce the Pakistan statistics communities to the applications of Bayesian Monte Carlo methods in the analysis of gravitational wave data with an overview of the Bayesian signal detection and estimation methods and demonstration by a couple of simplified examples.
An Intuitive Dashboard for Bayesian Network Inference
Reddy, Vikas; Farr, Anna Charisse; Wu, Paul; Mengersen, Kerrie; Yarlagadda, Prasad K D V
2014-01-01
Current Bayesian network software packages provide good graphical interface for users who design and develop Bayesian networks for various applications. However, the intended end-users of these networks may not necessarily find such an interface appealing and at times it could be overwhelming, particularly when the number of nodes in the network is large. To circumvent this problem, this paper presents an intuitive dashboard, which provides an additional layer of abstraction, enabling the end-users to easily perform inferences over the Bayesian networks. Unlike most software packages, which display the nodes and arcs of the network, the developed tool organises the nodes based on the cause-and-effect relationship, making the user-interaction more intuitive and friendly. In addition to performing various types of inferences, the users can conveniently use the tool to verify the behaviour of the developed Bayesian network. The tool has been developed using QT and SMILE libraries in C++
An Intuitive Dashboard for Bayesian Network Inference
Reddy, Vikas; Charisse Farr, Anna; Wu, Paul; Mengersen, Kerrie; Yarlagadda, Prasad K. D. V.
2014-03-01
Current Bayesian network software packages provide good graphical interface for users who design and develop Bayesian networks for various applications. However, the intended end-users of these networks may not necessarily find such an interface appealing and at times it could be overwhelming, particularly when the number of nodes in the network is large. To circumvent this problem, this paper presents an intuitive dashboard, which provides an additional layer of abstraction, enabling the end-users to easily perform inferences over the Bayesian networks. Unlike most software packages, which display the nodes and arcs of the network, the developed tool organises the nodes based on the cause-and-effect relationship, making the user-interaction more intuitive and friendly. In addition to performing various types of inferences, the users can conveniently use the tool to verify the behaviour of the developed Bayesian network. The tool has been developed using QT and SMILE libraries in C++.
A Bayesian Network Schema for Lessening Database Inference
Chang, LiWu; Moskowitz, Ira S
2001-01-01
.... The authors introduce a formal schema for database inference analysis, based upon a Bayesian network structure, which identifies critical parameters involved in the inference problem and represents...
Polynomial Chaos Surrogates for Bayesian Inference
Le Maitre, Olivier
2016-01-06
The Bayesian inference is a popular probabilistic method to solve inverse problems, such as the identification of field parameter in a PDE model. The inference rely on the Bayes rule to update the prior density of the sought field, from observations, and derive its posterior distribution. In most cases the posterior distribution has no explicit form and has to be sampled, for instance using a Markov-Chain Monte Carlo method. In practice the prior field parameter is decomposed and truncated (e.g. by means of Karhunen- Lo´eve decomposition) to recast the inference problem into the inference of a finite number of coordinates. Although proved effective in many situations, the Bayesian inference as sketched above faces several difficulties requiring improvements. First, sampling the posterior can be a extremely costly task as it requires multiple resolutions of the PDE model for different values of the field parameter. Second, when the observations are not very much informative, the inferred parameter field can highly depends on its prior which can be somehow arbitrary. These issues have motivated the introduction of reduced modeling or surrogates for the (approximate) determination of the parametrized PDE solution and hyperparameters in the description of the prior field. Our contribution focuses on recent developments in these two directions: the acceleration of the posterior sampling by means of Polynomial Chaos expansions and the efficient treatment of parametrized covariance functions for the prior field. We also discuss the possibility of making such approach adaptive to further improve its efficiency.
Fast Bayesian Inference in Dirichlet Process Mixture Models.
Wang, Lianming; Dunson, David B
2011-01-01
There has been increasing interest in applying Bayesian nonparametric methods in large samples and high dimensions. As Markov chain Monte Carlo (MCMC) algorithms are often infeasible, there is a pressing need for much faster algorithms. This article proposes a fast approach for inference in Dirichlet process mixture (DPM) models. Viewing the partitioning of subjects into clusters as a model selection problem, we propose a sequential greedy search algorithm for selecting the partition. Then, when conjugate priors are chosen, the resulting posterior conditionally on the selected partition is available in closed form. This approach allows testing of parametric models versus nonparametric alternatives based on Bayes factors. We evaluate the approach using simulation studies and compare it with four other fast nonparametric methods in the literature. We apply the proposed approach to three datasets including one from a large epidemiologic study. Matlab codes for the simulation and data analyses using the proposed approach are available online in the supplemental materials.
The NIFTY way of Bayesian signal inference
Selig, Marco
2014-01-01
We introduce NIFTY, 'Numerical Information Field Theory', a software package for the development of Bayesian signal inference algorithms that operate independently from any underlying spatial grid and its resolution. A large number of Bayesian and Maximum Entropy methods for 1D signal reconstruction, 2D imaging, as well as 3D tomography, appear formally similar, but one often finds individualized implementations that are neither flexible nor easily transferable. Signal inference in the framework of NIFTY can be done in an abstract way, such that algorithms, prototyped in 1D, can be applied to real world problems in higher-dimensional settings. NIFTY as a versatile library is applicable and already has been applied in 1D, 2D, 3D and spherical settings. A recent application is the D 3 PO algorithm targeting the non-trivial task of denoising, deconvolving, and decomposing photon observations in high energy astronomy
The NIFTy way of Bayesian signal inference
Selig, Marco
2014-12-01
We introduce NIFTy, "Numerical Information Field Theory", a software package for the development of Bayesian signal inference algorithms that operate independently from any underlying spatial grid and its resolution. A large number of Bayesian and Maximum Entropy methods for 1D signal reconstruction, 2D imaging, as well as 3D tomography, appear formally similar, but one often finds individualized implementations that are neither flexible nor easily transferable. Signal inference in the framework of NIFTy can be done in an abstract way, such that algorithms, prototyped in 1D, can be applied to real world problems in higher-dimensional settings. NIFTy as a versatile library is applicable and already has been applied in 1D, 2D, 3D and spherical settings. A recent application is the D3PO algorithm targeting the non-trivial task of denoising, deconvolving, and decomposing photon observations in high energy astronomy.
Bayesianism and inference to the best explanation
Valeriano IRANZO
2008-01-01
Full Text Available Bayesianism and Inference to the best explanation (IBE are two different models of inference. Recently there has been some debate about the possibility of “bayesianizing” IBE. Firstly I explore several alternatives to include explanatory considerations in Bayes’s Theorem. Then I distinguish two different interpretations of prior probabilities: “IBE-Bayesianism” (IBE-Bay and “frequentist-Bayesianism” (Freq-Bay. After detailing the content of the latter, I propose a rule for assessing the priors. I also argue that Freq-Bay: (i endorses a role for explanatory value in the assessment of scientific hypotheses; (ii avoids a purely subjectivist reading of prior probabilities; and (iii fits better than IBE-Bayesianism with two basic facts about science, i.e., the prominent role played by empirical testing and the existence of many scientific theories in the past that failed to fulfil their promises and were subsequently abandoned.
Optimal inference with suboptimal models: Addiction and active Bayesian inference
Schwartenbeck, Philipp; FitzGerald, Thomas H.B.; Mathys, Christoph; Dolan, Ray; Wurst, Friedrich; Kronbichler, Martin; Friston, Karl
2015-01-01
When casting behaviour as active (Bayesian) inference, optimal inference is defined with respect to an agent’s beliefs – based on its generative model of the world. This contrasts with normative accounts of choice behaviour, in which optimal actions are considered in relation to the true structure of the environment – as opposed to the agent’s beliefs about worldly states (or the task). This distinction shifts an understanding of suboptimal or pathological behaviour away from aberrant inference as such, to understanding the prior beliefs of a subject that cause them to behave less ‘optimally’ than our prior beliefs suggest they should behave. Put simply, suboptimal or pathological behaviour does not speak against understanding behaviour in terms of (Bayes optimal) inference, but rather calls for a more refined understanding of the subject’s generative model upon which their (optimal) Bayesian inference is based. Here, we discuss this fundamental distinction and its implications for understanding optimality, bounded rationality and pathological (choice) behaviour. We illustrate our argument using addictive choice behaviour in a recently described ‘limited offer’ task. Our simulations of pathological choices and addictive behaviour also generate some clear hypotheses, which we hope to pursue in ongoing empirical work. PMID:25561321
Using Alien Coins to Test Whether Simple Inference Is Bayesian
Cassey, Peter; Hawkins, Guy E.; Donkin, Chris; Brown, Scott D.
2016-01-01
Reasoning and inference are well-studied aspects of basic cognition that have been explained as statistically optimal Bayesian inference. Using a simplified experimental design, we conducted quantitative comparisons between Bayesian inference and human inference at the level of individuals. In 3 experiments, with more than 13,000 participants, we…
Constrained bayesian inference of project performance models
Sunmola, Funlade
2013-01-01
Project performance models play an important role in the management of project success. When used for monitoring projects, they can offer predictive ability such as indications of possible delivery problems. Approaches for monitoring project performance relies on available project information including restrictions imposed on the project, particularly the constraints of cost, quality, scope and time. We study in this paper a Bayesian inference methodology for project performance modelling in ...
Variational Bayesian Inference of Line Spectra
Badiu, Mihai Alin; Hansen, Thomas Lundgaard; Fleury, Bernard Henri
2017-01-01
parameters. We propose an accurate representation of the pdfs of the frequencies by mixtures of von Mises pdfs, which yields closed-form expectations. We define the algorithm VALSE in which the estimates of the pdfs and parameters are iteratively updated. VALSE is a gridless, convergent method, does......; and the coefficients are governed by a Bernoulli-Gaussian prior model turning model order selection into binary sequence detection. Unlike earlier works which retain only point estimates of the frequencies, we undertake a more complete Bayesian treatment by estimating the posterior probability density functions (pdfs......) of the frequencies and computing expectations over them. Thus, we additionally capture and operate with the uncertainty of the frequency estimates. Aiming to maximize the model evidence, variational optimization provides analytic approximations of the posterior pdfs and also gives estimates of the additional...
Bayesian structural inference for hidden processes
Strelioff, Christopher C.; Crutchfield, James P.
2014-04-01
We introduce a Bayesian approach to discovering patterns in structurally complex processes. The proposed method of Bayesian structural inference (BSI) relies on a set of candidate unifilar hidden Markov model (uHMM) topologies for inference of process structure from a data series. We employ a recently developed exact enumeration of topological ɛ-machines. (A sequel then removes the topological restriction.) This subset of the uHMM topologies has the added benefit that inferred models are guaranteed to be ɛ-machines, irrespective of estimated transition probabilities. Properties of ɛ-machines and uHMMs allow for the derivation of analytic expressions for estimating transition probabilities, inferring start states, and comparing the posterior probability of candidate model topologies, despite process internal structure being only indirectly present in data. We demonstrate BSI's effectiveness in estimating a process's randomness, as reflected by the Shannon entropy rate, and its structure, as quantified by the statistical complexity. We also compare using the posterior distribution over candidate models and the single, maximum a posteriori model for point estimation and show that the former more accurately reflects uncertainty in estimated values. We apply BSI to in-class examples of finite- and infinite-order Markov processes, as well to an out-of-class, infinite-state hidden process.
Bayesian Estimation and Inference using Stochastic Hardware
Chetan Singh Thakur
2016-03-01
Full Text Available In this paper, we present the implementation of two types of Bayesian inference problems to demonstrate the potential of building probabilistic algorithms in hardware using single set of building blocks with the ability to perform these computations in real time. The first implementation, referred to as the BEAST (Bayesian Estimation and Stochastic Tracker, demonstrates a simple problem where an observer uses an underlying Hidden Markov Model (HMM to track a target in one dimension. In this implementation, sensors make noisy observations of the target position at discrete time steps. The tracker learns the transition model for target movement, and the observation model for the noisy sensors, and uses these to estimate the target position by solving the Bayesian recursive equation online. We show the tracking performance of the system and demonstrate how it can learn the observation model, the transition model, and the external distractor (noise probability interfering with the observations. In the second implementation, referred to as the Bayesian INference in DAG (BIND, we show how inference can be performed in a Directed Acyclic Graph (DAG using stochastic circuits. We show how these building blocks can be easily implemented using simple digital logic gates. An advantage of the stochastic electronic implementation is that it is robust to certain types of noise, which may become an issue in integrated circuit (IC technology with feature sizes in the order of tens of nanometers due to their low noise margin, the effect of high-energy cosmic rays and the low supply voltage. In our framework, the flipping of random individual bits would not affect the system performance because information is encoded in a bit stream.
Bayesian Estimation and Inference Using Stochastic Electronics.
Thakur, Chetan Singh; Afshar, Saeed; Wang, Runchun M; Hamilton, Tara J; Tapson, Jonathan; van Schaik, André
2016-01-01
In this paper, we present the implementation of two types of Bayesian inference problems to demonstrate the potential of building probabilistic algorithms in hardware using single set of building blocks with the ability to perform these computations in real time. The first implementation, referred to as the BEAST (Bayesian Estimation and Stochastic Tracker), demonstrates a simple problem where an observer uses an underlying Hidden Markov Model (HMM) to track a target in one dimension. In this implementation, sensors make noisy observations of the target position at discrete time steps. The tracker learns the transition model for target movement, and the observation model for the noisy sensors, and uses these to estimate the target position by solving the Bayesian recursive equation online. We show the tracking performance of the system and demonstrate how it can learn the observation model, the transition model, and the external distractor (noise) probability interfering with the observations. In the second implementation, referred to as the Bayesian INference in DAG (BIND), we show how inference can be performed in a Directed Acyclic Graph (DAG) using stochastic circuits. We show how these building blocks can be easily implemented using simple digital logic gates. An advantage of the stochastic electronic implementation is that it is robust to certain types of noise, which may become an issue in integrated circuit (IC) technology with feature sizes in the order of tens of nanometers due to their low noise margin, the effect of high-energy cosmic rays and the low supply voltage. In our framework, the flipping of random individual bits would not affect the system performance because information is encoded in a bit stream.
Heuristics as Bayesian inference under extreme priors.
Parpart, Paula; Jones, Matt; Love, Bradley C
2018-05-01
Simple heuristics are often regarded as tractable decision strategies because they ignore a great deal of information in the input data. One puzzle is why heuristics can outperform full-information models, such as linear regression, which make full use of the available information. These "less-is-more" effects, in which a relatively simpler model outperforms a more complex model, are prevalent throughout cognitive science, and are frequently argued to demonstrate an inherent advantage of simplifying computation or ignoring information. In contrast, we show at the computational level (where algorithmic restrictions are set aside) that it is never optimal to discard information. Through a formal Bayesian analysis, we prove that popular heuristics, such as tallying and take-the-best, are formally equivalent to Bayesian inference under the limit of infinitely strong priors. Varying the strength of the prior yields a continuum of Bayesian models with the heuristics at one end and ordinary regression at the other. Critically, intermediate models perform better across all our simulations, suggesting that down-weighting information with the appropriate prior is preferable to entirely ignoring it. Rather than because of their simplicity, our analyses suggest heuristics perform well because they implement strong priors that approximate the actual structure of the environment. We end by considering how new heuristics could be derived by infinitely strengthening the priors of other Bayesian models. These formal results have implications for work in psychology, machine learning and economics. Copyright © 2017 The Authors. Published by Elsevier Inc. All rights reserved.
Bayesian Inference of a Multivariate Regression Model
Marick S. Sinay
2014-01-01
Full Text Available We explore Bayesian inference of a multivariate linear regression model with use of a flexible prior for the covariance structure. The commonly adopted Bayesian setup involves the conjugate prior, multivariate normal distribution for the regression coefficients and inverse Wishart specification for the covariance matrix. Here we depart from this approach and propose a novel Bayesian estimator for the covariance. A multivariate normal prior for the unique elements of the matrix logarithm of the covariance matrix is considered. Such structure allows for a richer class of prior distributions for the covariance, with respect to strength of beliefs in prior location hyperparameters, as well as the added ability, to model potential correlation amongst the covariance structure. The posterior moments of all relevant parameters of interest are calculated based upon numerical results via a Markov chain Monte Carlo procedure. The Metropolis-Hastings-within-Gibbs algorithm is invoked to account for the construction of a proposal density that closely matches the shape of the target posterior distribution. As an application of the proposed technique, we investigate a multiple regression based upon the 1980 High School and Beyond Survey.
Efficient Bayesian inference for ARFIMA processes
Graves, T.; Gramacy, R. B.; Franzke, C. L. E.; Watkins, N. W.
2015-03-01
Many geophysical quantities, like atmospheric temperature, water levels in rivers, and wind speeds, have shown evidence of long-range dependence (LRD). LRD means that these quantities experience non-trivial temporal memory, which potentially enhances their predictability, but also hampers the detection of externally forced trends. Thus, it is important to reliably identify whether or not a system exhibits LRD. In this paper we present a modern and systematic approach to the inference of LRD. Rather than Mandelbrot's fractional Gaussian noise, we use the more flexible Autoregressive Fractional Integrated Moving Average (ARFIMA) model which is widely used in time series analysis, and of increasing interest in climate science. Unlike most previous work on the inference of LRD, which is frequentist in nature, we provide a systematic treatment of Bayesian inference. In particular, we provide a new approximate likelihood for efficient parameter inference, and show how nuisance parameters (e.g. short memory effects) can be integrated over in order to focus on long memory parameters, and hypothesis testing more directly. We illustrate our new methodology on the Nile water level data, with favorable comparison to the standard estimators.
Integrating distributed Bayesian inference and reinforcement learning for sensor management
Grappiolo, C.; Whiteson, S.; Pavlin, G.; Bakker, B.
2009-01-01
This paper introduces a sensor management approach that integrates distributed Bayesian inference (DBI) and reinforcement learning (RL). DBI is implemented using distributed perception networks (DPNs), a multiagent approach to performing efficient inference, while RL is used to automatically
A Fast Iterative Bayesian Inference Algorithm for Sparse Channel Estimation
Pedersen, Niels Lovmand; Manchón, Carles Navarro; Fleury, Bernard Henri
2013-01-01
representation of the Bessel K probability density function; a highly efficient, fast iterative Bayesian inference method is then applied to the proposed model. The resulting estimator outperforms other state-of-the-art Bayesian and non-Bayesian estimators, either by yielding lower mean squared estimation error...
Comparative Study of Inference Methods for Bayesian Nonnegative Matrix Factorisation
Brouwer, Thomas; Frellsen, Jes; Liò, Pietro
2017-01-01
In this paper, we study the trade-offs of different inference approaches for Bayesian matrix factorisation methods, which are commonly used for predicting missing values, and for finding patterns in the data. In particular, we consider Bayesian nonnegative variants of matrix factorisation and tri......-factorisation, and compare non-probabilistic inference, Gibbs sampling, variational Bayesian inference, and a maximum-a-posteriori approach. The variational approach is new for the Bayesian nonnegative models. We compare their convergence, and robustness to noise and sparsity of the data, on both synthetic and real...
Towards Bayesian Inference of the Fast-Ion Distribution Function
Stagner, L.; Heidbrink, W.W.; Salewski, Mirko
2012-01-01
sensitivity of the measurements are incorporated into Bayesian likelihood probabilities, while prior probabilities enforce physical constraints. As an initial step, this poster uses Bayesian statistics to infer the DIII-D electron density profile from multiple diagnostic measurements. Likelihood functions....... However, when theory and experiment disagree (for one or more diagnostics), it is unclear how to proceed. Bayesian statistics provides a framework to infer the DF, quantify errors, and reconcile discrepant diagnostic measurements. Diagnostic errors and ``weight functions" that describe the phase space...
Quantum-Like Representation of Non-Bayesian Inference
Asano, M.; Basieva, I.; Khrennikov, A.; Ohya, M.; Tanaka, Y.
2013-01-01
This research is related to the problem of "irrational decision making or inference" that have been discussed in cognitive psychology. There are some experimental studies, and these statistical data cannot be described by classical probability theory. The process of decision making generating these data cannot be reduced to the classical Bayesian inference. For this problem, a number of quantum-like coginitive models of decision making was proposed. Our previous work represented in a natural way the classical Bayesian inference in the frame work of quantum mechanics. By using this representation, in this paper, we try to discuss the non-Bayesian (irrational) inference that is biased by effects like the quantum interference. Further, we describe "psychological factor" disturbing "rationality" as an "environment" correlating with the "main system" of usual Bayesian inference.
Universal Darwinism As a Process of Bayesian Inference.
Campbell, John O
2016-01-01
Many of the mathematical frameworks describing natural selection are equivalent to Bayes' Theorem, also known as Bayesian updating. By definition, a process of Bayesian Inference is one which involves a Bayesian update, so we may conclude that these frameworks describe natural selection as a process of Bayesian inference. Thus, natural selection serves as a counter example to a widely-held interpretation that restricts Bayesian Inference to human mental processes (including the endeavors of statisticians). As Bayesian inference can always be cast in terms of (variational) free energy minimization, natural selection can be viewed as comprising two components: a generative model of an "experiment" in the external world environment, and the results of that "experiment" or the "surprise" entailed by predicted and actual outcomes of the "experiment." Minimization of free energy implies that the implicit measure of "surprise" experienced serves to update the generative model in a Bayesian manner. This description closely accords with the mechanisms of generalized Darwinian process proposed both by Dawkins, in terms of replicators and vehicles, and Campbell, in terms of inferential systems. Bayesian inference is an algorithm for the accumulation of evidence-based knowledge. This algorithm is now seen to operate over a wide range of evolutionary processes, including natural selection, the evolution of mental models and cultural evolutionary processes, notably including science itself. The variational principle of free energy minimization may thus serve as a unifying mathematical framework for universal Darwinism, the study of evolutionary processes operating throughout nature.
Universal Darwinism as a process of Bayesian inference
John Oberon Campbell
2016-06-01
Full Text Available Many of the mathematical frameworks describing natural selection are equivalent to Bayes’ Theorem, also known as Bayesian updating. By definition, a process of Bayesian Inference is one which involves a Bayesian update, so we may conclude that these frameworks describe natural selection as a process of Bayesian inference. Thus natural selection serves as a counter example to a widely-held interpretation that restricts Bayesian Inference to human mental processes (including the endeavors of statisticians. As Bayesian inference can always be cast in terms of (variational free energy minimization, natural selection can be viewed as comprising two components: a generative model of an ‘experiment’ in the external world environment, and the results of that 'experiment' or the 'surprise' entailed by predicted and actual outcomes of the ‘experiment’. Minimization of free energy implies that the implicit measure of 'surprise' experienced serves to update the generative model in a Bayesian manner. This description closely accords with the mechanisms of generalized Darwinian process proposed both by Dawkins, in terms of replicators and vehicles, and Campbell, in terms of inferential systems. Bayesian inference is an algorithm for the accumulation of evidence-based knowledge. This algorithm is now seen to operate over a wide range of evolutionary processes, including natural selection, the evolution of mental models and cultural evolutionary processes, notably including science itself. The variational principle of free energy minimization may thus serve as a unifying mathematical framework for universal Darwinism, the study of evolutionary processes operating throughout nature.
Bayesian inference of radiation belt loss timescales.
Camporeale, E.; Chandorkar, M.
2017-12-01
Electron fluxes in the Earth's radiation belts are routinely studied using the classical quasi-linear radial diffusion model. Although this simplified linear equation has proven to be an indispensable tool in understanding the dynamics of the radiation belt, it requires specification of quantities such as the diffusion coefficient and electron loss timescales that are never directly measured. Researchers have so far assumed a-priori parameterisations for radiation belt quantities and derived the best fit using satellite data. The state of the art in this domain lacks a coherent formulation of this problem in a probabilistic framework. We present some recent progress that we have made in performing Bayesian inference of radial diffusion parameters. We achieve this by making extensive use of the theory connecting Gaussian Processes and linear partial differential equations, and performing Markov Chain Monte Carlo sampling of radial diffusion parameters. These results are important for understanding the role and the propagation of uncertainties in radiation belt simulations and, eventually, for providing a probabilistic forecast of energetic electron fluxes in a Space Weather context.
BAYESIAN INFERENCE OF CMB GRAVITATIONAL LENSING
Anderes, Ethan [Department of Statistics, University of California, Davis, CA 95616 (United States); Wandelt, Benjamin D.; Lavaux, Guilhem [Sorbonne Universités, UPMC Univ Paris 06 and CNRS, UMR7095, Institut d’Astrophysique de Paris, F-75014, Paris (France)
2015-08-01
The Planck satellite, along with several ground-based telescopes, has mapped the cosmic microwave background (CMB) at sufficient resolution and signal-to-noise so as to allow a detection of the subtle distortions due to the gravitational influence of the intervening matter distribution. A natural modeling approach is to write a Bayesian hierarchical model for the lensed CMB in terms of the unlensed CMB and the lensing potential. So far there has been no feasible algorithm for inferring the posterior distribution of the lensing potential from the lensed CMB map. We propose a solution that allows efficient Markov Chain Monte Carlo sampling from the joint posterior of the lensing potential and the unlensed CMB map using the Hamiltonian Monte Carlo technique. The main conceptual step in the solution is a re-parameterization of CMB lensing in terms of the lensed CMB and the “inverse lensing” potential. We demonstrate a fast implementation on simulated data, including noise and a sky cut, that uses a further acceleration based on a very mild approximation of the inverse lensing potential. We find that the resulting Markov Chain has short correlation lengths and excellent convergence properties, making it promising for applications to high-resolution CMB data sets in the future.
Bayesian inference of chemical kinetic models from proposed reactions
Galagali, Nikhil; Marzouk, Youssef M.
2015-01-01
© 2014 Elsevier Ltd. Bayesian inference provides a natural framework for combining experimental data with prior knowledge to develop chemical kinetic models and quantify the associated uncertainties, not only in parameter values but also in model
Efficient design and inference in distributed Bayesian networks: an overview
de Oude, P.; Groen, F.C.A.; Pavlin, G.; Bezhanishvili, N.; Löbner, S.; Schwabe, K.; Spada, L.
2011-01-01
This paper discusses an approach to distributed Bayesian modeling and inference, which is relevant for an important class of contemporary real world situation assessment applications. By explicitly considering the locality of causal relations, the presented approach (i) supports coherent distributed
Bayesian Information Criterion as an Alternative way of Statistical Inference
Nadejda Yu. Gubanova
2012-05-01
Full Text Available The article treats Bayesian information criterion as an alternative to traditional methods of statistical inference, based on NHST. The comparison of ANOVA and BIC results for psychological experiment is discussed.
On Bayesian Inference under Sampling from Scale Mixtures of Normals
Fernández, C.; Steel, M.F.J.
1996-01-01
This paper considers a Bayesian analysis of the linear regression model under independent sampling from general scale mixtures of Normals.Using a common reference prior, we investigate the validity of Bayesian inference and the existence of posterior moments of the regression and precision
Bayesian inference for disease prevalence using negative binomial group testing
Pritchard, Nicholas A.; Tebbs, Joshua M.
2011-01-01
Group testing, also known as pooled testing, and inverse sampling are both widely used methods of data collection when the goal is to estimate a small proportion. Taking a Bayesian approach, we consider the new problem of estimating disease prevalence from group testing when inverse (negative binomial) sampling is used. Using different distributions to incorporate prior knowledge of disease incidence and different loss functions, we derive closed form expressions for posterior distributions and resulting point and credible interval estimators. We then evaluate our new estimators, on Bayesian and classical grounds, and apply our methods to a West Nile Virus data set. PMID:21259308
Cortical hierarchies perform Bayesian causal inference in multisensory perception.
Tim Rohe
2015-02-01
Full Text Available To form a veridical percept of the environment, the brain needs to integrate sensory signals from a common source but segregate those from independent sources. Thus, perception inherently relies on solving the "causal inference problem." Behaviorally, humans solve this problem optimally as predicted by Bayesian Causal Inference; yet, the underlying neural mechanisms are unexplored. Combining psychophysics, Bayesian modeling, functional magnetic resonance imaging (fMRI, and multivariate decoding in an audiovisual spatial localization task, we demonstrate that Bayesian Causal Inference is performed by a hierarchy of multisensory processes in the human brain. At the bottom of the hierarchy, in auditory and visual areas, location is represented on the basis that the two signals are generated by independent sources (= segregation. At the next stage, in posterior intraparietal sulcus, location is estimated under the assumption that the two signals are from a common source (= forced fusion. Only at the top of the hierarchy, in anterior intraparietal sulcus, the uncertainty about the causal structure of the world is taken into account and sensory signals are combined as predicted by Bayesian Causal Inference. Characterizing the computational operations of signal interactions reveals the hierarchical nature of multisensory perception in human neocortex. It unravels how the brain accomplishes Bayesian Causal Inference, a statistical computation fundamental for perception and cognition. Our results demonstrate how the brain combines information in the face of uncertainty about the underlying causal structure of the world.
Empirical Bayesian inference and model uncertainty
Poern, K.
1994-01-01
This paper presents a hierarchical or multistage empirical Bayesian approach for the estimation of uncertainty concerning the intensity of a homogeneous Poisson process. A class of contaminated gamma distributions is considered to describe the uncertainty concerning the intensity. These distributions in turn are defined through a set of secondary parameters, the knowledge of which is also described and updated via Bayes formula. This two-stage Bayesian approach is an example where the modeling uncertainty is treated in a comprehensive way. Each contaminated gamma distributions, represented by a point in the 3D space of secondary parameters, can be considered as a specific model of the uncertainty about the Poisson intensity. Then, by the empirical Bayesian method each individual model is assigned a posterior probability
Bayesian Inference and Online Learning in Poisson Neuronal Networks.
Huang, Yanping; Rao, Rajesh P N
2016-08-01
Motivated by the growing evidence for Bayesian computation in the brain, we show how a two-layer recurrent network of Poisson neurons can perform both approximate Bayesian inference and learning for any hidden Markov model. The lower-layer sensory neurons receive noisy measurements of hidden world states. The higher-layer neurons infer a posterior distribution over world states via Bayesian inference from inputs generated by sensory neurons. We demonstrate how such a neuronal network with synaptic plasticity can implement a form of Bayesian inference similar to Monte Carlo methods such as particle filtering. Each spike in a higher-layer neuron represents a sample of a particular hidden world state. The spiking activity across the neural population approximates the posterior distribution over hidden states. In this model, variability in spiking is regarded not as a nuisance but as an integral feature that provides the variability necessary for sampling during inference. We demonstrate how the network can learn the likelihood model, as well as the transition probabilities underlying the dynamics, using a Hebbian learning rule. We present results illustrating the ability of the network to perform inference and learning for arbitrary hidden Markov models.
Progress on Bayesian Inference of the Fast Ion Distribution Function
Stagner, L.; Heidbrink, W.W,; Chen, X.
2013-01-01
. However, when theory and experiment disagree (for one or more diagnostics), it is unclear how to proceed. Bayesian statistics provides a framework to infer the DF, quantify errors, and reconcile discrepant diagnostic measurements. Diagnostic errors and weight functions that describe the phase space...... sensitivity of the measurements are incorporated into Bayesian likelihood probabilities. Prior probabilities describe physical constraints. This poster will show reconstructions of classically described, low-power, MHD-quiescent distribution functions from actual FIDA measurements. A description of the full...
Robust bayesian inference of generalized Pareto distribution ...
En utilisant une etude exhaustive de Monte Carlo, nous prouvons que, moyennant une fonction perte generalisee adequate, on peut construire un estimateur Bayesien robuste du modele. Key words: Bayesian estimation; Extreme value; Generalized Fisher information; Gener- alized Pareto distribution; Monte Carlo; ...
A Bayesian nonparametric approach to causal inference on quantiles.
Xu, Dandan; Daniels, Michael J; Winterstein, Almut G
2018-02-25
We propose a Bayesian nonparametric approach (BNP) for causal inference on quantiles in the presence of many confounders. In particular, we define relevant causal quantities and specify BNP models to avoid bias from restrictive parametric assumptions. We first use Bayesian additive regression trees (BART) to model the propensity score and then construct the distribution of potential outcomes given the propensity score using a Dirichlet process mixture (DPM) of normals model. We thoroughly evaluate the operating characteristics of our approach and compare it to Bayesian and frequentist competitors. We use our approach to answer an important clinical question involving acute kidney injury using electronic health records. © 2018, The International Biometric Society.
Neuronal integration of dynamic sources: Bayesian learning and Bayesian inference.
Siegelmann, Hava T; Holzman, Lars E
2010-09-01
One of the brain's most basic functions is integrating sensory data from diverse sources. This ability causes us to question whether the neural system is computationally capable of intelligently integrating data, not only when sources have known, fixed relative dependencies but also when it must determine such relative weightings based on dynamic conditions, and then use these learned weightings to accurately infer information about the world. We suggest that the brain is, in fact, fully capable of computing this parallel task in a single network and describe a neural inspired circuit with this property. Our implementation suggests the possibility that evidence learning requires a more complex organization of the network than was previously assumed, where neurons have different specialties, whose emergence brings the desired adaptivity seen in human online inference.
Bayesian inference with information content model check for Langevin equations
Krog, Jens F. C.; Lomholt, Michael Andersen
2017-01-01
The Bayesian data analysis framework has been proven to be a systematic and effective method of parameter inference and model selection for stochastic processes. In this work we introduce an information content model check which may serve as a goodness-of-fit, like the chi-square procedure...
Bayesian inference model for fatigue life of laminated composites
Dimitrov, Nikolay Krasimirov; Kiureghian, Armen Der; Berggreen, Christian
2016-01-01
A probabilistic model for estimating the fatigue life of laminated composite plates is developed. The model is based on lamina-level input data, making it possible to predict fatigue properties for a wide range of laminate configurations. Model parameters are estimated by Bayesian inference. The ...
Stan: A Probabilistic Programming Language for Bayesian Inference and Optimization
Gelman, Andrew; Lee, Daniel; Guo, Jiqiang
2015-01-01
Stan is a free and open-source C++ program that performs Bayesian inference or optimization for arbitrary user-specified models and can be called from the command line, R, Python, Matlab, or Julia and has great promise for fitting large and complex statistical models in many areas of application. We discuss Stan from users' and developers'…
Bayesian inference of substrate properties from film behavior
Aggarwal, R; Demkowicz, M J; Marzouk, Y M
2015-01-01
We demonstrate that by observing the behavior of a film deposited on a substrate, certain features of the substrate may be inferred with quantified uncertainty using Bayesian methods. We carry out this demonstration on an illustrative film/substrate model where the substrate is a Gaussian random field and the film is a two-component mixture that obeys the Cahn–Hilliard equation. We construct a stochastic reduced order model to describe the film/substrate interaction and use it to infer substrate properties from film behavior. This quantitative inference strategy may be adapted to other film/substrate systems. (paper)
Bayesian inference of chemical kinetic models from proposed reactions
Galagali, Nikhil
2015-02-01
© 2014 Elsevier Ltd. Bayesian inference provides a natural framework for combining experimental data with prior knowledge to develop chemical kinetic models and quantify the associated uncertainties, not only in parameter values but also in model structure. Most existing applications of Bayesian model selection methods to chemical kinetics have been limited to comparisons among a small set of models, however. The significant computational cost of evaluating posterior model probabilities renders traditional Bayesian methods infeasible when the model space becomes large. We present a new framework for tractable Bayesian model inference and uncertainty quantification using a large number of systematically generated model hypotheses. The approach involves imposing point-mass mixture priors over rate constants and exploring the resulting posterior distribution using an adaptive Markov chain Monte Carlo method. The posterior samples are used to identify plausible models, to quantify rate constant uncertainties, and to extract key diagnostic information about model structure-such as the reactions and operating pathways most strongly supported by the data. We provide numerical demonstrations of the proposed framework by inferring kinetic models for catalytic steam and dry reforming of methane using available experimental data.
Bayesian Inference of High-Dimensional Dynamical Ocean Models
Lin, J.; Lermusiaux, P. F. J.; Lolla, S. V. T.; Gupta, A.; Haley, P. J., Jr.
2015-12-01
This presentation addresses a holistic set of challenges in high-dimension ocean Bayesian nonlinear estimation: i) predict the probability distribution functions (pdfs) of large nonlinear dynamical systems using stochastic partial differential equations (PDEs); ii) assimilate data using Bayes' law with these pdfs; iii) predict the future data that optimally reduce uncertainties; and (iv) rank the known and learn the new model formulations themselves. Overall, we allow the joint inference of the state, equations, geometry, boundary conditions and initial conditions of dynamical models. Examples are provided for time-dependent fluid and ocean flows, including cavity, double-gyre and Strait flows with jets and eddies. The Bayesian model inference, based on limited observations, is illustrated first by the estimation of obstacle shapes and positions in fluid flows. Next, the Bayesian inference of biogeochemical reaction equations and of their states and parameters is presented, illustrating how PDE-based machine learning can rigorously guide the selection and discovery of complex ecosystem models. Finally, the inference of multiscale bottom gravity current dynamics is illustrated, motivated in part by classic overflows and dense water formation sites and their relevance to climate monitoring and dynamics. This is joint work with our MSEAS group at MIT.
Bayesian inference data evaluation and decisions
Harney, Hanns Ludwig
2016-01-01
This new edition offers a comprehensive introduction to the analysis of data using Bayes rule. It generalizes Gaussian error intervals to situations in which the data follow distributions other than Gaussian. This is particularly useful when the observed parameter is barely above the background or the histogram of multiparametric data contains many empty bins, so that the determination of the validity of a theory cannot be based on the chi-squared-criterion. In addition to the solutions of practical problems, this approach provides an epistemic insight: the logic of quantum mechanics is obtained as the logic of unbiased inference from counting data. New sections feature factorizing parameters, commuting parameters, observables in quantum mechanics, the art of fitting with coherent and with incoherent alternatives and fitting with multinomial distribution. Additional problems and examples help deepen the knowledge. Requiring no knowledge of quantum mechanics, the book is written on introductory level, with man...
Bayesian inference and updating of reliability data
Sabri, Z.A.; Cullingford, M.C.; David, H.T.; Husseiny, A.A.
1980-01-01
A Bayes methodology for inference of reliability values using available but scarce current data is discussed. The method can be used to update failure rates as more information becomes available from field experience, assuming that the performance of a given component (or system) exhibits a nonhomogeneous Poisson process. Bayes' theorem is used to summarize the historical evidence and current component data in the form of a posterior distribution suitable for prediction and for smoothing or interpolation. An example is given. It may be appropriate to apply the methodology developed here to human error data, in which case the exponential model might be used to describe the learning behavior of the operator or maintenance crew personnel
Evolution in Mind: Evolutionary Dynamics, Cognitive Processes, and Bayesian Inference.
Suchow, Jordan W; Bourgin, David D; Griffiths, Thomas L
2017-07-01
Evolutionary theory describes the dynamics of population change in settings affected by reproduction, selection, mutation, and drift. In the context of human cognition, evolutionary theory is most often invoked to explain the origins of capacities such as language, metacognition, and spatial reasoning, framing them as functional adaptations to an ancestral environment. However, evolutionary theory is useful for understanding the mind in a second way: as a mathematical framework for describing evolving populations of thoughts, ideas, and memories within a single mind. In fact, deep correspondences exist between the mathematics of evolution and of learning, with perhaps the deepest being an equivalence between certain evolutionary dynamics and Bayesian inference. This equivalence permits reinterpretation of evolutionary processes as algorithms for Bayesian inference and has relevance for understanding diverse cognitive capacities, including memory and creativity. Copyright © 2017 Elsevier Ltd. All rights reserved.
Application of Bayesian inference to stochastic analytic continuation
Fuchs, S; Pruschke, T; Jarrell, M
2010-01-01
We present an algorithm for the analytic continuation of imaginary-time quantum Monte Carlo data. The algorithm is strictly based on principles of Bayesian statistical inference. It utilizes Monte Carlo simulations to calculate a weighted average of possible energy spectra. We apply the algorithm to imaginary-time quantum Monte Carlo data and compare the resulting energy spectra with those from a standard maximum entropy calculation.
Practical Statistics for LHC Physicists: Bayesian Inference (3/3)
CERN. Geneva
2015-01-01
These lectures cover those principles and practices of statistics that are most relevant for work at the LHC. The first lecture discusses the basic ideas of descriptive statistics, probability and likelihood. The second lecture covers the key ideas in the frequentist approach, including confidence limits, profile likelihoods, p-values, and hypothesis testing. The third lecture covers inference in the Bayesian approach. Throughout, real-world examples will be used to illustrate the practical application of the ideas. No previous knowledge is assumed.
Bayesian inference in processing experimental data: principles and basic applications
D'Agostini, G
2003-01-01
This paper introduces general ideas and some basic methods of the Bayesian probability theory applied to physics measurements. Our aim is to make the reader familiar, through examples rather than rigorous formalism, with concepts such as the following: model comparison (including the automatic Ockham's Razor filter provided by the Bayesian approach); parametric inference; quantification of the uncertainty about the value of physical quantities, also taking into account systematic effects; role of marginalization; posterior characterization; predictive distributions; hierarchical modelling and hyperparameters; Gaussian approximation of the posterior and recovery of conventional methods, especially maximum likelihood and chi-square fits under well-defined conditions; conjugate priors, transformation invariance and maximum entropy motivated priors; and Monte Carlo (MC) estimates of expectation, including a short introduction to Markov Chain MC methods
Fast model updating coupling Bayesian inference and PGD model reduction
Rubio, Paul-Baptiste; Louf, François; Chamoin, Ludovic
2018-04-01
The paper focuses on a coupled Bayesian-Proper Generalized Decomposition (PGD) approach for the real-time identification and updating of numerical models. The purpose is to use the most general case of Bayesian inference theory in order to address inverse problems and to deal with different sources of uncertainties (measurement and model errors, stochastic parameters). In order to do so with a reasonable CPU cost, the idea is to replace the direct model called for Monte-Carlo sampling by a PGD reduced model, and in some cases directly compute the probability density functions from the obtained analytical formulation. This procedure is first applied to a welding control example with the updating of a deterministic parameter. In the second application, the identification of a stochastic parameter is studied through a glued assembly example.
Sparse linear models: Variational approximate inference and Bayesian experimental design
Seeger, Matthias W
2009-01-01
A wide range of problems such as signal reconstruction, denoising, source separation, feature selection, and graphical model search are addressed today by posterior maximization for linear models with sparsity-favouring prior distributions. The Bayesian posterior contains useful information far beyond its mode, which can be used to drive methods for sampling optimization (active learning), feature relevance ranking, or hyperparameter estimation, if only this representation of uncertainty can be approximated in a tractable manner. In this paper, we review recent results for variational sparse inference, and show that they share underlying computational primitives. We discuss how sampling optimization can be implemented as sequential Bayesian experimental design. While there has been tremendous recent activity to develop sparse estimation, little attendance has been given to sparse approximate inference. In this paper, we argue that many problems in practice, such as compressive sensing for real-world image reconstruction, are served much better by proper uncertainty approximations than by ever more aggressive sparse estimation algorithms. Moreover, since some variational inference methods have been given strong convex optimization characterizations recently, theoretical analysis may become possible, promising new insights into nonlinear experimental design.
Inference algorithms and learning theory for Bayesian sparse factor analysis
Rattray, Magnus; Sharp, Kevin; Stegle, Oliver; Winn, John
2009-01-01
Bayesian sparse factor analysis has many applications; for example, it has been applied to the problem of inferring a sparse regulatory network from gene expression data. We describe a number of inference algorithms for Bayesian sparse factor analysis using a slab and spike mixture prior. These include well-established Markov chain Monte Carlo (MCMC) and variational Bayes (VB) algorithms as well as a novel hybrid of VB and Expectation Propagation (EP). For the case of a single latent factor we derive a theory for learning performance using the replica method. We compare the MCMC and VB/EP algorithm results with simulated data to the theoretical prediction. The results for MCMC agree closely with the theory as expected. Results for VB/EP are slightly sub-optimal but show that the new algorithm is effective for sparse inference. In large-scale problems MCMC is infeasible due to computational limitations and the VB/EP algorithm then provides a very useful computationally efficient alternative.
Sparse linear models: Variational approximate inference and Bayesian experimental design
Seeger, Matthias W [Saarland University and Max Planck Institute for Informatics, Campus E1.4, 66123 Saarbruecken (Germany)
2009-12-01
A wide range of problems such as signal reconstruction, denoising, source separation, feature selection, and graphical model search are addressed today by posterior maximization for linear models with sparsity-favouring prior distributions. The Bayesian posterior contains useful information far beyond its mode, which can be used to drive methods for sampling optimization (active learning), feature relevance ranking, or hyperparameter estimation, if only this representation of uncertainty can be approximated in a tractable manner. In this paper, we review recent results for variational sparse inference, and show that they share underlying computational primitives. We discuss how sampling optimization can be implemented as sequential Bayesian experimental design. While there has been tremendous recent activity to develop sparse estimation, little attendance has been given to sparse approximate inference. In this paper, we argue that many problems in practice, such as compressive sensing for real-world image reconstruction, are served much better by proper uncertainty approximations than by ever more aggressive sparse estimation algorithms. Moreover, since some variational inference methods have been given strong convex optimization characterizations recently, theoretical analysis may become possible, promising new insights into nonlinear experimental design.
Inference algorithms and learning theory for Bayesian sparse factor analysis
Rattray, Magnus; Sharp, Kevin [School of Computer Science, University of Manchester, Manchester M13 9PL (United Kingdom); Stegle, Oliver [Max-Planck-Institute for Biological Cybernetics, Tuebingen (Germany); Winn, John, E-mail: magnus.rattray@manchester.ac.u [Microsoft Research Cambridge, Roger Needham Building, Cambridge, CB3 0FB (United Kingdom)
2009-12-01
Bayesian sparse factor analysis has many applications; for example, it has been applied to the problem of inferring a sparse regulatory network from gene expression data. We describe a number of inference algorithms for Bayesian sparse factor analysis using a slab and spike mixture prior. These include well-established Markov chain Monte Carlo (MCMC) and variational Bayes (VB) algorithms as well as a novel hybrid of VB and Expectation Propagation (EP). For the case of a single latent factor we derive a theory for learning performance using the replica method. We compare the MCMC and VB/EP algorithm results with simulated data to the theoretical prediction. The results for MCMC agree closely with the theory as expected. Results for VB/EP are slightly sub-optimal but show that the new algorithm is effective for sparse inference. In large-scale problems MCMC is infeasible due to computational limitations and the VB/EP algorithm then provides a very useful computationally efficient alternative.
ANUBIS: artificial neuromodulation using a Bayesian inference system.
Smith, Benjamin J H; Saaj, Chakravarthini M; Allouis, Elie
2013-01-01
Gain tuning is a crucial part of controller design and depends not only on an accurate understanding of the system in question, but also on the designer's ability to predict what disturbances and other perturbations the system will encounter throughout its operation. This letter presents ANUBIS (artificial neuromodulation using a Bayesian inference system), a novel biologically inspired technique for automatically tuning controller parameters in real time. ANUBIS is based on the Bayesian brain concept and modifies it by incorporating a model of the neuromodulatory system comprising four artificial neuromodulators. It has been applied to the controller of EchinoBot, a prototype walking rover for Martian exploration. ANUBIS has been implemented at three levels of the controller; gait generation, foot trajectory planning using Bézier curves, and foot trajectory tracking using a terminal sliding mode controller. We compare the results to a similar system that has been tuned using a multilayer perceptron. The use of Bayesian inference means that the system retains mathematical interpretability, unlike other intelligent tuning techniques, which use neural networks, fuzzy logic, or evolutionary algorithms. The simulation results show that ANUBIS provides significant improvements in efficiency and adaptability of the three controller components; it allows the robot to react to obstacles and uncertainties faster than the system tuned with the MLP, while maintaining stability and accuracy. As well as advancing rover autonomy, ANUBIS could also be applied to other situations where operating conditions are likely to change or cannot be accurately modeled in advance, such as process control. In addition, it demonstrates one way in which neuromodulation could fit into the Bayesian brain framework.
GPU Computing in Bayesian Inference of Realized Stochastic Volatility Model
Takaishi, Tetsuya
2015-01-01
The realized stochastic volatility (RSV) model that utilizes the realized volatility as additional information has been proposed to infer volatility of financial time series. We consider the Bayesian inference of the RSV model by the Hybrid Monte Carlo (HMC) algorithm. The HMC algorithm can be parallelized and thus performed on the GPU for speedup. The GPU code is developed with CUDA Fortran. We compare the computational time in performing the HMC algorithm on GPU (GTX 760) and CPU (Intel i7-4770 3.4GHz) and find that the GPU can be up to 17 times faster than the CPU. We also code the program with OpenACC and find that appropriate coding can achieve the similar speedup with CUDA Fortran
Inferring on the Intentions of Others by Hierarchical Bayesian Learning
Diaconescu, Andreea O.; Mathys, Christoph; Weber, Lilian A. E.; Daunizeau, Jean; Kasper, Lars; Lomakina, Ekaterina I.; Fehr, Ernst; Stephan, Klaas E.
2014-01-01
Inferring on others' (potentially time-varying) intentions is a fundamental problem during many social transactions. To investigate the underlying mechanisms, we applied computational modeling to behavioral data from an economic game in which 16 pairs of volunteers (randomly assigned to “player” or “adviser” roles) interacted. The player performed a probabilistic reinforcement learning task, receiving information about a binary lottery from a visual pie chart. The adviser, who received more predictive information, issued an additional recommendation. Critically, the game was structured such that the adviser's incentives to provide helpful or misleading information varied in time. Using a meta-Bayesian modeling framework, we found that the players' behavior was best explained by the deployment of hierarchical learning: they inferred upon the volatility of the advisers' intentions in order to optimize their predictions about the validity of their advice. Beyond learning, volatility estimates also affected the trial-by-trial variability of decisions: participants were more likely to rely on their estimates of advice accuracy for making choices when they believed that the adviser's intentions were presently stable. Finally, our model of the players' inference predicted the players' interpersonal reactivity index (IRI) scores, explicit ratings of the advisers' helpfulness and the advisers' self-reports on their chosen strategy. Overall, our results suggest that humans (i) employ hierarchical generative models to infer on the changing intentions of others, (ii) use volatility estimates to inform decision-making in social interactions, and (iii) integrate estimates of advice accuracy with non-social sources of information. The Bayesian framework presented here can quantify individual differences in these mechanisms from simple behavioral readouts and may prove useful in future clinical studies of maladaptive social cognition. PMID:25187943
Bayesian inference method for stochastic damage accumulation modeling
Jiang, Xiaomo; Yuan, Yong; Liu, Xian
2013-01-01
Damage accumulation based reliability model plays an increasingly important role in successful realization of condition based maintenance for complicated engineering systems. This paper developed a Bayesian framework to establish stochastic damage accumulation model from historical inspection data, considering data uncertainty. Proportional hazards modeling technique is developed to model the nonlinear effect of multiple influencing factors on system reliability. Different from other hazard modeling techniques such as normal linear regression model, the approach does not require any distribution assumption for the hazard model, and can be applied for a wide variety of distribution models. A Bayesian network is created to represent the nonlinear proportional hazards models and to estimate model parameters by Bayesian inference with Markov Chain Monte Carlo simulation. Both qualitative and quantitative approaches are developed to assess the validity of the established damage accumulation model. Anderson–Darling goodness-of-fit test is employed to perform the normality test, and Box–Cox transformation approach is utilized to convert the non-normality data into normal distribution for hypothesis testing in quantitative model validation. The methodology is illustrated with the seepage data collected from real-world subway tunnels.
Bayesian inference for hybrid discrete-continuous stochastic kinetic models
Sherlock, Chris; Golightly, Andrew; Gillespie, Colin S
2014-01-01
We consider the problem of efficiently performing simulation and inference for stochastic kinetic models. Whilst it is possible to work directly with the resulting Markov jump process (MJP), computational cost can be prohibitive for networks of realistic size and complexity. In this paper, we consider an inference scheme based on a novel hybrid simulator that classifies reactions as either ‘fast’ or ‘slow’ with fast reactions evolving as a continuous Markov process whilst the remaining slow reaction occurrences are modelled through a MJP with time-dependent hazards. A linear noise approximation (LNA) of fast reaction dynamics is employed and slow reaction events are captured by exploiting the ability to solve the stochastic differential equation driving the LNA. This simulation procedure is used as a proposal mechanism inside a particle MCMC scheme, thus allowing Bayesian inference for the model parameters. We apply the scheme to a simple application and compare the output with an existing hybrid approach and also a scheme for performing inference for the underlying discrete stochastic model. (paper)
Bayesian inference for Markov jump processes with informative observations.
Golightly, Andrew; Wilkinson, Darren J
2015-04-01
In this paper we consider the problem of parameter inference for Markov jump process (MJP) representations of stochastic kinetic models. Since transition probabilities are intractable for most processes of interest yet forward simulation is straightforward, Bayesian inference typically proceeds through computationally intensive methods such as (particle) MCMC. Such methods ostensibly require the ability to simulate trajectories from the conditioned jump process. When observations are highly informative, use of the forward simulator is likely to be inefficient and may even preclude an exact (simulation based) analysis. We therefore propose three methods for improving the efficiency of simulating conditioned jump processes. A conditioned hazard is derived based on an approximation to the jump process, and used to generate end-point conditioned trajectories for use inside an importance sampling algorithm. We also adapt a recently proposed sequential Monte Carlo scheme to our problem. Essentially, trajectories are reweighted at a set of intermediate time points, with more weight assigned to trajectories that are consistent with the next observation. We consider two implementations of this approach, based on two continuous approximations of the MJP. We compare these constructs for a simple tractable jump process before using them to perform inference for a Lotka-Volterra system. The best performing construct is used to infer the parameters governing a simple model of motility regulation in Bacillus subtilis.
Bayesian inference from count data using discrete uniform priors.
Federico Comoglio
Full Text Available We consider a set of sample counts obtained by sampling arbitrary fractions of a finite volume containing an homogeneously dispersed population of identical objects. We report a Bayesian derivation of the posterior probability distribution of the population size using a binomial likelihood and non-conjugate, discrete uniform priors under sampling with or without replacement. Our derivation yields a computationally feasible formula that can prove useful in a variety of statistical problems involving absolute quantification under uncertainty. We implemented our algorithm in the R package dupiR and compared it with a previously proposed Bayesian method based on a Gamma prior. As a showcase, we demonstrate that our inference framework can be used to estimate bacterial survival curves from measurements characterized by extremely low or zero counts and rather high sampling fractions. All in all, we provide a versatile, general purpose algorithm to infer population sizes from count data, which can find application in a broad spectrum of biological and physical problems.
Bayesian Inference for Signal-Based Seismic Monitoring
Moore, D.
2015-12-01
Traditional seismic monitoring systems rely on discrete detections produced by station processing software, discarding significant information present in the original recorded signal. SIG-VISA (Signal-based Vertically Integrated Seismic Analysis) is a system for global seismic monitoring through Bayesian inference on seismic signals. By modeling signals directly, our forward model is able to incorporate a rich representation of the physics underlying the signal generation process, including source mechanisms, wave propagation, and station response. This allows inference in the model to recover the qualitative behavior of recent geophysical methods including waveform matching and double-differencing, all as part of a unified Bayesian monitoring system that simultaneously detects and locates events from a global network of stations. We demonstrate recent progress in scaling up SIG-VISA to efficiently process the data stream of global signals recorded by the International Monitoring System (IMS), including comparisons against existing processing methods that show increased sensitivity from our signal-based model and in particular the ability to locate events (including aftershock sequences that can tax analyst processing) precisely from waveform correlation effects. We also provide a Bayesian analysis of an alleged low-magnitude event near the DPRK test site in May 2010 [1] [2], investigating whether such an event could plausibly be detected through automated processing in a signal-based monitoring system. [1] Zhang, Miao and Wen, Lianxing. "Seismological Evidence for a Low-Yield Nuclear Test on 12 May 2010 in North Korea". Seismological Research Letters, January/February 2015. [2] Richards, Paul. "A Seismic Event in North Korea on 12 May 2010". CTBTO SnT 2015 oral presentation, video at https://video-archive.ctbto.org/index.php/kmc/preview/partner_id/103/uiconf_id/4421629/entry_id/0_ymmtpps0/delivery/http
Bayesian inference for identifying interaction rules in moving animal groups.
Richard P Mann
Full Text Available The emergence of similar collective patterns from different self-propelled particle models of animal groups points to a restricted set of "universal" classes for these patterns. While universality is interesting, it is often the fine details of animal interactions that are of biological importance. Universality thus presents a challenge to inferring such interactions from macroscopic group dynamics since these can be consistent with many underlying interaction models. We present a Bayesian framework for learning animal interaction rules from fine scale recordings of animal movements in swarms. We apply these techniques to the inverse problem of inferring interaction rules from simulation models, showing that parameters can often be inferred from a small number of observations. Our methodology allows us to quantify our confidence in parameter fitting. For example, we show that attraction and alignment terms can be reliably estimated when animals are milling in a torus shape, while interaction radius cannot be reliably measured in such a situation. We assess the importance of rate of data collection and show how to test different models, such as topological and metric neighbourhood models. Taken together our results both inform the design of experiments on animal interactions and suggest how these data should be best analysed.
Bayesian inference on genetic merit under uncertain paternity
Tempelman Robert J
2003-09-01
Full Text Available Abstract A hierarchical animal model was developed for inference on genetic merit of livestock with uncertain paternity. Fully conditional posterior distributions for fixed and genetic effects, variance components, sire assignments and their probabilities are derived to facilitate a Bayesian inference strategy using MCMC methods. We compared this model to a model based on the Henderson average numerator relationship (ANRM in a simulation study with 10 replicated datasets generated for each of two traits. Trait 1 had a medium heritability (h2 for each of direct and maternal genetic effects whereas Trait 2 had a high h2 attributable only to direct effects. The average posterior probabilities inferred on the true sire were between 1 and 10% larger than the corresponding priors (the inverse of the number of candidate sires in a mating pasture for Trait 1 and between 4 and 13% larger than the corresponding priors for Trait 2. The predicted additive and maternal genetic effects were very similar using both models; however, model choice criteria (Pseudo Bayes Factor and Deviance Information Criterion decisively favored the proposed hierarchical model over the ANRM model.
Bayesian inference for psychology. Part I : Theoretical advantages and practical ramifications
Wagenmakers, E.-J.; Marsman, M.; Jamil, T.; Ly, A.; Verhagen, J.; Love, J.; Selker, R.; Gronau, Q.F.; Šmíra, M.; Epskamp, S.; Matzke, D.; Rouder, J.N.; Morey, R.D.
2018-01-01
Bayesian parameter estimation and Bayesian hypothesis testing present attractive alternatives to classical inference using confidence intervals and p values. In part I of this series we outline ten prominent advantages of the Bayesian approach. Many of these advantages translate to concrete
Bayesian Inference for Linear Parabolic PDEs with Noisy Boundary Conditions
Ruggeri, Fabrizio; Sawlan, Zaid A; Scavino, Marco; Tempone, Raul
2016-01-01
In this work we develop a hierarchical Bayesian setting to infer unknown parameters in initial-boundary value problems (IBVPs) for one-dimensional linear parabolic partial differential equations. Noisy boundary data and known initial condition are assumed. We derive the likelihood function associated with the forward problem, given some measurements of the solution field subject to Gaussian noise. Such function is then analytically marginalized using the linearity of the equation. Gaussian priors have been assumed for the time-dependent Dirichlet boundary values. Our approach is applied to synthetic data for the one-dimensional heat equation model, where the thermal diffusivity is the unknown parameter. We show how to infer the thermal diffusivity parameter when its prior distribution is lognormal or modeled by means of a space-dependent stationary lognormal random field. We use the Laplace method to provide approximated Gaussian posterior distributions for the thermal diffusivity. Expected information gains and predictive posterior densities for observable quantities are numerically estimated for different experimental setups.
Bayesian Inference for Linear Parabolic PDEs with Noisy Boundary Conditions
Ruggeri, Fabrizio
2015-01-07
In this work we develop a hierarchical Bayesian setting to infer unknown parameters in initial-boundary value problems (IBVPs) for one-dimensional linear parabolic partial differential equations. Noisy boundary data and known initial condition are assumed. We derive the likelihood function associated with the forward problem, given some measurements of the solution field subject to Gaussian noise. Such function is then analytically marginalized using the linearity of the equation. Gaussian priors have been assumed for the time-dependent Dirichlet boundary values. Our approach is applied to synthetic data for the one-dimensional heat equation model, where the thermal diffusivity is the unknown parameter. We show how to infer the thermal diffusivity parameter when its prior distribution is lognormal or modeled by means of a space-dependent stationary lognormal random field. We use the Laplace method to provide approximated Gaussian posterior distributions for the thermal diffusivity. Expected information gains and predictive posterior densities for observable quantities are numerically estimated for different experimental setups.
Bayesian Inference for Linear Parabolic PDEs with Noisy Boundary Conditions
Ruggeri, Fabrizio
2016-01-06
In this work we develop a hierarchical Bayesian setting to infer unknown parameters in initial-boundary value problems (IBVPs) for one-dimensional linear parabolic partial differential equations. Noisy boundary data and known initial condition are assumed. We derive the likelihood function associated with the forward problem, given some measurements of the solution field subject to Gaussian noise. Such function is then analytically marginalized using the linearity of the equation. Gaussian priors have been assumed for the time-dependent Dirichlet boundary values. Our approach is applied to synthetic data for the one-dimensional heat equation model, where the thermal diffusivity is the unknown parameter. We show how to infer the thermal diffusivity parameter when its prior distribution is lognormal or modeled by means of a space-dependent stationary lognormal random field. We use the Laplace method to provide approximated Gaussian posterior distributions for the thermal diffusivity. Expected information gains and predictive posterior densities for observable quantities are numerically estimated for different experimental setups.
Bayesian inference for partially identified models exploring the limits of limited data
Gustafson, Paul
2015-01-01
Introduction Identification What Is against Us? What Is for Us? Some Simple Examples of Partially Identified ModelsThe Road Ahead The Structure of Inference in Partially Identified Models Bayesian Inference The Structure of Posterior Distributions in PIMs Computational Strategies Strength of Bayesian Updating, Revisited Posterior MomentsCredible Intervals Evaluating the Worth of Inference Partial Identification versus Model Misspecification The Siren Call of Identification Comp
Rajabi, Mohammad Mahdi; Ataie-Ashtiani, Behzad
2016-05-01
Bayesian inference has traditionally been conceived as the proper framework for the formal incorporation of expert knowledge in parameter estimation of groundwater models. However, conventional Bayesian inference is incapable of taking into account the imprecision essentially embedded in expert provided information. In order to solve this problem, a number of extensions to conventional Bayesian inference have been introduced in recent years. One of these extensions is 'fuzzy Bayesian inference' which is the result of integrating fuzzy techniques into Bayesian statistics. Fuzzy Bayesian inference has a number of desirable features which makes it an attractive approach for incorporating expert knowledge in the parameter estimation process of groundwater models: (1) it is well adapted to the nature of expert provided information, (2) it allows to distinguishably model both uncertainty and imprecision, and (3) it presents a framework for fusing expert provided information regarding the various inputs of the Bayesian inference algorithm. However an important obstacle in employing fuzzy Bayesian inference in groundwater numerical modeling applications is the computational burden, as the required number of numerical model simulations often becomes extremely exhaustive and often computationally infeasible. In this paper, a novel approach of accelerating the fuzzy Bayesian inference algorithm is proposed which is based on using approximate posterior distributions derived from surrogate modeling, as a screening tool in the computations. The proposed approach is first applied to a synthetic test case of seawater intrusion (SWI) in a coastal aquifer. It is shown that for this synthetic test case, the proposed approach decreases the number of required numerical simulations by an order of magnitude. Then the proposed approach is applied to a real-world test case involving three-dimensional numerical modeling of SWI in Kish Island, located in the Persian Gulf. An expert
Bayesian Inference for Functional Dynamics Exploring in fMRI Data
Xuan Guo
2016-01-01
Full Text Available This paper aims to review state-of-the-art Bayesian-inference-based methods applied to functional magnetic resonance imaging (fMRI data. Particularly, we focus on one specific long-standing challenge in the computational modeling of fMRI datasets: how to effectively explore typical functional interactions from fMRI time series and the corresponding boundaries of temporal segments. Bayesian inference is a method of statistical inference which has been shown to be a powerful tool to encode dependence relationships among the variables with uncertainty. Here we provide an introduction to a group of Bayesian-inference-based methods for fMRI data analysis, which were designed to detect magnitude or functional connectivity change points and to infer their functional interaction patterns based on corresponding temporal boundaries. We also provide a comparison of three popular Bayesian models, that is, Bayesian Magnitude Change Point Model (BMCPM, Bayesian Connectivity Change Point Model (BCCPM, and Dynamic Bayesian Variable Partition Model (DBVPM, and give a summary of their applications. We envision that more delicate Bayesian inference models will be emerging and play increasingly important roles in modeling brain functions in the years to come.
Bayesian inference in probabilistic risk assessment-The current state of the art
Kelly, Dana L.; Smith, Curtis L.
2009-01-01
Markov chain Monte Carlo (MCMC) approaches to sampling directly from the joint posterior distribution of aleatory model parameters have led to tremendous advances in Bayesian inference capability in a wide variety of fields, including probabilistic risk analysis. The advent of freely available software coupled with inexpensive computing power has catalyzed this advance. This paper examines where the risk assessment community is with respect to implementing modern computational-based Bayesian approaches to inference. Through a series of examples in different topical areas, it introduces salient concepts and illustrates the practical application of Bayesian inference via MCMC sampling to a variety of important problems
BayesCLUMPY: BAYESIAN INFERENCE WITH CLUMPY DUSTY TORUS MODELS
Asensio Ramos, A.; Ramos Almeida, C.
2009-01-01
Our aim is to present a fast and general Bayesian inference framework based on the synergy between machine learning techniques and standard sampling methods and apply it to infer the physical properties of clumpy dusty torus using infrared photometric high spatial resolution observations of active galactic nuclei. We make use of the Metropolis-Hastings Markov Chain Monte Carlo algorithm for sampling the posterior distribution function. Such distribution results from combining all a priori knowledge about the parameters of the model and the information introduced by the observations. The main difficulty resides in the fact that the model used to explain the observations is computationally demanding and the sampling is very time consuming. For this reason, we apply a set of artificial neural networks that are used to approximate and interpolate a database of models. As a consequence, models not present in the original database can be computed ensuring continuity. We focus on the application of this solution scheme to the recently developed public database of clumpy dusty torus models. The machine learning scheme used in this paper allows us to generate any model from the database using only a factor of 10 -4 of the original size of the database and a factor of 10 -3 in computing time. The posterior distribution obtained for each model parameter allows us to investigate how the observations constrain the parameters and which ones remain partially or completely undetermined, providing statistically relevant confidence intervals. As an example, the application to the nuclear region of Centaurus A shows that the optical depth of the clouds, the total number of clouds, and the radial extent of the cloud distribution zone are well constrained using only six filters. The code is freely available from the authors.
Bayesian Inference for NASA Probabilistic Risk and Reliability Analysis
Dezfuli, Homayoon; Kelly, Dana; Smith, Curtis; Vedros, Kurt; Galyean, William
2009-01-01
This document, Bayesian Inference for NASA Probabilistic Risk and Reliability Analysis, is intended to provide guidelines for the collection and evaluation of risk and reliability-related data. It is aimed at scientists and engineers familiar with risk and reliability methods and provides a hands-on approach to the investigation and application of a variety of risk and reliability data assessment methods, tools, and techniques. This document provides both: A broad perspective on data analysis collection and evaluation issues. A narrow focus on the methods to implement a comprehensive information repository. The topics addressed herein cover the fundamentals of how data and information are to be used in risk and reliability analysis models and their potential role in decision making. Understanding these topics is essential to attaining a risk informed decision making environment that is being sought by NASA requirements and procedures such as 8000.4 (Agency Risk Management Procedural Requirements), NPR 8705.05 (Probabilistic Risk Assessment Procedures for NASA Programs and Projects), and the System Safety requirements of NPR 8715.3 (NASA General Safety Program Requirements).
Bayesian Inference of Ecological Interactions from Spatial Data
Christopher R. Stephens
2017-11-01
Full Text Available The characterization and quantification of ecological interactions and the construction of species’ distributions and their associated ecological niches are of fundamental theoretical and practical importance. In this paper, we discuss a Bayesian inference framework, which, using spatial data, offers a general formalism within which ecological interactions may be characterized and quantified. Interactions are identified through deviations of the spatial distribution of co-occurrences of spatial variables relative to a benchmark for the non-interacting system and based on a statistical ensemble of spatial cells. The formalism allows for the integration of both biotic and abiotic factors of arbitrary resolution. We concentrate on the conceptual and mathematical underpinnings of the formalism, showing how, using the naive Bayes approximation, it can be used to not only compare and contrast the relative contribution from each variable, but also to construct species’ distributions and ecological niches based on an arbitrary variable type. We also show how non-linear interactions between distinct niche variables can be identified and the degree of confounding between variables accounted for.
Metainference: A Bayesian inference method for heterogeneous systems.
Bonomi, Massimiliano; Camilloni, Carlo; Cavalli, Andrea; Vendruscolo, Michele
2016-01-01
Modeling a complex system is almost invariably a challenging task. The incorporation of experimental observations can be used to improve the quality of a model and thus to obtain better predictions about the behavior of the corresponding system. This approach, however, is affected by a variety of different errors, especially when a system simultaneously populates an ensemble of different states and experimental data are measured as averages over such states. To address this problem, we present a Bayesian inference method, called "metainference," that is able to deal with errors in experimental measurements and with experimental measurements averaged over multiple states. To achieve this goal, metainference models a finite sample of the distribution of models using a replica approach, in the spirit of the replica-averaging modeling based on the maximum entropy principle. To illustrate the method, we present its application to a heterogeneous model system and to the determination of an ensemble of structures corresponding to the thermal fluctuations of a protein molecule. Metainference thus provides an approach to modeling complex systems with heterogeneous components and interconverting between different states by taking into account all possible sources of errors.
Self-Associations Influence Task-Performance through Bayesian Inference.
Bengtsson, Sara L; Penny, Will D
2013-01-01
The way we think about ourselves impacts greatly on our behavior. This paper describes a behavioral study and a computational model that shed new light on this important area. Participants were primed "clever" and "stupid" using a scrambled sentence task, and we measured the effect on response time and error-rate on a rule-association task. First, we observed a confirmation bias effect in that associations to being "stupid" led to a gradual decrease in performance, whereas associations to being "clever" did not. Second, we observed that the activated self-concepts selectively modified attention toward one's performance. There was an early to late double dissociation in RTs in that primed "clever" resulted in RT increase following error responses, whereas primed "stupid" resulted in RT increase following correct responses. We propose a computational model of subjects' behavior based on the logic of the experimental task that involves two processes; memory for rules and the integration of rules with subsequent visual cues. The model incorporates an adaptive decision threshold based on Bayes rule, whereby decision thresholds are increased if integration was inferred to be faulty. Fitting the computational model to experimental data confirmed our hypothesis that priming affects the memory process. This model explains both the confirmation bias and double dissociation effects and demonstrates that Bayesian inferential principles can be used to study the effect of self-concepts on behavior.
Self-associations influence task-performance through Bayesian inference
Sara L Bengtsson
2013-08-01
Full Text Available The way we think about ourselves impacts greatly on our behaviour. This paper describes a behavioural study and a computational model that sheds new light on this important area. Participants were primed 'clever' and 'stupid' using a scrambled sentence task, and we measured the effect on response time and error-rate on a rule-association task. First, we observed a confirmation bias effect in that associations to being 'stupid' led to a gradual decrease in performance, whereas associations to being 'clever' did not. Second, we observed that the activated self-concepts selectively modified attention towards one's performance. There was an early to late double dissociation in RTs in that primed 'clever' resulted in RT increase following error responses, whereas primed 'stupid' resulted in RT increase following correct responses. We propose a computational model of subjects' behaviour based on the logic of the experimental task that involves two processes; memory for rules and the integration of rules with subsequent visual cues. The model also incorporates an adaptive decision threshold based on Bayes rule, whereby decision thresholds are increased if integration was inferred to be faulty. Fitting the computational model to experimental data confirmed our hypothesis that priming affects the memory process. This model explains both the confirmation bias and double dissociation effects and demonstrates that Bayesian inferential principles can be used to study the effect of self-concepts on behaviour.
Bayesian inference on EMRI signals using low frequency approximations
Ali, Asad; Meyer, Renate; Christensen, Nelson; Röver, Christian
2012-01-01
Extreme mass ratio inspirals (EMRIs) are thought to be one of the most exciting gravitational wave sources to be detected with LISA. Due to their complicated nature and weak amplitudes the detection and parameter estimation of such sources is a challenging task. In this paper we present a statistical methodology based on Bayesian inference in which the estimation of parameters is carried out by advanced Markov chain Monte Carlo (MCMC) algorithms such as parallel tempering MCMC. We analysed high and medium mass EMRI systems that fall well inside the low frequency range of LISA. In the context of the Mock LISA Data Challenges, our investigation and results are also the first instance in which a fully Markovian algorithm is applied for EMRI searches. Results show that our algorithm worked well in recovering EMRI signals from different (simulated) LISA data sets having single and multiple EMRI sources and holds great promise for posterior computation under more realistic conditions. The search and estimation methods presented in this paper are general in their nature, and can be applied in any other scenario such as AdLIGO, AdVIRGO and Einstein Telescope with their respective response functions. (paper)
Serang, Oliver
2014-01-01
Exact Bayesian inference can sometimes be performed efficiently for special cases where a function has commutative and associative symmetry of its inputs (called “causal independence”). For this reason, it is desirable to exploit such symmetry on big data sets. Here we present a method to exploit a general form of this symmetry on probabilistic adder nodes by transforming those probabilistic adder nodes into a probabilistic convolution tree with which dynamic programming computes exact probabilities. A substantial speedup is demonstrated using an illustration example that can arise when identifying splice forms with bottom-up mass spectrometry-based proteomics. On this example, even state-of-the-art exact inference algorithms require a runtime more than exponential in the number of splice forms considered. By using the probabilistic convolution tree, we reduce the runtime to and the space to where is the number of variables joined by an additive or cardinal operator. This approach, which can also be used with junction tree inference, is applicable to graphs with arbitrary dependency on counting variables or cardinalities and can be used on diverse problems and fields like forward error correcting codes, elemental decomposition, and spectral demixing. The approach also trivially generalizes to multiple dimensions. PMID:24626234
Mocapy++ - a toolkit for inference and learning in dynamic Bayesian networks
Paluszewski, Martin; Hamelryck, Thomas Wim
2010-01-01
Background Mocapy++ is a toolkit for parameter learning and inference in dynamic Bayesian networks (DBNs). It supports a wide range of DBN architectures and probability distributions, including distributions from directional statistics (the statistics of angles, directions and orientations...
Inconsistency of Bayesian Inference for Misspecified Linear Models, and a Proposal for Repairing It
Grünwald, P.; van Ommen, T.
2017-01-01
We empirically show that Bayesian inference can be inconsistent under misspecification in simple linear regression problems, both in a model averaging/selection and in a Bayesian ridge regression setting. We use the standard linear model, which assumes homoskedasticity, whereas the data are
Inconsistency of Bayesian inference for misspecified linear models, and a proposal for repairing it
P.D. Grünwald (Peter); T. van Ommen (Thijs)
2017-01-01
textabstractWe empirically show that Bayesian inference can be inconsistent under misspecification in simple linear regression problems, both in a model averaging/selection and in a Bayesian ridge regression setting. We use the standard linear model, which assumes homoskedasticity, whereas the data
UNSUPERVISED TRANSIENT LIGHT CURVE ANALYSIS VIA HIERARCHICAL BAYESIAN INFERENCE
Sanders, N. E.; Soderberg, A. M. [Harvard-Smithsonian Center for Astrophysics, 60 Garden Street, Cambridge, MA 02138 (United States); Betancourt, M., E-mail: nsanders@cfa.harvard.edu [Department of Statistics, University of Warwick, Coventry CV4 7AL (United Kingdom)
2015-02-10
Historically, light curve studies of supernovae (SNe) and other transient classes have focused on individual objects with copious and high signal-to-noise observations. In the nascent era of wide field transient searches, objects with detailed observations are decreasing as a fraction of the overall known SN population, and this strategy sacrifices the majority of the information contained in the data about the underlying population of transients. A population level modeling approach, simultaneously fitting all available observations of objects in a transient sub-class of interest, fully mines the data to infer the properties of the population and avoids certain systematic biases. We present a novel hierarchical Bayesian statistical model for population level modeling of transient light curves, and discuss its implementation using an efficient Hamiltonian Monte Carlo technique. As a test case, we apply this model to the Type IIP SN sample from the Pan-STARRS1 Medium Deep Survey, consisting of 18,837 photometric observations of 76 SNe, corresponding to a joint posterior distribution with 9176 parameters under our model. Our hierarchical model fits provide improved constraints on light curve parameters relevant to the physical properties of their progenitor stars relative to modeling individual light curves alone. Moreover, we directly evaluate the probability for occurrence rates of unseen light curve characteristics from the model hyperparameters, addressing observational biases in survey methodology. We view this modeling framework as an unsupervised machine learning technique with the ability to maximize scientific returns from data to be collected by future wide field transient searches like LSST.
UNSUPERVISED TRANSIENT LIGHT CURVE ANALYSIS VIA HIERARCHICAL BAYESIAN INFERENCE
Sanders, N. E.; Soderberg, A. M.; Betancourt, M.
2015-01-01
Historically, light curve studies of supernovae (SNe) and other transient classes have focused on individual objects with copious and high signal-to-noise observations. In the nascent era of wide field transient searches, objects with detailed observations are decreasing as a fraction of the overall known SN population, and this strategy sacrifices the majority of the information contained in the data about the underlying population of transients. A population level modeling approach, simultaneously fitting all available observations of objects in a transient sub-class of interest, fully mines the data to infer the properties of the population and avoids certain systematic biases. We present a novel hierarchical Bayesian statistical model for population level modeling of transient light curves, and discuss its implementation using an efficient Hamiltonian Monte Carlo technique. As a test case, we apply this model to the Type IIP SN sample from the Pan-STARRS1 Medium Deep Survey, consisting of 18,837 photometric observations of 76 SNe, corresponding to a joint posterior distribution with 9176 parameters under our model. Our hierarchical model fits provide improved constraints on light curve parameters relevant to the physical properties of their progenitor stars relative to modeling individual light curves alone. Moreover, we directly evaluate the probability for occurrence rates of unseen light curve characteristics from the model hyperparameters, addressing observational biases in survey methodology. We view this modeling framework as an unsupervised machine learning technique with the ability to maximize scientific returns from data to be collected by future wide field transient searches like LSST
Bayesian inference for psychology. Part II: Example applications with JASP.
Wagenmakers, Eric-Jan; Love, Jonathon; Marsman, Maarten; Jamil, Tahira; Ly, Alexander; Verhagen, Josine; Selker, Ravi; Gronau, Quentin F; Dropmann, Damian; Boutin, Bruno; Meerhoff, Frans; Knight, Patrick; Raj, Akash; van Kesteren, Erik-Jan; van Doorn, Johnny; Šmíra, Martin; Epskamp, Sacha; Etz, Alexander; Matzke, Dora; de Jong, Tim; van den Bergh, Don; Sarafoglou, Alexandra; Steingroever, Helen; Derks, Koen; Rouder, Jeffrey N; Morey, Richard D
2018-02-01
Bayesian hypothesis testing presents an attractive alternative to p value hypothesis testing. Part I of this series outlined several advantages of Bayesian hypothesis testing, including the ability to quantify evidence and the ability to monitor and update this evidence as data come in, without the need to know the intention with which the data were collected. Despite these and other practical advantages, Bayesian hypothesis tests are still reported relatively rarely. An important impediment to the widespread adoption of Bayesian tests is arguably the lack of user-friendly software for the run-of-the-mill statistical problems that confront psychologists for the analysis of almost every experiment: the t-test, ANOVA, correlation, regression, and contingency tables. In Part II of this series we introduce JASP ( http://www.jasp-stats.org ), an open-source, cross-platform, user-friendly graphical software package that allows users to carry out Bayesian hypothesis tests for standard statistical problems. JASP is based in part on the Bayesian analyses implemented in Morey and Rouder's BayesFactor package for R. Armed with JASP, the practical advantages of Bayesian hypothesis testing are only a mouse click away.
Narimani, Zahra; Beigy, Hamid; Ahmad, Ashar; Masoudi-Nejad, Ali; Fröhlich, Holger
2017-01-01
Inferring the structure of molecular networks from time series protein or gene expression data provides valuable information about the complex biological processes of the cell. Causal network structure inference has been approached using different methods in the past. Most causal network inference techniques, such as Dynamic Bayesian Networks and ordinary differential equations, are limited by their computational complexity and thus make large scale inference infeasible. This is specifically true if a Bayesian framework is applied in order to deal with the unavoidable uncertainty about the correct model. We devise a novel Bayesian network reverse engineering approach using ordinary differential equations with the ability to include non-linearity. Besides modeling arbitrary, possibly combinatorial and time dependent perturbations with unknown targets, one of our main contributions is the use of Expectation Propagation, an algorithm for approximate Bayesian inference over large scale network structures in short computation time. We further explore the possibility of integrating prior knowledge into network inference. We evaluate the proposed model on DREAM4 and DREAM8 data and find it competitive against several state-of-the-art existing network inference methods.
Numerical methods for Bayesian inference in the face of aging
Clarotti, C.A.; Villain, B.; Procaccia, H.
1996-01-01
In recent years, much attention has been paid to Bayesian methods for Risk Assessment. Until now, these methods have been studied from a theoretical point of view. Researchers have been mainly interested in: studying the effectiveness of Bayesian methods in handling rare events; debating about the problem of priors and other philosophical issues. An aspect central to the Bayesian approach is numerical computation because any safety/reliability problem, in a Bayesian frame, ends with a problem of numerical integration. This aspect has been neglected until now because most Risk studies assumed the Exponential model as the basic probabilistic model. The existence of conjugate priors makes numerical integration unnecessary in this case. If aging is to be taken into account, no conjugate family is available and the use of numerical integration becomes compulsory. EDF (National Board of Electricity, of France) and ENEA (National Committee for Energy, New Technologies and Environment, of Italy) jointly carried out a research program aimed at developing quadrature methods suitable for Bayesian Interference with underlying Weibull or gamma distributions. The paper will illustrate the main results achieved during the above research program and will discuss, via some sample cases, the performances of the numerical algorithms which on the appearance of stress corrosion cracking in the tubes of Steam Generators of PWR French power plants. (authors)
Picchini, Umberto; Forman, Julie Lyng
2016-01-01
a nonlinear stochastic differential equation model observed with correlated measurement errors and an application to protein folding modelling. An approximate Bayesian computation (ABC)-MCMC algorithm is suggested to allow inference for model parameters within reasonable time constraints. The ABC algorithm......In recent years, dynamical modelling has been provided with a range of breakthrough methods to perform exact Bayesian inference. However, it is often computationally unfeasible to apply exact statistical methodologies in the context of large data sets and complex models. This paper considers...... applications. A simulation study is conducted to compare our strategy with exact Bayesian inference, the latter resulting two orders of magnitude slower than ABC-MCMC for the considered set-up. Finally, the ABC algorithm is applied to a large size protein data. The suggested methodology is fairly general...
Sparse Bayesian Inference and the Temperature Structure of the Solar Corona
Warren, Harry P. [Space Science Division, Naval Research Laboratory, Washington, DC 20375 (United States); Byers, Jeff M. [Materials Science and Technology Division, Naval Research Laboratory, Washington, DC 20375 (United States); Crump, Nicholas A. [Naval Center for Space Technology, Naval Research Laboratory, Washington, DC 20375 (United States)
2017-02-20
Measuring the temperature structure of the solar atmosphere is critical to understanding how it is heated to high temperatures. Unfortunately, the temperature of the upper atmosphere cannot be observed directly, but must be inferred from spectrally resolved observations of individual emission lines that span a wide range of temperatures. Such observations are “inverted” to determine the distribution of plasma temperatures along the line of sight. This inversion is ill posed and, in the absence of regularization, tends to produce wildly oscillatory solutions. We introduce the application of sparse Bayesian inference to the problem of inferring the temperature structure of the solar corona. Within a Bayesian framework a preference for solutions that utilize a minimum number of basis functions can be encoded into the prior and many ad hoc assumptions can be avoided. We demonstrate the efficacy of the Bayesian approach by considering a test library of 40 assumed temperature distributions.
Sraj, Ihab; Zedler, Sarah E.; Knio, Omar; Jackson, Charles S.; Hoteit, Ibrahim
2016-01-01
The authors present a polynomial chaos (PC)-based Bayesian inference method for quantifying the uncertainties of the K-profile parameterization (KPP) within the MIT general circulation model (MITgcm) of the tropical Pacific. The inference
Nonparametric Bayesian inference for multidimensional compound Poisson processes
Gugushvili, S.; van der Meulen, F.; Spreij, P.
2015-01-01
Given a sample from a discretely observed multidimensional compound Poisson process, we study the problem of nonparametric estimation of its jump size density r0 and intensity λ0. We take a nonparametric Bayesian approach to the problem and determine posterior contraction rates in this context,
Bayesian inference using WBDev: a tutorial for social scientists
Wetzels, R.; Lee, M.D.; Wagenmakers, E.-J.
2010-01-01
Over the last decade, the popularity of Bayesian data analysis in the empirical sciences has greatly increased. This is partly due to the availability of WinBUGS, a free and flexible statistical software package that comes with an array of predefined functions and distributions, allowing users to
Metis: A Pure Metropolis Markov Chain Monte Carlo Bayesian Inference Library
Bates, Cameron Russell [Los Alamos National Lab. (LANL), Los Alamos, NM (United States); Mckigney, Edward Allen [Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
2018-01-09
The use of Bayesian inference in data analysis has become the standard for large scienti c experiments [1, 2]. The Monte Carlo Codes Group(XCP-3) at Los Alamos has developed a simple set of algorithms currently implemented in C++ and Python to easily perform at-prior Markov Chain Monte Carlo Bayesian inference with pure Metropolis sampling. These implementations are designed to be user friendly and extensible for customization based on speci c application requirements. This document describes the algorithmic choices made and presents two use cases.
Inference method using bayesian network for diagnosis of pulmonary nodules
Kawagishi, Masami; Iizuka, Yoshio; Yamamoto, Hiroyuki; Yakami, Masahiro; Kubo, Takeshi; Fujimoto, Koji; Togashi, Kaori
2010-01-01
This report describes the improvements of a naive Bayes model that infers the diagnosis of pulmonary nodules in chest CT images based on the findings obtained when a radiologist interprets the CT images. We have previously introduced an inference model using a naive Bayes classifier and have reported its clinical value based on evaluation using clinical data. In the present report, we introduce the following improvements to the original inference model: the selection of findings based on correlations and the generation of a model using only these findings, and the introduction of classifiers that integrate several simple classifiers each of which is specialized for specific diagnosis. These improvements were found to increase the inference accuracy by 10.4% (p<.01) as compared to the original model in 100 cases (222 nodules) based on leave-one-out evaluation. (author)
On a full Bayesian inference for force reconstruction problems
Aucejo, M.; De Smet, O.
2018-05-01
In a previous paper, the authors introduced a flexible methodology for reconstructing mechanical sources in the frequency domain from prior local information on both their nature and location over a linear and time invariant structure. The proposed approach was derived from Bayesian statistics, because of its ability in mathematically accounting for experimenter's prior knowledge. However, since only the Maximum a Posteriori estimate was computed, the posterior uncertainty about the regularized solution given the measured vibration field, the mechanical model and the regularization parameter was not assessed. To answer this legitimate question, this paper fully exploits the Bayesian framework to provide, from a Markov Chain Monte Carlo algorithm, credible intervals and other statistical measures (mean, median, mode) for all the parameters of the force reconstruction problem.
Operational modal analysis modeling, Bayesian inference, uncertainty laws
Au, Siu-Kui
2017-01-01
This book presents operational modal analysis (OMA), employing a coherent and comprehensive Bayesian framework for modal identification and covering stochastic modeling, theoretical formulations, computational algorithms, and practical applications. Mathematical similarities and philosophical differences between Bayesian and classical statistical approaches to system identification are discussed, allowing their mathematical tools to be shared and their results correctly interpreted. Many chapters can be used as lecture notes for the general topic they cover beyond the OMA context. After an introductory chapter (1), Chapters 2–7 present the general theory of stochastic modeling and analysis of ambient vibrations. Readers are first introduced to the spectral analysis of deterministic time series (2) and structural dynamics (3), which do not require the use of probability concepts. The concepts and techniques in these chapters are subsequently extended to a probabilistic context in Chapter 4 (on stochastic pro...
Boos, Moritz; Seer, Caroline; Lange, Florian; Kopp, Bruno
2016-01-01
Cognitive determinants of probabilistic inference were examined using hierarchical Bayesian modeling techniques. A classic urn-ball paradigm served as experimental strategy, involving a factorial two (prior probabilities) by two (likelihoods) design. Five computational models of cognitive processes were compared with the observed behavior. Parameter-free Bayesian posterior probabilities and parameter-free base rate neglect provided inadequate models of probabilistic inference. The introduction of distorted subjective probabilities yielded more robust and generalizable results. A general class of (inverted) S-shaped probability weighting functions had been proposed; however, the possibility of large differences in probability distortions not only across experimental conditions, but also across individuals, seems critical for the model's success. It also seems advantageous to consider individual differences in parameters of probability weighting as being sampled from weakly informative prior distributions of individual parameter values. Thus, the results from hierarchical Bayesian modeling converge with previous results in revealing that probability weighting parameters show considerable task dependency and individual differences. Methodologically, this work exemplifies the usefulness of hierarchical Bayesian modeling techniques for cognitive psychology. Theoretically, human probabilistic inference might be best described as the application of individualized strategic policies for Bayesian belief revision.
Moritz eBoos
2016-05-01
Full Text Available Cognitive determinants of probabilistic inference were examined using hierarchical Bayesian modelling techniques. A classic urn-ball paradigm served as experimental strategy, involving a factorial two (prior probabilities by two (likelihoods design. Five computational models of cognitive processes were compared with the observed behaviour. Parameter-free Bayesian posterior probabilities and parameter-free base rate neglect provided inadequate models of probabilistic inference. The introduction of distorted subjective probabilities yielded more robust and generalizable results. A general class of (inverted S-shaped probability weighting functions had been proposed; however, the possibility of large differences in probability distortions not only across experimental conditions, but also across individuals, seems critical for the model’s success. It also seems advantageous to consider individual differences in parameters of probability weighting as being sampled from weakly informative prior distributions of individual parameter values. Thus, the results from hierarchical Bayesian modelling converge with previous results in revealing that probability weighting parameters show considerable task dependency and individual differences. Methodologically, this work exemplifies the usefulness of hierarchical Bayesian modelling techniques for cognitive psychology. Theoretically, human probabilistic inference might be best described as the application of individualized strategic policies for Bayesian belief revision.
Bayesian inference and the analytic continuation of imaginary-time quantum Monte Carlo data
Gubernatis, J.E.; Bonca, J.; Jarrell, M.
1995-01-01
We present brief description of how methods of Bayesian inference are used to obtain real frequency information by the analytic continuation of imaginary-time quantum Monte Carlo data. We present the procedure we used, which is due to R. K. Bryan, and summarize several bottleneck issues
Jacobsen, Christian Robert Dahl; Møller, Jesper
2017-01-01
We introduce new estimation methods for a subclass of the Gaussian scale mixture models for wavelet trees by Wainwright, Simoncelli and Willsky that rely on modern results for composite likelihoods and approximate Bayesian inference. Our methodology is illustrated for denoising and edge detection...
Paudel, Y.; Botzen, W.J.W.; Aerts, J.C.J.H.
2013-01-01
This study applies Bayesian Inference to estimate flood risk for 53 dyke ring areas in the Netherlands, and focuses particularly on the data scarcity and extreme behaviour of catastrophe risk. The probability density curves of flood damage are estimated through Monte Carlo simulations. Based on
Bayesian Inference for Linear Parabolic PDEs with Noisy Boundary Conditions
Ruggeri, Fabrizio; Sawlan, Zaid A; Scavino, Marco; Tempone, Raul
2015-01-01
have been assumed for the time-dependent Dirichlet boundary values. Our approach is applied to synthetic data for the one-dimensional heat equation model, where the thermal diffusivity is the unknown parameter. We show how to infer the thermal
Bayesian inference and model comparison for metallic fatigue data
Babuška, Ivo
2016-02-23
In this work, we present a statistical treatment of stress-life (S-N) data drawn from a collection of records of fatigue experiments that were performed on 75S-T6 aluminum alloys. Our main objective is to predict the fatigue life of materials by providing a systematic approach to model calibration, model selection and model ranking with reference to S-N data. To this purpose, we consider fatigue-limit models and random fatigue-limit models that are specially designed to allow the treatment of the run-outs (right-censored data). We first fit the models to the data by maximum likelihood methods and estimate the quantiles of the life distribution of the alloy specimen. To assess the robustness of the estimation of the quantile functions, we obtain bootstrap confidence bands by stratified resampling with respect to the cycle ratio. We then compare and rank the models by classical measures of fit based on information criteria. We also consider a Bayesian approach that provides, under the prior distribution of the model parameters selected by the user, their simulation-based posterior distributions. We implement and apply Bayesian model comparison methods, such as Bayes factor ranking and predictive information criteria based on cross-validation techniques under various a priori scenarios.
Bayesian inference and model comparison for metallic fatigue data
Babuška, Ivo; Sawlan, Zaid A; Scavino, Marco; Szabó , Barna; Tempone, Raul
2016-01-01
In this work, we present a statistical treatment of stress-life (S-N) data drawn from a collection of records of fatigue experiments that were performed on 75S-T6 aluminum alloys. Our main objective is to predict the fatigue life of materials by providing a systematic approach to model calibration, model selection and model ranking with reference to S-N data. To this purpose, we consider fatigue-limit models and random fatigue-limit models that are specially designed to allow the treatment of the run-outs (right-censored data). We first fit the models to the data by maximum likelihood methods and estimate the quantiles of the life distribution of the alloy specimen. To assess the robustness of the estimation of the quantile functions, we obtain bootstrap confidence bands by stratified resampling with respect to the cycle ratio. We then compare and rank the models by classical measures of fit based on information criteria. We also consider a Bayesian approach that provides, under the prior distribution of the model parameters selected by the user, their simulation-based posterior distributions. We implement and apply Bayesian model comparison methods, such as Bayes factor ranking and predictive information criteria based on cross-validation techniques under various a priori scenarios.
Practical Bayesian inference a primer for physical scientists
Bailer-Jones, Coryn A L
2017-01-01
Science is fundamentally about learning from data, and doing so in the presence of uncertainty. This volume is an introduction to the major concepts of probability and statistics, and the computational tools for analysing and interpreting data. It describes the Bayesian approach, and explains how this can be used to fit and compare models in a range of problems. Topics covered include regression, parameter estimation, model assessment, and Monte Carlo methods, as well as widely used classical methods such as regularization and hypothesis testing. The emphasis throughout is on the principles, the unifying probabilistic approach, and showing how the methods can be implemented in practice. R code (with explanations) is included and is available online, so readers can reproduce the plots and results for themselves. Aimed primarily at undergraduate and graduate students, these techniques can be applied to a wide range of data analysis problems beyond the scope of this work.
A. A. Zolotin
2015-07-01
Full Text Available Posteriori inference is one of the three kinds of probabilistic-logic inferences in the probabilistic graphical models theory and the base for processing of knowledge patterns with probabilistic uncertainty using Bayesian networks. The paper deals with a task of local posteriori inference description in algebraic Bayesian networks that represent a class of probabilistic graphical models by means of matrix-vector equations. The latter are essentially based on the use of tensor product of matrices, Kronecker degree and Hadamard product. Matrix equations for calculating posteriori probabilities vectors within posteriori inference in knowledge patterns with quanta propositions are obtained. Similar equations of the same type have already been discussed within the confines of the theory of algebraic Bayesian networks, but they were built only for the case of posteriori inference in the knowledge patterns on the ideals of conjuncts. During synthesis and development of matrix-vector equations on quanta propositions probability vectors, a number of earlier results concerning normalizing factors in posteriori inference and assignment of linear projective operator with a selector vector was adapted. We consider all three types of incoming evidences - deterministic, stochastic and inaccurate - combined with scalar and interval estimation of probability truth of propositional formulas in the knowledge patterns. Linear programming problems are formed. Their solution gives the desired interval values of posterior probabilities in the case of inaccurate evidence or interval estimates in a knowledge pattern. That sort of description of a posteriori inference gives the possibility to extend the set of knowledge pattern types that we can use in the local and global posteriori inference, as well as simplify complex software implementation by use of existing third-party libraries, effectively supporting submission and processing of matrices and vectors when
Von Nessi, G T; Hole, M J
2014-01-01
We present recent results and technical breakthroughs for the Bayesian inference of tokamak equilibria using force-balance as a prior constraint. Issues surrounding model parameter representation and posterior analysis are discussed and addressed. These points motivate the recent advancements embodied in the Bayesian Equilibrium Analysis and Simulation Tool (BEAST) software being presently utilized to study equilibria on the Mega-Ampere Spherical Tokamak (MAST) experiment in the UK (von Nessi et al 2012 J. Phys. A 46 185501). State-of-the-art results of using BEAST to study MAST equilibria are reviewed, with recent code advancements being systematically presented though out the manuscript. (paper)
Bayesian Inference on the Memory Parameter for Gamma-Modulated Regression Models
Plinio Andrade
2015-09-01
Full Text Available In this work, we propose a Bayesian methodology to make inferences for the memory parameter and other characteristics under non-standard assumptions for a class of stochastic processes. This class generalizes the Gamma-modulated process, with trajectories that exhibit long memory behavior, as well as decreasing variability as time increases. Different values of the memory parameter influence the speed of this decrease, making this heteroscedastic model very flexible. Its properties are used to implement an approximate Bayesian computation and MCMC scheme to obtain posterior estimates. We test and validate our method through simulations and real data from the big earthquake that occurred in 2010 in Chile.
Bayesian inference and model comparison for metallic fatigue data
Babuska, Ivo
2016-01-06
In this work, we present a statistical treatment of stress-life (S-N) data drawn from a collection of records of fatigue experiments that were performed on 75S-T6 aluminum alloys. Our main objective is to predict the fatigue life of materials by providing a systematic approach to model calibration, model selection and model ranking with reference to S-N data. To this purpose, we consider fatigue-limit models and random fatigue-limit models that are specially designed to allow the treatment of the run-outs (right-censored data). We first fit the models to the data by maximum likelihood methods and estimate the quantiles of the life distribution of the alloy specimen. We then compare and rank the models by classical measures of fit based on information criteria. We also consider a Bayesian approach that provides, under the prior distribution of the model parameters selected by the user, their simulation-based posterior distributions.
Estimating mountain basin-mean precipitation from streamflow using Bayesian inference
Henn, Brian; Clark, Martyn P.; Kavetski, Dmitri; Lundquist, Jessica D.
2015-10-01
Estimating basin-mean precipitation in complex terrain is difficult due to uncertainty in the topographical representativeness of precipitation gauges relative to the basin. To address this issue, we use Bayesian methodology coupled with a multimodel framework to infer basin-mean precipitation from streamflow observations, and we apply this approach to snow-dominated basins in the Sierra Nevada of California. Using streamflow observations, forcing data from lower-elevation stations, the Bayesian Total Error Analysis (BATEA) methodology and the Framework for Understanding Structural Errors (FUSE), we infer basin-mean precipitation, and compare it to basin-mean precipitation estimated using topographically informed interpolation from gauges (PRISM, the Parameter-elevation Regression on Independent Slopes Model). The BATEA-inferred spatial patterns of precipitation show agreement with PRISM in terms of the rank of basins from wet to dry but differ in absolute values. In some of the basins, these differences may reflect biases in PRISM, because some implied PRISM runoff ratios may be inconsistent with the regional climate. We also infer annual time series of basin precipitation using a two-step calibration approach. Assessment of the precision and robustness of the BATEA approach suggests that uncertainty in the BATEA-inferred precipitation is primarily related to uncertainties in hydrologic model structure. Despite these limitations, time series of inferred annual precipitation under different model and parameter assumptions are strongly correlated with one another, suggesting that this approach is capable of resolving year-to-year variability in basin-mean precipitation.
Gunji, Yukio-Pegio; Shinohara, Shuji; Haruna, Taichi; Basios, Vasileios
2017-02-01
To overcome the dualism between mind and matter and to implement consciousness in science, a physical entity has to be embedded with a measurement process. Although quantum mechanics have been regarded as a candidate for implementing consciousness, nature at its macroscopic level is inconsistent with quantum mechanics. We propose a measurement-oriented inference system comprising Bayesian and inverse Bayesian inferences. While Bayesian inference contracts probability space, the newly defined inverse one relaxes the space. These two inferences allow an agent to make a decision corresponding to an immediate change in their environment. They generate a particular pattern of joint probability for data and hypotheses, comprising multiple diagonal and noisy matrices. This is expressed as a nondistributive orthomodular lattice equivalent to quantum logic. We also show that an orthomodular lattice can reveal information generated by inverse syllogism as well as the solutions to the frame and symbol-grounding problems. Our model is the first to connect macroscopic cognitive processes with the mathematical structure of quantum mechanics with no additional assumptions. Copyright © 2016 Elsevier Ireland Ltd. All rights reserved.
An empirical Bayesian approach for model-based inference of cellular signaling networks
Klinke David J
2009-11-01
Full Text Available Abstract Background A common challenge in systems biology is to infer mechanistic descriptions of biological process given limited observations of a biological system. Mathematical models are frequently used to represent a belief about the causal relationships among proteins within a signaling network. Bayesian methods provide an attractive framework for inferring the validity of those beliefs in the context of the available data. However, efficient sampling of high-dimensional parameter space and appropriate convergence criteria provide barriers for implementing an empirical Bayesian approach. The objective of this study was to apply an Adaptive Markov chain Monte Carlo technique to a typical study of cellular signaling pathways. Results As an illustrative example, a kinetic model for the early signaling events associated with the epidermal growth factor (EGF signaling network was calibrated against dynamic measurements observed in primary rat hepatocytes. A convergence criterion, based upon the Gelman-Rubin potential scale reduction factor, was applied to the model predictions. The posterior distributions of the parameters exhibited complicated structure, including significant covariance between specific parameters and a broad range of variance among the parameters. The model predictions, in contrast, were narrowly distributed and were used to identify areas of agreement among a collection of experimental studies. Conclusion In summary, an empirical Bayesian approach was developed for inferring the confidence that one can place in a particular model that describes signal transduction mechanisms and for inferring inconsistencies in experimental measurements.
Large-Scale Optimization for Bayesian Inference in Complex Systems
Willcox, Karen [MIT; Marzouk, Youssef [MIT
2013-11-12
The SAGUARO (Scalable Algorithms for Groundwater Uncertainty Analysis and Robust Optimization) Project focused on the development of scalable numerical algorithms for large-scale Bayesian inversion in complex systems that capitalize on advances in large-scale simulation-based optimization and inversion methods. The project was a collaborative effort among MIT, the University of Texas at Austin, Georgia Institute of Technology, and Sandia National Laboratories. The research was directed in three complementary areas: efficient approximations of the Hessian operator, reductions in complexity of forward simulations via stochastic spectral approximations and model reduction, and employing large-scale optimization concepts to accelerate sampling. The MIT--Sandia component of the SAGUARO Project addressed the intractability of conventional sampling methods for large-scale statistical inverse problems by devising reduced-order models that are faithful to the full-order model over a wide range of parameter values; sampling then employs the reduced model rather than the full model, resulting in very large computational savings. Results indicate little effect on the computed posterior distribution. On the other hand, in the Texas--Georgia Tech component of the project, we retain the full-order model, but exploit inverse problem structure (adjoint-based gradients and partial Hessian information of the parameter-to-observation map) to implicitly extract lower dimensional information on the posterior distribution; this greatly speeds up sampling methods, so that fewer sampling points are needed. We can think of these two approaches as ``reduce then sample'' and ``sample then reduce.'' In fact, these two approaches are complementary, and can be used in conjunction with each other. Moreover, they both exploit deterministic inverse problem structure, in the form of adjoint-based gradient and Hessian information of the underlying parameter-to-observation map, to
Bayesian inference of shared recombination hotspots between humans and chimpanzees.
Wang, Ying; Rannala, Bruce
2014-12-01
Recombination generates variation and facilitates evolution. Recombination (or lack thereof) also contributes to human genetic disease. Methods for mapping genes influencing complex genetic diseases via association rely on linkage disequilibrium (LD) in human populations, which is influenced by rates of recombination across the genome. Comparative population genomic analyses of recombination using related primate species can identify factors influencing rates of recombination in humans. Such studies can indicate how variable hotspots for recombination may be both among individuals (or populations) and over evolutionary timescales. Previous studies have suggested that locations of recombination hotspots are not conserved between humans and chimpanzees. We made use of the data sets from recent resequencing projects and applied a Bayesian method for identifying hotspots and estimating recombination rates. We also reanalyzed SNP data sets for regions with known hotspots in humans using samples from the human and chimpanzee. The Bayes factors (BF) of shared recombination hotspots between human and chimpanzee across regions were obtained. Based on the analysis of the aligned regions of human chromosome 21, locations where the two species show evidence of shared recombination hotspots (with high BFs) were identified. Interestingly, previous comparative studies of human and chimpanzee that focused on the known human recombination hotspots within the β-globin and HLA regions did not find overlapping of hotspots. Our results show high BFs of shared hotspots at locations within both regions, and the estimated locations of shared hotspots overlap with the locations of human recombination hotspots obtained from sperm-typing studies. Copyright © 2014 by the Genetics Society of America.
Møller, Jesper
2010-01-01
Chapter 9: This contribution concerns statistical inference for parametric models used in stochastic geometry and based on quick and simple simulation free procedures as well as more comprehensive methods based on a maximum likelihood or Bayesian approach combined with markov chain Monte Carlo...... (MCMC) techniques. Due to space limitations the focus is on spatial point processes....
Heller, Rasmus; Chikhi, Lounes; Siegismund, Hans
2013-01-01
Many coalescent-based methods aiming to infer the demographic history of populations assume a single, isolated and panmictic population (i.e. a Wright-Fisher model). While this assumption may be reasonable under many conditions, several recent studies have shown that the results can be misleading...... when it is violated. Among the most widely applied demographic inference methods are Bayesian skyline plots (BSPs), which are used across a range of biological fields. Violations of the panmixia assumption are to be expected in many biological systems, but the consequences for skyline plot inferences...... the best scheme for inferring demographic change over a typical time scale. Analyses of data from a structured African buffalo population demonstrate how BSP results can be strengthened by simulations. We recommend that sample selection should be carefully considered in relation to population structure...
Closed forms for conformally flat Green's functions
Brown, M.R.; Grove, P.G.; Ottewill, A.C.
1981-01-01
A closed form is obtained for the massless scalar Green's function on Rindler space. This is related by conformal transformation to the Green's function for a massless, conformally coupled scalar field on the open Einstein universe. A closed form is also obtained for the corresponding Green's function on the Einstein static universe. (author)
Detection of multiple damages employing best achievable eigenvectors under Bayesian inference
Prajapat, Kanta; Ray-Chaudhuri, Samit
2018-05-01
A novel approach is presented in this work to localize simultaneously multiple damaged elements in a structure along with the estimation of damage severity for each of the damaged elements. For detection of damaged elements, a best achievable eigenvector based formulation has been derived. To deal with noisy data, Bayesian inference is employed in the formulation wherein the likelihood of the Bayesian algorithm is formed on the basis of errors between the best achievable eigenvectors and the measured modes. In this approach, the most probable damage locations are evaluated under Bayesian inference by generating combinations of various possible damaged elements. Once damage locations are identified, damage severities are estimated using a Bayesian inference Markov chain Monte Carlo simulation. The efficiency of the proposed approach has been demonstrated by carrying out a numerical study involving a 12-story shear building. It has been found from this study that damage scenarios involving as low as 10% loss of stiffness in multiple elements are accurately determined (localized and severities quantified) even when 2% noise contaminated modal data are utilized. Further, this study introduces a term parameter impact (evaluated based on sensitivity of modal parameters towards structural parameters) to decide the suitability of selecting a particular mode, if some idea about the damaged elements are available. It has been demonstrated here that the accuracy and efficiency of the Bayesian quantification algorithm increases if damage localization is carried out a-priori. An experimental study involving a laboratory scale shear building and different stiffness modification scenarios shows that the proposed approach is efficient enough to localize the stories with stiffness modification.
Bayesian Inference using Neural Net Likelihood Models for Protein Secondary Structure Prediction
Seong-Gon Kim
2011-06-01
Full Text Available Several techniques such as Neural Networks, Genetic Algorithms, Decision Trees and other statistical or heuristic methods have been used to approach the complex non-linear task of predicting Alpha-helicies, Beta-sheets and Turns of a proteins secondary structure in the past. This project introduces a new machine learning method by using an offline trained Multilayered Perceptrons (MLP as the likelihood models within a Bayesian Inference framework to predict secondary structures proteins. Varying window sizes are used to extract neighboring amino acid information and passed back and forth between the Neural Net models and the Bayesian Inference process until there is a convergence of the posterior secondary structure probability.
Prudhomme, Serge; Bryant, Corey M.
2015-01-01
Parameter estimation for complex models using Bayesian inference is usually a very costly process as it requires a large number of solves of the forward problem. We show here how the construction of adaptive surrogate models using a posteriori error estimates for quantities of interest can significantly reduce the computational cost in problems of statistical inference. As surrogate models provide only approximations of the true solutions of the forward problem, it is nevertheless necessary to control these errors in order to construct an accurate reduced model with respect to the observables utilized in the identification of the model parameters. Effectiveness of the proposed approach is demonstrated on a numerical example dealing with the Spalart–Allmaras model for the simulation of turbulent channel flows. In particular, we illustrate how Bayesian model selection using the adapted surrogate model in place of solving the coupled nonlinear equations leads to the same quality of results while requiring fewer nonlinear PDE solves.
Prudhomme, Serge
2015-09-17
Parameter estimation for complex models using Bayesian inference is usually a very costly process as it requires a large number of solves of the forward problem. We show here how the construction of adaptive surrogate models using a posteriori error estimates for quantities of interest can significantly reduce the computational cost in problems of statistical inference. As surrogate models provide only approximations of the true solutions of the forward problem, it is nevertheless necessary to control these errors in order to construct an accurate reduced model with respect to the observables utilized in the identification of the model parameters. Effectiveness of the proposed approach is demonstrated on a numerical example dealing with the Spalart–Allmaras model for the simulation of turbulent channel flows. In particular, we illustrate how Bayesian model selection using the adapted surrogate model in place of solving the coupled nonlinear equations leads to the same quality of results while requiring fewer nonlinear PDE solves.
A method for crack sizing using Bayesian inference arising in eddy current testing
Kojima, Fumio; Kikuchi, Mitsuhiro
2008-01-01
This paper is concerned with a sizing methodology of crack using Bayesian inference arising in eddy current testing. There is often uncertainty about data through quantitative measurements of nondestructive testing and this can yield misleading inference of crack sizing at on-site monitoring. In this paper, we propose optimal strategies of measurements in eddy current testing using Bayesian prior-to-posteriori analysis. First our likelihood functional is given by Gaussian distribution with the measurement model based on the hybrid use of finite and boundary element methods. Secondly, given a priori distributions of crack sizing, we propose a method for estimating the region of interest for sizing cracks. Finally an optimal sensing method is demonstrated using our idea. (author)
Hea-Jung Kim
2017-06-01
Full Text Available This paper develops Bayesian inference in reliability of a class of scale mixtures of log-normal failure time (SMLNFT models with stochastic (or uncertain constraint in their reliability measures. The class is comprehensive and includes existing failure time (FT models (such as log-normal, log-Cauchy, and log-logistic FT models as well as new models that are robust in terms of heavy-tailed FT observations. Since classical frequency approaches to reliability analysis based on the SMLNFT model with stochastic constraint are intractable, the Bayesian method is pursued utilizing a Markov chain Monte Carlo (MCMC sampling based approach. This paper introduces a two-stage maximum entropy (MaxEnt prior, which elicits a priori uncertain constraint and develops Bayesian hierarchical SMLNFT model by using the prior. The paper also proposes an MCMC method for Bayesian inference in the SMLNFT model reliability and calls attention to properties of the MaxEnt prior that are useful for method development. Finally, two data sets are used to illustrate how the proposed methodology works.
Benjamin W. Y. Lo
2013-01-01
Full Text Available Objective. The novel clinical prediction approach of Bayesian neural networks with fuzzy logic inferences is created and applied to derive prognostic decision rules in cerebral aneurysmal subarachnoid hemorrhage (aSAH. Methods. The approach of Bayesian neural networks with fuzzy logic inferences was applied to data from five trials of Tirilazad for aneurysmal subarachnoid hemorrhage (3551 patients. Results. Bayesian meta-analyses of observational studies on aSAH prognostic factors gave generalizable posterior distributions of population mean log odd ratios (ORs. Similar trends were noted in Bayesian and linear regression ORs. Significant outcome predictors include normal motor response, cerebral infarction, history of myocardial infarction, cerebral edema, history of diabetes mellitus, fever on day 8, prior subarachnoid hemorrhage, admission angiographic vasospasm, neurological grade, intraventricular hemorrhage, ruptured aneurysm size, history of hypertension, vasospasm day, age and mean arterial pressure. Heteroscedasticity was present in the nontransformed dataset. Artificial neural networks found nonlinear relationships with 11 hidden variables in 1 layer, using the multilayer perceptron model. Fuzzy logic decision rules (centroid defuzzification technique denoted cut-off points for poor prognosis at greater than 2.5 clusters. Discussion. This aSAH prognostic system makes use of existing knowledge, recognizes unknown areas, incorporates one's clinical reasoning, and compensates for uncertainty in prognostication.
2016-03-01
each IDF curve and subsequently used to force a calibrated and validated precipitation - runoff model. Probability-based, risk-informed hydrologic...ERDC/CHL CHETN-X-2 March 2016 Approved for public release; distribution is unlimited. Bayesian Inference of Nonstationary Precipitation Intensity...based means by which to develop local precipitation Intensity-Duration-Frequency (IDF) curves using historical rainfall time series data collected for
Khan, Haseeb A.; Arif, Ibrahim A.; Bahkali, Ali H.; Al Farhan, Ahmad H.; Al Homaidan, Ali A.
2008-01-01
This investigation was aimed to compare the inference of antelope phylogenies resulting from the 16S rRNA, cytochrome-b (cyt-b) and d-loop segments of mitochondrial DNA using three different computational models including Bayesian (BA), maximum parsimony (MP) and unweighted pair group method with arithmetic mean (UPGMA). The respective nucleotide sequences of three Oryx species (Oryx leucoryx, Oryx dammah and Oryx gazella) and an out-group (Addax nasomaculatus) were aligned and subjected to B...
Dorazio, R.M.; Johnson, F.A.
2003-01-01
Bayesian inference and decision theory may be used in the solution of relatively complex problems of natural resource management, owing to recent advances in statistical theory and computing. In particular, Markov chain Monte Carlo algorithms provide a computational framework for fitting models of adequate complexity and for evaluating the expected consequences of alternative management actions. We illustrate these features using an example based on management of waterfowl habitat.
Statistical detection of EEG synchrony using empirical bayesian inference.
Archana K Singh
Full Text Available There is growing interest in understanding how the brain utilizes synchronized oscillatory activity to integrate information across functionally connected regions. Computing phase-locking values (PLV between EEG signals is a popular method for quantifying such synchronizations and elucidating their role in cognitive tasks. However, high-dimensionality in PLV data incurs a serious multiple testing problem. Standard multiple testing methods in neuroimaging research (e.g., false discovery rate, FDR suffer severe loss of power, because they fail to exploit complex dependence structure between hypotheses that vary in spectral, temporal and spatial dimension. Previously, we showed that a hierarchical FDR and optimal discovery procedures could be effectively applied for PLV analysis to provide better power than FDR. In this article, we revisit the multiple comparison problem from a new Empirical Bayes perspective and propose the application of the local FDR method (locFDR; Efron, 2001 for PLV synchrony analysis to compute FDR as a posterior probability that an observed statistic belongs to a null hypothesis. We demonstrate the application of Efron's Empirical Bayes approach for PLV synchrony analysis for the first time. We use simulations to validate the specificity and sensitivity of locFDR and a real EEG dataset from a visual search study for experimental validation. We also compare locFDR with hierarchical FDR and optimal discovery procedures in both simulation and experimental analyses. Our simulation results showed that the locFDR can effectively control false positives without compromising on the power of PLV synchrony inference. Our results from the application locFDR on experiment data detected more significant discoveries than our previously proposed methods whereas the standard FDR method failed to detect any significant discoveries.
Statistical detection of EEG synchrony using empirical bayesian inference.
Singh, Archana K; Asoh, Hideki; Takeda, Yuji; Phillips, Steven
2015-01-01
There is growing interest in understanding how the brain utilizes synchronized oscillatory activity to integrate information across functionally connected regions. Computing phase-locking values (PLV) between EEG signals is a popular method for quantifying such synchronizations and elucidating their role in cognitive tasks. However, high-dimensionality in PLV data incurs a serious multiple testing problem. Standard multiple testing methods in neuroimaging research (e.g., false discovery rate, FDR) suffer severe loss of power, because they fail to exploit complex dependence structure between hypotheses that vary in spectral, temporal and spatial dimension. Previously, we showed that a hierarchical FDR and optimal discovery procedures could be effectively applied for PLV analysis to provide better power than FDR. In this article, we revisit the multiple comparison problem from a new Empirical Bayes perspective and propose the application of the local FDR method (locFDR; Efron, 2001) for PLV synchrony analysis to compute FDR as a posterior probability that an observed statistic belongs to a null hypothesis. We demonstrate the application of Efron's Empirical Bayes approach for PLV synchrony analysis for the first time. We use simulations to validate the specificity and sensitivity of locFDR and a real EEG dataset from a visual search study for experimental validation. We also compare locFDR with hierarchical FDR and optimal discovery procedures in both simulation and experimental analyses. Our simulation results showed that the locFDR can effectively control false positives without compromising on the power of PLV synchrony inference. Our results from the application locFDR on experiment data detected more significant discoveries than our previously proposed methods whereas the standard FDR method failed to detect any significant discoveries.
Constraining East Antarctic mass trends using a Bayesian inference approach
Martin-Español, Alba; Bamber, Jonathan L.
2016-04-01
East Antarctica is an order of magnitude larger than its western neighbour and the Greenland ice sheet. It has the greatest potential to contribute to sea level rise of any source, including non-glacial contributors. It is, however, the most challenging ice mass to constrain because of a range of factors including the relative paucity of in-situ observations and the poor signal to noise ratio of Earth Observation data such as satellite altimetry and gravimetry. A recent study using satellite radar and laser altimetry (Zwally et al. 2015) concluded that the East Antarctic Ice Sheet (EAIS) had been accumulating mass at a rate of 136±28 Gt/yr for the period 2003-08. Here, we use a Bayesian hierarchical model, which has been tested on, and applied to, the whole of Antarctica, to investigate the impact of different assumptions regarding the origin of elevation changes of the EAIS. We combined GRACE, satellite laser and radar altimeter data and GPS measurements to solve simultaneously for surface processes (primarily surface mass balance, SMB), ice dynamics and glacio-isostatic adjustment over the period 2003-13. The hierarchical model partitions mass trends between SMB and ice dynamics based on physical principles and measures of statistical likelihood. Without imposing the division between these processes, the model apportions about a third of the mass trend to ice dynamics, +18 Gt/yr, and two thirds, +39 Gt/yr, to SMB. The total mass trend for that period for the EAIS was 57±20 Gt/yr. Over the period 2003-08, we obtain an ice dynamic trend of 12 Gt/yr and a SMB trend of 15 Gt/yr, with a total mass trend of 27 Gt/yr. We then imposed the condition that the surface mass balance is tightly constrained by the regional climate model RACMO2.3 and allowed height changes due to ice dynamics to occur in areas of low surface velocities (solution that satisfies all the input data, given these constraints. By imposing these conditions, over the period 2003-13 we obtained a mass
Kang, Seong Keun; Seong, Poong Hyun [KAIST, Daejeon (Korea, Republic of)
2014-08-15
Bayesian methodology has been used widely used in various research fields. It is method of inference using Bayes' rule to update the estimation of probability for the certain hypothesis when additional evidences are acquired. According to the current researches, malfunction of nuclear power plant can be detected by using this Bayesian inference which consistently piles up the newly incoming data and updates its estimation. However, those researches are based on the assumption that people are doing like computer perfectly, which can be criticized and may cause a problem in real world application. Studies in cognitive psychology indicates that when the amount of information becomes larger, people can't save the whole data because people have limited memory capacity which is well known as working memory, and also they have attention problem. The purpose of this paper is to consider the psychological factors and confirm how much this working memory and attention will affect the resulted estimation based on the Bayesian inference. To confirm this, experiment on human is needed, and the tool of experiment is Compact Nuclear Simulator (CNS)
Kang, Seong Keun; Seong, Poong Hyun
2014-01-01
Bayesian methodology has been used widely used in various research fields. It is method of inference using Bayes' rule to update the estimation of probability for the certain hypothesis when additional evidences are acquired. According to the current researches, malfunction of nuclear power plant can be detected by using this Bayesian inference which consistently piles up the newly incoming data and updates its estimation. However, those researches are based on the assumption that people are doing like computer perfectly, which can be criticized and may cause a problem in real world application. Studies in cognitive psychology indicates that when the amount of information becomes larger, people can't save the whole data because people have limited memory capacity which is well known as working memory, and also they have attention problem. The purpose of this paper is to consider the psychological factors and confirm how much this working memory and attention will affect the resulted estimation based on the Bayesian inference. To confirm this, experiment on human is needed, and the tool of experiment is Compact Nuclear Simulator (CNS)
Adaptability and phenotypic stability of common bean genotypes through Bayesian inference.
Corrêa, A M; Teodoro, P E; Gonçalves, M C; Barroso, L M A; Nascimento, M; Santos, A; Torres, F E
2016-04-27
This study used Bayesian inference to investigate the genotype x environment interaction in common bean grown in Mato Grosso do Sul State, and it also evaluated the efficiency of using informative and minimally informative a priori distributions. Six trials were conducted in randomized blocks, and the grain yield of 13 common bean genotypes was assessed. To represent the minimally informative a priori distributions, a probability distribution with high variance was used, and a meta-analysis concept was adopted to represent the informative a priori distributions. Bayes factors were used to conduct comparisons between the a priori distributions. The Bayesian inference was effective for the selection of upright common bean genotypes with high adaptability and phenotypic stability using the Eberhart and Russell method. Bayes factors indicated that the use of informative a priori distributions provided more accurate results than minimally informative a priori distributions. According to Bayesian inference, the EMGOPA-201, BAMBUÍ, CNF 4999, CNF 4129 A 54, and CNFv 8025 genotypes had specific adaptability to favorable environments, while the IAPAR 14 and IAC CARIOCA ETE genotypes had specific adaptability to unfavorable environments.
Sraj, Ihab; Le Maî tre, Olivier P.; Knio, Omar; Hoteit, Ibrahim
2015-01-01
using a coordinate transformation to account for the dependence with respect to the covariance hyper-parameters. Polynomial Chaos expansions are employed for the acceleration of the Bayesian inference using similar coordinate transformations, enabling us
A Bayesian Framework That Integrates Heterogeneous Data for Inferring Gene Regulatory Networks
Santra, Tapesh, E-mail: tapesh.santra@ucd.ie [Systems Biology Ireland, University College Dublin, Dublin (Ireland)
2014-05-20
Reconstruction of gene regulatory networks (GRNs) from experimental data is a fundamental challenge in systems biology. A number of computational approaches have been developed to infer GRNs from mRNA expression profiles. However, expression profiles alone are proving to be insufficient for inferring GRN topologies with reasonable accuracy. Recently, it has been shown that integration of external data sources (such as gene and protein sequence information, gene ontology data, protein–protein interactions) with mRNA expression profiles may increase the reliability of the inference process. Here, I propose a new approach that incorporates transcription factor binding sites (TFBS) and physical protein interactions (PPI) among transcription factors (TFs) in a Bayesian variable selection (BVS) algorithm which can infer GRNs from mRNA expression profiles subjected to genetic perturbations. Using real experimental data, I show that the integration of TFBS and PPI data with mRNA expression profiles leads to significantly more accurate networks than those inferred from expression profiles alone. Additionally, the performance of the proposed algorithm is compared with a series of least absolute shrinkage and selection operator (LASSO) regression-based network inference methods that can also incorporate prior knowledge in the inference framework. The results of this comparison suggest that BVS can outperform LASSO regression-based method in some circumstances.
A Bayesian Framework That Integrates Heterogeneous Data for Inferring Gene Regulatory Networks
Santra, Tapesh
2014-01-01
Reconstruction of gene regulatory networks (GRNs) from experimental data is a fundamental challenge in systems biology. A number of computational approaches have been developed to infer GRNs from mRNA expression profiles. However, expression profiles alone are proving to be insufficient for inferring GRN topologies with reasonable accuracy. Recently, it has been shown that integration of external data sources (such as gene and protein sequence information, gene ontology data, protein–protein interactions) with mRNA expression profiles may increase the reliability of the inference process. Here, I propose a new approach that incorporates transcription factor binding sites (TFBS) and physical protein interactions (PPI) among transcription factors (TFs) in a Bayesian variable selection (BVS) algorithm which can infer GRNs from mRNA expression profiles subjected to genetic perturbations. Using real experimental data, I show that the integration of TFBS and PPI data with mRNA expression profiles leads to significantly more accurate networks than those inferred from expression profiles alone. Additionally, the performance of the proposed algorithm is compared with a series of least absolute shrinkage and selection operator (LASSO) regression-based network inference methods that can also incorporate prior knowledge in the inference framework. The results of this comparison suggest that BVS can outperform LASSO regression-based method in some circumstances.
Anderson, Eric C; Ng, Thomas C
2016-02-01
We develop a computational framework for addressing pedigree inference problems using small numbers (80-400) of single nucleotide polymorphisms (SNPs). Our approach relaxes the assumptions, which are commonly made, that sampling is complete with respect to the pedigree and that there is no genotyping error. It relies on representing the inferred pedigree as a factor graph and invoking the Sum-Product algorithm to compute and store quantities that allow the joint probability of the data to be rapidly computed under a large class of rearrangements of the pedigree structure. This allows efficient MCMC sampling over the space of pedigrees, and, hence, Bayesian inference of pedigree structure. In this paper we restrict ourselves to inference of pedigrees without loops using SNPs assumed to be unlinked. We present the methodology in general for multigenerational inference, and we illustrate the method by applying it to the inference of full sibling groups in a large sample (n=1157) of Chinook salmon typed at 95 SNPs. The results show that our method provides a better point estimate and estimate of uncertainty than the currently best-available maximum-likelihood sibling reconstruction method. Extensions of this work to more complex scenarios are briefly discussed. Published by Elsevier Inc.
Empirical verification for application of Bayesian inference in situation awareness evaluations
Kang, Seongkeun; Kim, Ar Ryum; Seong, Poong Hyun
2017-01-01
Highlights: • Situation awareness (SA) of human operators is significantly important for safe operation in nuclear power plants (NPPs). • SA of human operators was empirically estimated using Bayesian inference. • In this empirical study, the effect of attention and working memory to SA was considered. • Complexcity of the given task and design of human machine interface (HMI) considerably affect SA of human operators. - Abstract: Bayesian methodology has been widely used in various research fields. According to current research, malfunctions of nuclear power plants can be detected using this Bayesian inference, which consistently piles up newly incoming data and updates the estimation. However, these studies have been based on the assumption that people work like computers—perfectly—a supposition that may cause a problem in real world applications. Studies in cognitive psychology indicate that when the amount of information to be processed becomes larger, people cannot save the whole set of data in their heads due to limited attention and limited memory capacity, also known as working memory. The purpose of the current research is to consider how actual human aware the situation contrasts with our expectations, and how such disparity affects the results of conventional Bayesian inference, if at all. We compared situation awareness (SA) of ideal operators with SA of human operators, and for the human operator we used both text-based human machine interface (HMI) and infographic-based HMI to further compare two existing human operators. In addition, two different scenarios were selected how scenario complexity affects SA of human operators. As a results, when a malfunction occurred, the ideal operator found the malfunction nearly 100% probability of the time using Bayesian inference. In contrast, out of forty-six human operators, only 69.57% found the correct malfunction with simple scenario and 58.70% with complex scenario in the text-based HMI. In
McGeachie, Michael J; Chang, Hsun-Hsien; Weiss, Scott T
2014-06-01
Bayesian Networks (BN) have been a popular predictive modeling formalism in bioinformatics, but their application in modern genomics has been slowed by an inability to cleanly handle domains with mixed discrete and continuous variables. Existing free BN software packages either discretize continuous variables, which can lead to information loss, or do not include inference routines, which makes prediction with the BN impossible. We present CGBayesNets, a BN package focused around prediction of a clinical phenotype from mixed discrete and continuous variables, which fills these gaps. CGBayesNets implements Bayesian likelihood and inference algorithms for the conditional Gaussian Bayesian network (CGBNs) formalism, one appropriate for predicting an outcome of interest from, e.g., multimodal genomic data. We provide four different network learning algorithms, each making a different tradeoff between computational cost and network likelihood. CGBayesNets provides a full suite of functions for model exploration and verification, including cross validation, bootstrapping, and AUC manipulation. We highlight several results obtained previously with CGBayesNets, including predictive models of wood properties from tree genomics, leukemia subtype classification from mixed genomic data, and robust prediction of intensive care unit mortality outcomes from metabolomic profiles. We also provide detailed example analysis on public metabolomic and gene expression datasets. CGBayesNets is implemented in MATLAB and available as MATLAB source code, under an Open Source license and anonymous download at http://www.cgbayesnets.com.
Ross H Johnstone
2017-03-01
Full Text Available Dose-response (or ‘concentration-effect’ relationships commonly occur in biological and pharmacological systems and are well characterised by Hill curves. These curves are described by an equation with two parameters: the inhibitory concentration 50% (IC50; and the Hill coefficient. Typically just the ‘best fit’ parameter values are reported in the literature. Here we introduce a Python-based software tool, PyHillFit , and describe the underlying Bayesian inference methods that it uses, to infer probability distributions for these parameters as well as the level of experimental observation noise. The tool also allows for hierarchical fitting, characterising the effect of inter-experiment variability. We demonstrate the use of the tool on a recently published dataset on multiple ion channel inhibition by multiple drug compounds. We compare the maximum likelihood, Bayesian and hierarchical Bayesian approaches. We then show how uncertainty in dose-response inputs can be characterised and propagated into a cardiac action potential simulation to give a probability distribution on model outputs.
Ma Xiang; Zabaras, Nicholas
2009-01-01
A new approach to modeling inverse problems using a Bayesian inference method is introduced. The Bayesian approach considers the unknown parameters as random variables and seeks the probabilistic distribution of the unknowns. By introducing the concept of the stochastic prior state space to the Bayesian formulation, we reformulate the deterministic forward problem as a stochastic one. The adaptive hierarchical sparse grid collocation (ASGC) method is used for constructing an interpolant to the solution of the forward model in this prior space which is large enough to capture all the variability/uncertainty in the posterior distribution of the unknown parameters. This solution can be considered as a function of the random unknowns and serves as a stochastic surrogate model for the likelihood calculation. Hierarchical Bayesian formulation is used to derive the posterior probability density function (PPDF). The spatial model is represented as a convolution of a smooth kernel and a Markov random field. The state space of the PPDF is explored using Markov chain Monte Carlo algorithms to obtain statistics of the unknowns. The likelihood calculation is performed by directly sampling the approximate stochastic solution obtained through the ASGC method. The technique is assessed on two nonlinear inverse problems: source inversion and permeability estimation in flow through porous media
Bayesian techniques for fatigue life prediction and for inference in linear time dependent PDEs
Scavino, Marco
2016-01-08
In this talk we introduce first the main characteristics of a systematic statistical approach to model calibration, model selection and model ranking when stress-life data are drawn from a collection of records of fatigue experiments. Focusing on Bayesian prediction assessment, we consider fatigue-limit models and random fatigue-limit models under different a priori assumptions. In the second part of the talk, we present a hierarchical Bayesian technique for the inference of the coefficients of time dependent linear PDEs, under the assumption that noisy measurements are available in both the interior of a domain of interest and from boundary conditions. We present a computational technique based on the marginalization of the contribution of the boundary parameters and apply it to inverse heat conduction problems.
A Bayesian inference approach to unveil supply curves in electricity markets
Mitridati, Lesia Marie-Jeanne Mariane; Pinson, Pierre
2017-01-01
in the literature on modeling this uncertainty. In this study we introduce a Bayesian inference approach to reveal the aggregate supply curve in a day-ahead electricity market. The proposed algorithm relies on Markov Chain Monte Carlo and Sequential Monte Carlo methods. The major appeal of this approach......With increased competition in wholesale electricity markets, the need for new decision-making tools for strategic producers has arisen. Optimal bidding strategies have traditionally been modeled as stochastic profit maximization problems. However, for producers with non-negligible market power...
Bayesian inference for multivariate point processes observed at sparsely distributed times
Rasmussen, Jakob Gulddahl; Møller, Jesper; Aukema, B.H.
We consider statistical and computational aspects of simulation-based Bayesian inference for a multivariate point process which is only observed at sparsely distributed times. For specicity we consider a particular data set which has earlier been analyzed by a discrete time model involving unknown...... normalizing constants. We discuss the advantages and disadvantages of using continuous time processes compared to discrete time processes in the setting of the present paper as well as other spatial-temporal situations. Keywords: Bark beetle, conditional intensity, forest entomology, Markov chain Monte Carlo...
Y. Paudel
2013-03-01
Full Text Available This study applies Bayesian Inference to estimate flood risk for 53 dyke ring areas in the Netherlands, and focuses particularly on the data scarcity and extreme behaviour of catastrophe risk. The probability density curves of flood damage are estimated through Monte Carlo simulations. Based on these results, flood insurance premiums are estimated using two different practical methods that each account in different ways for an insurer's risk aversion and the dispersion rate of loss data. This study is of practical relevance because insurers have been considering the introduction of flood insurance in the Netherlands, which is currently not generally available.
Meng, Weizhi; Li, Wenjuan; Xiang, Yang
2017-01-01
and experience for both patients and healthcare workers, and the underlying network architecture to support such devices is also referred to as medical smartphone networks (MSNs). MSNs, similar to other networks, are subject to a wide range of attacks (e.g. leakage of sensitive patient information by a malicious...... insider). In this work, we focus on MSNs and present a compact but efficient trust-based approach using Bayesian inference to identify malicious nodes in such an environment. We then demonstrate the effectiveness of our approach in detecting malicious nodes by evaluating the deployment of our proposed...
Paudel, Y.; Botzen, W. J. W.; Aerts, J. C. J. H.
2013-03-01
This study applies Bayesian Inference to estimate flood risk for 53 dyke ring areas in the Netherlands, and focuses particularly on the data scarcity and extreme behaviour of catastrophe risk. The probability density curves of flood damage are estimated through Monte Carlo simulations. Based on these results, flood insurance premiums are estimated using two different practical methods that each account in different ways for an insurer's risk aversion and the dispersion rate of loss data. This study is of practical relevance because insurers have been considering the introduction of flood insurance in the Netherlands, which is currently not generally available.
Zonta, Zivko J; Flotats, Xavier; Magrí, Albert
2014-08-01
The procedure commonly used for the assessment of the parameters included in activated sludge models (ASMs) relies on the estimation of their optimal value within a confidence region (i.e. frequentist inference). Once optimal values are estimated, parameter uncertainty is computed through the covariance matrix. However, alternative approaches based on the consideration of the model parameters as probability distributions (i.e. Bayesian inference), may be of interest. The aim of this work is to apply (and compare) both Bayesian and frequentist inference methods when assessing uncertainty for an ASM-type model, which considers intracellular storage and biomass growth, simultaneously. Practical identifiability was addressed exclusively considering respirometric profiles based on the oxygen uptake rate and with the aid of probabilistic global sensitivity analysis. Parameter uncertainty was thus estimated according to both the Bayesian and frequentist inferential procedures. Results were compared in order to evidence the strengths and weaknesses of both approaches. Since it was demonstrated that Bayesian inference could be reduced to a frequentist approach under particular hypotheses, the former can be considered as a more generalist methodology. Hence, the use of Bayesian inference is encouraged for tackling inferential issues in ASM environments.
Inferring gene and protein interactions using PubMed citations and consensus Bayesian networks.
Deeter, Anthony; Dalman, Mark; Haddad, Joseph; Duan, Zhong-Hui
2017-01-01
The PubMed database offers an extensive set of publication data that can be useful, yet inherently complex to use without automated computational techniques. Data repositories such as the Genomic Data Commons (GDC) and the Gene Expression Omnibus (GEO) offer experimental data storage and retrieval as well as curated gene expression profiles. Genetic interaction databases, including Reactome and Ingenuity Pathway Analysis, offer pathway and experiment data analysis using data curated from these publications and data repositories. We have created a method to generate and analyze consensus networks, inferring potential gene interactions, using large numbers of Bayesian networks generated by data mining publications in the PubMed database. Through the concept of network resolution, these consensus networks can be tailored to represent possible genetic interactions. We designed a set of experiments to confirm that our method is stable across variation in both sample and topological input sizes. Using gene product interactions from the KEGG pathway database and data mining PubMed publication abstracts, we verify that regardless of the network resolution or the inferred consensus network, our method is capable of inferring meaningful gene interactions through consensus Bayesian network generation with multiple, randomized topological orderings. Our method can not only confirm the existence of currently accepted interactions, but has the potential to hypothesize new ones as well. We show our method confirms the existence of known gene interactions such as JAK-STAT-PI3K-AKT-mTOR, infers novel gene interactions such as RAS- Bcl-2 and RAS-AKT, and found significant pathway-pathway interactions between the JAK-STAT signaling and Cardiac Muscle Contraction KEGG pathways.
Closed forms and multi-moment maps
Madsen, Thomas Bruun; Swann, Andrew Francis
2013-01-01
We extend the notion of multi-moment map to geometries defined by closed forms of arbitrary degree. We give fundamental existence and uniqueness results and discuss a number of essential examples, including geometries related to special holonomy. For forms of degree four, multi-moment maps are gu...
Wavelet-Bayesian inference of cosmic strings embedded in the cosmic microwave background
McEwen, J. D.; Feeney, S. M.; Peiris, H. V.; Wiaux, Y.; Ringeval, C.; Bouchet, F. R.
2017-12-01
Cosmic strings are a well-motivated extension to the standard cosmological model and could induce a subdominant component in the anisotropies of the cosmic microwave background (CMB), in addition to the standard inflationary component. The detection of strings, while observationally challenging, would provide a direct probe of physics at very high-energy scales. We develop a framework for cosmic string inference from observations of the CMB made over the celestial sphere, performing a Bayesian analysis in wavelet space where the string-induced CMB component has distinct statistical properties to the standard inflationary component. Our wavelet-Bayesian framework provides a principled approach to compute the posterior distribution of the string tension Gμ and the Bayesian evidence ratio comparing the string model to the standard inflationary model. Furthermore, we present a technique to recover an estimate of any string-induced CMB map embedded in observational data. Using Planck-like simulations, we demonstrate the application of our framework and evaluate its performance. The method is sensitive to Gμ ∼ 5 × 10-7 for Nambu-Goto string simulations that include an integrated Sachs-Wolfe contribution only and do not include any recombination effects, before any parameters of the analysis are optimized. The sensitivity of the method compares favourably with other techniques applied to the same simulations.
Multi-model polynomial chaos surrogate dictionary for Bayesian inference in elasticity problems
Contreras, Andres A.
2016-09-19
A method is presented for inferring the presence of an inclusion inside a domain; the proposed approach is suitable to be used in a diagnostic device with low computational power. Specifically, we use the Bayesian framework for the inference of stiff inclusions embedded in a soft matrix, mimicking tumors in soft tissues. We rely on a polynomial chaos (PC) surrogate to accelerate the inference process. The PC surrogate predicts the dependence of the displacements field with the random elastic moduli of the materials, and are computed by means of the stochastic Galerkin (SG) projection method. Moreover, the inclusion\\'s geometry is assumed to be unknown, and this is addressed by using a dictionary consisting of several geometrical models with different configurations. A model selection approach based on the evidence provided by the data (Bayes factors) is used to discriminate among the different geometrical models and select the most suitable one. The idea of using a dictionary of pre-computed geometrical models helps to maintain the computational cost of the inference process very low, as most of the computational burden is carried out off-line for the resolution of the SG problems. Numerical tests are used to validate the methodology, assess its performance, and analyze the robustness to model errors. © 2016 Elsevier Ltd
Hadwin, Paul J.; Sipkens, T. A.; Thomson, K. A.; Liu, F.; Daun, K. J.
2016-01-01
Auto-correlated laser-induced incandescence (AC-LII) infers the soot volume fraction (SVF) of soot particles by comparing the spectral incandescence from laser-energized particles to the pyrometrically inferred peak soot temperature. This calculation requires detailed knowledge of model parameters such as the absorption function of soot, which may vary with combustion chemistry, soot age, and the internal structure of the soot. This work presents a Bayesian methodology to quantify such uncertainties. This technique treats the additional "nuisance" model parameters, including the soot absorption function, as stochastic variables and incorporates the current state of knowledge of these parameters into the inference process through maximum entropy priors. While standard AC-LII analysis provides a point estimate of the SVF, Bayesian techniques infer the posterior probability density, which will allow scientists and engineers to better assess the reliability of AC-LII inferred SVFs in the context of environmental regulations and competing diagnostics.
Bayesian inference of earthquake parameters from buoy data using a polynomial chaos-based surrogate
Giraldi, Loic
2017-04-07
This work addresses the estimation of the parameters of an earthquake model by the consequent tsunami, with an application to the Chile 2010 event. We are particularly interested in the Bayesian inference of the location, the orientation, and the slip of an Okada-based model of the earthquake ocean floor displacement. The tsunami numerical model is based on the GeoClaw software while the observational data is provided by a single DARTⓇ buoy. We propose in this paper a methodology based on polynomial chaos expansion to construct a surrogate model of the wave height at the buoy location. A correlated noise model is first proposed in order to represent the discrepancy between the computational model and the data. This step is necessary, as a classical independent Gaussian noise is shown to be unsuitable for modeling the error, and to prevent convergence of the Markov Chain Monte Carlo sampler. Second, the polynomial chaos model is subsequently improved to handle the variability of the arrival time of the wave, using a preconditioned non-intrusive spectral method. Finally, the construction of a reduced model dedicated to Bayesian inference is proposed. Numerical results are presented and discussed.
Hierarchical Bayesian inference of the initial mass function in composite stellar populations
Dries, M.; Trager, S. C.; Koopmans, L. V. E.; Popping, G.; Somerville, R. S.
2018-03-01
The initial mass function (IMF) is a key ingredient in many studies of galaxy formation and evolution. Although the IMF is often assumed to be universal, there is continuing evidence that it is not universal. Spectroscopic studies that derive the IMF of the unresolved stellar populations of a galaxy often assume that this spectrum can be described by a single stellar population (SSP). To alleviate these limitations, in this paper we have developed a unique hierarchical Bayesian framework for modelling composite stellar populations (CSPs). Within this framework, we use a parametrized IMF prior to regulate a direct inference of the IMF. We use this new framework to determine the number of SSPs that is required to fit a set of realistic CSP mock spectra. The CSP mock spectra that we use are based on semi-analytic models and have an IMF that varies as a function of stellar velocity dispersion of the galaxy. Our results suggest that using a single SSP biases the determination of the IMF slope to a higher value than the true slope, although the trend with stellar velocity dispersion is overall recovered. If we include more SSPs in the fit, the Bayesian evidence increases significantly and the inferred IMF slopes of our mock spectra converge, within the errors, to their true values. Most of the bias is already removed by using two SSPs instead of one. We show that we can reconstruct the variable IMF of our mock spectra for signal-to-noise ratios exceeding ˜75.
Unkelbach, J; Oelfke, U
2005-01-01
We present a method to calculate dose uncertainties due to inter-fraction organ movements in fractionated radiotherapy, i.e. in addition to the expectation value of the dose distribution a variance distribution is calculated. To calculate the expectation value of the dose distribution in the presence of organ movements, one estimates a probability distribution of possible patient geometries. The respective variance of the expected dose distribution arises for two reasons: first, the patient is irradiated with a finite number of fractions only and second, the probability distribution of patient geometries has to be estimated from a small number of images and is therefore not exactly known. To quantify the total dose variance, we propose a method that is based on the principle of Bayesian inference. The method is of particular interest when organ motion is incorporated in inverse IMRT planning by means of inverse planning performed on a probability distribution of patient geometries. In order to make this a robust approach, it turns out that the dose variance should be considered (and minimized) in the optimization process. As an application of the presented concept of Bayesian inference, we compare three approaches to inverse planning based on probability distributions that account for an increasing degree of uncertainty. The Bayes theorem further provides a concept to interpolate between patient specific data and population-based knowledge on organ motion which is relevant since the number of CT images of a patient is typically small
Sraj, Ihab
2015-10-22
This paper addresses model dimensionality reduction for Bayesian inference based on prior Gaussian fields with uncertainty in the covariance function hyper-parameters. The dimensionality reduction is traditionally achieved using the Karhunen-Loève expansion of a prior Gaussian process assuming covariance function with fixed hyper-parameters, despite the fact that these are uncertain in nature. The posterior distribution of the Karhunen-Loève coordinates is then inferred using available observations. The resulting inferred field is therefore dependent on the assumed hyper-parameters. Here, we seek to efficiently estimate both the field and covariance hyper-parameters using Bayesian inference. To this end, a generalized Karhunen-Loève expansion is derived using a coordinate transformation to account for the dependence with respect to the covariance hyper-parameters. Polynomial Chaos expansions are employed for the acceleration of the Bayesian inference using similar coordinate transformations, enabling us to avoid expanding explicitly the solution dependence on the uncertain hyper-parameters. We demonstrate the feasibility of the proposed method on a transient diffusion equation by inferring spatially-varying log-diffusivity fields from noisy data. The inferred profiles were found closer to the true profiles when including the hyper-parameters’ uncertainty in the inference formulation.
Evidence cross-validation and Bayesian inference of MAST plasma equilibria
Nessi, G. T. von; Hole, M. J. [Research School of Physical Sciences and Engineering, Australian National University, Canberra ACT 0200 (Australia); Svensson, J. [Max-Planck-Institut fuer Plasmaphysik, D-17491 Greifswald (Germany); Appel, L. [EURATOM/CCFE Fusion Association, Culham Science Centre, Abingdon, Oxon OX14 3DB (United Kingdom)
2012-01-15
In this paper, current profiles for plasma discharges on the mega-ampere spherical tokamak are directly calculated from pickup coil, flux loop, and motional-Stark effect observations via methods based in the statistical theory of Bayesian analysis. By representing toroidal plasma current as a series of axisymmetric current beams with rectangular cross-section and inferring the current for each one of these beams, flux-surface geometry and q-profiles are subsequently calculated by elementary application of Biot-Savart's law. The use of this plasma model in the context of Bayesian analysis was pioneered by Svensson and Werner on the joint-European tokamak [Svensson and Werner,Plasma Phys. Controlled Fusion 50(8), 085002 (2008)]. In this framework, linear forward models are used to generate diagnostic predictions, and the probability distribution for the currents in the collection of plasma beams was subsequently calculated directly via application of Bayes' formula. In this work, we introduce a new diagnostic technique to identify and remove outlier observations associated with diagnostics falling out of calibration or suffering from an unidentified malfunction. These modifications enable a good agreement between Bayesian inference of the last-closed flux-surface with other corroborating data, such as that from force balance considerations using EFIT++[Appel et al., ''A unified approach to equilibrium reconstruction'' Proceedings of the 33rd EPS Conference on Plasma Physics (Rome, Italy, 2006)]. In addition, this analysis also yields errors on the plasma current profile and flux-surface geometry as well as directly predicting the Shafranov shift of the plasma core.
Evidence cross-validation and Bayesian inference of MAST plasma equilibria
Nessi, G. T. von; Hole, M. J.; Svensson, J.; Appel, L.
2012-01-01
In this paper, current profiles for plasma discharges on the mega-ampere spherical tokamak are directly calculated from pickup coil, flux loop, and motional-Stark effect observations via methods based in the statistical theory of Bayesian analysis. By representing toroidal plasma current as a series of axisymmetric current beams with rectangular cross-section and inferring the current for each one of these beams, flux-surface geometry and q-profiles are subsequently calculated by elementary application of Biot-Savart's law. The use of this plasma model in the context of Bayesian analysis was pioneered by Svensson and Werner on the joint-European tokamak [Svensson and Werner,Plasma Phys. Controlled Fusion 50(8), 085002 (2008)]. In this framework, linear forward models are used to generate diagnostic predictions, and the probability distribution for the currents in the collection of plasma beams was subsequently calculated directly via application of Bayes' formula. In this work, we introduce a new diagnostic technique to identify and remove outlier observations associated with diagnostics falling out of calibration or suffering from an unidentified malfunction. These modifications enable a good agreement between Bayesian inference of the last-closed flux-surface with other corroborating data, such as that from force balance considerations using EFIT++[Appel et al., ''A unified approach to equilibrium reconstruction'' Proceedings of the 33rd EPS Conference on Plasma Physics (Rome, Italy, 2006)]. In addition, this analysis also yields errors on the plasma current profile and flux-surface geometry as well as directly predicting the Shafranov shift of the plasma core.
Nakamura, Makoto
2009-01-01
It is important for Level 1 PSA to quantify input reliability parameters and their uncertainty. Bayesian methods for inference of system/component unavailability, however, are not well studied. At present practitioners allocate the uncertainty (i.e. error factor) of the unavailability based on engineering judgment. Systematic methods based on Bayesian statistics are needed for quantification of such uncertainty. In this study we have developed a new method for Bayesian inference of unavailability, where the posterior of system/component unavailability is described by the inverted gamma distribution. We show that the average of the posterior comes close to the point estimate of the unavailability as the number of outages goes to infinity. That indicates validity of the new method. Using plant data recorded in NUCIA, we have applied the new method to inference of system unavailability under unplanned outages due to violations of LCO at BWRs in Japan. According to the inference results, the unavailability is populated in the order of 10 -5 -10 -4 and the error factor is within 1-2. Thus, the new Bayesian method allows one to quantify magnitudes and widths (i.e. error factor) of uncertainty distributions of unavailability. (author)
A framework for Bayesian nonparametric inference for causal effects of mediation.
Kim, Chanmin; Daniels, Michael J; Marcus, Bess H; Roy, Jason A
2017-06-01
We propose a Bayesian non-parametric (BNP) framework for estimating causal effects of mediation, the natural direct, and indirect, effects. The strategy is to do this in two parts. Part 1 is a flexible model (using BNP) for the observed data distribution. Part 2 is a set of uncheckable assumptions with sensitivity parameters that in conjunction with Part 1 allows identification and estimation of the causal parameters and allows for uncertainty about these assumptions via priors on the sensitivity parameters. For Part 1, we specify a Dirichlet process mixture of multivariate normals as a prior on the joint distribution of the outcome, mediator, and covariates. This approach allows us to obtain a (simple) closed form of each marginal distribution. For Part 2, we consider two sets of assumptions: (a) the standard sequential ignorability (Imai et al., 2010) and (b) weakened set of the conditional independence type assumptions introduced in Daniels et al. (2012) and propose sensitivity analyses for both. We use this approach to assess mediation in a physical activity promotion trial. © 2016, The International Biometric Society.
Kim, Daesang; El Gharamti, Iman; Bisetti, Fabrizio; Farooq, Aamir; Knio, Omar
2016-01-01
A new Bayesian inference method has been developed and applied to Furan shock tube experimental data for efficient statistical inferences of the Arrhenius parameters of two OH radical consumption reactions. The collected experimental data, which
TYPE Ia SUPERNOVA LIGHT-CURVE INFERENCE: HIERARCHICAL BAYESIAN ANALYSIS IN THE NEAR-INFRARED
Mandel, Kaisey S.; Friedman, Andrew S.; Kirshner, Robert P.; Wood-Vasey, W. Michael
2009-01-01
We present a comprehensive statistical analysis of the properties of Type Ia supernova (SN Ia) light curves in the near-infrared using recent data from Peters Automated InfraRed Imaging TELescope and the literature. We construct a hierarchical Bayesian framework, incorporating several uncertainties including photometric error, peculiar velocities, dust extinction, and intrinsic variations, for principled and coherent statistical inference. SN Ia light-curve inferences are drawn from the global posterior probability of parameters describing both individual supernovae and the population conditioned on the entire SN Ia NIR data set. The logical structure of the hierarchical model is represented by a directed acyclic graph. Fully Bayesian analysis of the model and data is enabled by an efficient Markov Chain Monte Carlo algorithm exploiting the conditional probabilistic structure using Gibbs sampling. We apply this framework to the JHK s SN Ia light-curve data. A new light-curve model captures the observed J-band light-curve shape variations. The marginal intrinsic variances in peak absolute magnitudes are σ(M J ) = 0.17 ± 0.03, σ(M H ) = 0.11 ± 0.03, and σ(M Ks ) = 0.19 ± 0.04. We describe the first quantitative evidence for correlations between the NIR absolute magnitudes and J-band light-curve shapes, and demonstrate their utility for distance estimation. The average residual in the Hubble diagram for the training set SNe at cz > 2000kms -1 is 0.10 mag. The new application of bootstrap cross-validation to SN Ia light-curve inference tests the sensitivity of the statistical model fit to the finite sample and estimates the prediction error at 0.15 mag. These results demonstrate that SN Ia NIR light curves are as effective as corrected optical light curves, and, because they are less vulnerable to dust absorption, they have great potential as precise and accurate cosmological distance indicators.
Calibrated birth-death phylogenetic time-tree priors for bayesian inference.
Heled, Joseph; Drummond, Alexei J
2015-05-01
Here we introduce a general class of multiple calibration birth-death tree priors for use in Bayesian phylogenetic inference. All tree priors in this class separate ancestral node heights into a set of "calibrated nodes" and "uncalibrated nodes" such that the marginal distribution of the calibrated nodes is user-specified whereas the density ratio of the birth-death prior is retained for trees with equal values for the calibrated nodes. We describe two formulations, one in which the calibration information informs the prior on ranked tree topologies, through the (conditional) prior, and the other which factorizes the prior on divergence times and ranked topologies, thus allowing uniform, or any arbitrary prior distribution on ranked topologies. Although the first of these formulations has some attractive properties, the algorithm we present for computing its prior density is computationally intensive. However, the second formulation is always faster and computationally efficient for up to six calibrations. We demonstrate the utility of the new class of multiple-calibration tree priors using both small simulations and a real-world analysis and compare the results to existing schemes. The two new calibrated tree priors described in this article offer greater flexibility and control of prior specification in calibrated time-tree inference and divergence time dating, and will remove the need for indirect approaches to the assessment of the combined effect of calibration densities and tree priors in Bayesian phylogenetic inference. © The Author(s) 2014. Published by Oxford University Press, on behalf of the Society of Systematic Biologists.
Inference of reactive transport model parameters using a Bayesian multivariate approach
Carniato, Luca; Schoups, Gerrit; van de Giesen, Nick
2014-08-01
Parameter estimation of subsurface transport models from multispecies data requires the definition of an objective function that includes different types of measurements. Common approaches are weighted least squares (WLS), where weights are specified a priori for each measurement, and weighted least squares with weight estimation (WLS(we)) where weights are estimated from the data together with the parameters. In this study, we formulate the parameter estimation task as a multivariate Bayesian inference problem. The WLS and WLS(we) methods are special cases in this framework, corresponding to specific prior assumptions about the residual covariance matrix. The Bayesian perspective allows for generalizations to cases where residual correlation is important and for efficient inference by analytically integrating out the variances (weights) and selected covariances from the joint posterior. Specifically, the WLS and WLS(we) methods are compared to a multivariate (MV) approach that accounts for specific residual correlations without the need for explicit estimation of the error parameters. When applied to inference of reactive transport model parameters from column-scale data on dissolved species concentrations, the following results were obtained: (1) accounting for residual correlation between species provides more accurate parameter estimation for high residual correlation levels whereas its influence for predictive uncertainty is negligible, (2) integrating out the (co)variances leads to an efficient estimation of the full joint posterior with a reduced computational effort compared to the WLS(we) method, and (3) in the presence of model structural errors, none of the methods is able to identify the correct parameter values.
Image charges revisited: a closed form solution
Choy, T. C.
2000-01-01
We demonstrate that the corrections to the classical Kelvin image theory due to finite electron screening length )λ, recently discussed by Roulet and Saint Jean, Am. J. Phys. 68(4) 319, is amenable to an exact closed form solution in terms of an integral involving Bessel functions. An error arising from an incorrect choice of boundary conditions is rectified as well, enabling also a complete solution for all potentials - both inside and outside the metal surface
Le Maitre, Olivier
2015-01-07
We address model dimensionality reduction in the Bayesian inference of Gaussian fields, considering prior covariance function with unknown hyper-parameters. The Karhunen-Loeve (KL) expansion of a prior Gaussian process is traditionally derived assuming fixed covariance function with pre-assigned hyperparameter values. Thus, the modes strengths of the Karhunen-Loeve expansion inferred using available observations, as well as the resulting inferred process, dependent on the pre-assigned values for the covariance hyper-parameters. Here, we seek to infer the process and its the covariance hyper-parameters in a single Bayesian inference. To this end, the uncertainty in the hyper-parameters is treated by means of a coordinate transformation, leading to a KL-type expansion on a fixed reference basis of spatial modes, but with random coordinates conditioned on the hyper-parameters. A Polynomial Chaos (PC) expansion of the model prediction is also introduced to accelerate the Bayesian inference and the sampling of the posterior distribution with MCMC method. The PC expansion of the model prediction also rely on a coordinates transformation, enabling us to avoid expanding the dependence of the prediction with respect to the covariance hyper-parameters. We demonstrate the efficiency of the proposed method on a transient diffusion equation by inferring spatially-varying log-diffusivity fields from noisy data.
Albert, Carlo; Ulzega, Simone; Stoop, Ruedi
2016-04-01
Parameter inference is a fundamental problem in data-driven modeling. Given observed data that is believed to be a realization of some parameterized model, the aim is to find parameter values that are able to explain the observed data. In many situations, the dominant sources of uncertainty must be included into the model for making reliable predictions. This naturally leads to stochastic models. Stochastic models render parameter inference much harder, as the aim then is to find a distribution of likely parameter values. In Bayesian statistics, which is a consistent framework for data-driven learning, this so-called posterior distribution can be used to make probabilistic predictions. We propose a novel, exact, and very efficient approach for generating posterior parameter distributions for stochastic differential equation models calibrated to measured time series. The algorithm is inspired by reinterpreting the posterior distribution as a statistical mechanics partition function of an object akin to a polymer, where the measurements are mapped on heavier beads compared to those of the simulated data. To arrive at distribution samples, we employ a Hamiltonian Monte Carlo approach combined with a multiple time-scale integration. A separation of time scales naturally arises if either the number of measurement points or the number of simulation points becomes large. Furthermore, at least for one-dimensional problems, we can decouple the harmonic modes between measurement points and solve the fastest part of their dynamics analytically. Our approach is applicable to a wide range of inference problems and is highly parallelizable.
Nonparametric Bayesian inference for mean residual life functions in survival analysis.
Poynor, Valerie; Kottas, Athanasios
2018-01-19
Modeling and inference for survival analysis problems typically revolves around different functions related to the survival distribution. Here, we focus on the mean residual life (MRL) function, which provides the expected remaining lifetime given that a subject has survived (i.e. is event-free) up to a particular time. This function is of direct interest in reliability, medical, and actuarial fields. In addition to its practical interpretation, the MRL function characterizes the survival distribution. We develop general Bayesian nonparametric inference for MRL functions built from a Dirichlet process mixture model for the associated survival distribution. The resulting model for the MRL function admits a representation as a mixture of the kernel MRL functions with time-dependent mixture weights. This model structure allows for a wide range of shapes for the MRL function. Particular emphasis is placed on the selection of the mixture kernel, taken to be a gamma distribution, to obtain desirable properties for the MRL function arising from the mixture model. The inference method is illustrated with a data set of two experimental groups and a data set involving right censoring. The supplementary material available at Biostatistics online provides further results on empirical performance of the model, using simulated data examples. © The Author 2018. Published by Oxford University Press. All rights reserved. For permissions, please e-mail: journals.permissions@oup.com.
Extreme-Scale Bayesian Inference for Uncertainty Quantification of Complex Simulations
Biros, George [Univ. of Texas, Austin, TX (United States)
2018-01-12
Uncertainty quantification (UQ)—that is, quantifying uncertainties in complex mathematical models and their large-scale computational implementations—is widely viewed as one of the outstanding challenges facing the field of CS&E over the coming decade. The EUREKA project set to address the most difficult class of UQ problems: those for which both the underlying PDE model as well as the uncertain parameters are of extreme scale. In the project we worked on these extreme-scale challenges in the following four areas: 1. Scalable parallel algorithms for sampling and characterizing the posterior distribution that exploit the structure of the underlying PDEs and parameter-to-observable map. These include structure-exploiting versions of the randomized maximum likelihood method, which aims to overcome the intractability of employing conventional MCMC methods for solving extreme-scale Bayesian inversion problems by appealing to and adapting ideas from large-scale PDE-constrained optimization, which have been very successful at exploring high-dimensional spaces. 2. Scalable parallel algorithms for construction of prior and likelihood functions based on learning methods and non-parametric density estimation. Constructing problem-specific priors remains a critical challenge in Bayesian inference, and more so in high dimensions. Another challenge is construction of likelihood functions that capture unmodeled couplings between observations and parameters. We will create parallel algorithms for non-parametric density estimation using high dimensional N-body methods and combine them with supervised learning techniques for the construction of priors and likelihood functions. 3. Bayesian inadequacy models, which augment physics models with stochastic models that represent their imperfections. The success of the Bayesian inference framework depends on the ability to represent the uncertainty due to imperfections of the mathematical model of the phenomena of interest. This is a
A Bayesian method for inferring transmission chains in a partially observed epidemic.
Marzouk, Youssef M.; Ray, Jaideep
2008-10-01
We present a Bayesian approach for estimating transmission chains and rates in the Abakaliki smallpox epidemic of 1967. The epidemic affected 30 individuals in a community of 74; only the dates of appearance of symptoms were recorded. Our model assumes stochastic transmission of the infections over a social network. Distinct binomial random graphs model intra- and inter-compound social connections, while disease transmission over each link is treated as a Poisson process. Link probabilities and rate parameters are objects of inference. Dates of infection and recovery comprise the remaining unknowns. Distributions for smallpox incubation and recovery periods are obtained from historical data. Using Markov chain Monte Carlo, we explore the joint posterior distribution of the scalar parameters and provide an expected connectivity pattern for the social graph and infection pathway.
Mohammad-Djafari, Ali
2015-01-01
The main object of this tutorial article is first to review the main inference tools using Bayesian approach, Entropy, Information theory and their corresponding geometries. This review is focused mainly on the ways these tools have been used in data, signal and image processing. After a short introduction of the different quantities related to the Bayes rule, the entropy and the Maximum Entropy Principle (MEP), relative entropy and the Kullback-Leibler divergence, Fisher information, we will study their use in different fields of data and signal processing such as: entropy in source separation, Fisher information in model order selection, different Maximum Entropy based methods in time series spectral estimation and finally, general linear inverse problems.
Mocapy++ - A toolkit for inference and learning in dynamic Bayesian networks
Hamelryck Thomas
2010-03-01
Full Text Available Abstract Background Mocapy++ is a toolkit for parameter learning and inference in dynamic Bayesian networks (DBNs. It supports a wide range of DBN architectures and probability distributions, including distributions from directional statistics (the statistics of angles, directions and orientations. Results The program package is freely available under the GNU General Public Licence (GPL from SourceForge http://sourceforge.net/projects/mocapy. The package contains the source for building the Mocapy++ library, several usage examples and the user manual. Conclusions Mocapy++ is especially suitable for constructing probabilistic models of biomolecular structure, due to its support for directional statistics. In particular, it supports the Kent distribution on the sphere and the bivariate von Mises distribution on the torus. These distributions have proven useful to formulate probabilistic models of protein and RNA structure in atomic detail.
BayesTwin: An R Package for Bayesian Inference of Item-Level Twin Data
Inga Schwabe
2017-11-01
Full Text Available BayesTwin is an open-source R package that serves as a pipeline to the MCMC program JAGS to perform Bayesian inference on genetically-informative hierarchical twin data. Simultaneously to the biometric model, an item response theory (IRT measurement model is estimated, allowing analysis of the raw phenotypic (item-level data. The integration of such a measurement model is important since earlier research has shown that an analysis based on an aggregated measure (e.g., a sum-score based analysis can lead to an underestimation of heritability and the spurious finding of genotype-environment interactions. The package includes all common biometric and IRT models as well as functions that help plot relevant information or determine whether the analysis was performed well. Funding statement: Partly funded by the PROO grant 411-12-623 from the Netherlands Organisation for Scientific Research (NWO.
Chakraborty, Shubhankar; Das, Prasanta Kr., E-mail: pkd@mech.iitkgp.ernet.in [Department of Mechanical Engineering, Indian Institute of Technology Kharagpur, Kharagpur 721302 (India); Roy Chaudhuri, Partha [Department of Physics, Indian Institute of Technology Kharagpur, Kharagpur 721302 (India)
2016-07-15
In this communication, a novel optical technique has been proposed for the reconstruction of the shape of a Taylor bubble using measurements from multiple arrays of optical sensors. The deviation of an optical beam passing through the bubble depends on the contour of bubble surface. A theoretical model of the deviation of a beam during the traverse of a Taylor bubble through it has been developed. Using this model and the time history of the deviation captured by the sensor array, the bubble shape has been reconstructed. The reconstruction has been performed using an inverse algorithm based on Bayesian inference technique and Markov chain Monte Carlo sampling algorithm. The reconstructed nose shape has been compared with the true shape, extracted through image processing of high speed images. Finally, an error analysis has been performed to pinpoint the sources of the errors.
Multi-Objective data analysis using Bayesian Inference for MagLIF experiments
Knapp, Patrick; Glinksy, Michael; Evans, Matthew; Gom, Matth; Han, Stephanie; Harding, Eric; Slutz, Steve; Hahn, Kelly; Harvey-Thompson, Adam; Geissel, Matthias; Ampleford, David; Jennings, Christopher; Schmit, Paul; Smith, Ian; Schwarz, Jens; Peterson, Kyle; Jones, Brent; Rochau, Gregory; Sinars, Daniel
2017-10-01
The MagLIF concept has recently demonstrated Gbar pressures and confinement of charged fusion products at stagnation. We present a new analysis methodology that allows for integration of multiple diagnostics including nuclear, x-ray imaging, and x-ray power to determine the temperature, pressure, liner areal density, and mix fraction. A simplified hot-spot model is used with a Bayesian inference network to determine the most probable model parameters that describe the observations while simultaneously revealing the principal uncertainties in the analysis. Sandia National Laboratories is a multimission laboratory managed and operated by National Technology and Engineering Solutions of Sandia, LLC., a wholly owned subsidiary of Honeywell International, Inc., for the U.S. Department of Energy's National Nuclear Security Administration under contract DE-NA-0003525.
A combined evidence Bayesian method for human ancestry inference applied to Afro-Colombians.
Rishishwar, Lavanya; Conley, Andrew B; Vidakovic, Brani; Jordan, I King
2015-12-15
Uniparental genetic markers, mitochondrial DNA (mtDNA) and Y chromosomal DNA, are widely used for the inference of human ancestry. However, the resolution of ancestral origins based on mtDNA haplotypes is limited by the fact that such haplotypes are often found to be distributed across wide geographical regions. We have addressed this issue here by combining two sources of ancestry information that have typically been considered separately: historical records regarding population origins and genetic information on mtDNA haplotypes. To combine these distinct data sources, we applied a Bayesian approach that considers historical records, in the form of prior probabilities, together with data on the geographical distribution of mtDNA haplotypes, formulated as likelihoods, to yield ancestry assignments from posterior probabilities. This combined evidence Bayesian approach to ancestry assignment was evaluated for its ability to accurately assign sub-continental African ancestral origins to Afro-Colombians based on their mtDNA haplotypes. We demonstrate that the incorporation of historical prior probabilities via this analytical framework can provide for substantially increased resolution in sub-continental African ancestry assignment for members of this population. In addition, a personalized approach to ancestry assignment that involves the tuning of priors to individual mtDNA haplotypes yields even greater resolution for individual ancestry assignment. Despite the fact that Colombia has a large population of Afro-descendants, the ancestry of this community has been understudied relative to populations with primarily European and Native American ancestry. Thus, the application of the kind of combined evidence approach developed here to the study of ancestry in the Afro-Colombian population has the potential to be impactful. The formal Bayesian analytical framework we propose for combining historical and genetic information also has the potential to be widely applied
Khan, Haseeb A; Arif, Ibrahim A; Bahkali, Ali H; Al Farhan, Ahmad H; Al Homaidan, Ali A
2008-10-06
This investigation was aimed to compare the inference of antelope phylogenies resulting from the 16S rRNA, cytochrome-b (cyt-b) and d-loop segments of mitochondrial DNA using three different computational models including Bayesian (BA), maximum parsimony (MP) and unweighted pair group method with arithmetic mean (UPGMA). The respective nucleotide sequences of three Oryx species (Oryx leucoryx, Oryx dammah and Oryx gazella) and an out-group (Addax nasomaculatus) were aligned and subjected to BA, MP and UPGMA models for comparing the topologies of respective phylogenetic trees. The 16S rRNA region possessed the highest frequency of conserved sequences (97.65%) followed by cyt-b (94.22%) and d-loop (87.29%). There were few transitions (2.35%) and none transversions in 16S rRNA as compared to cyt-b (5.61% transitions and 0.17% transversions) and d-loop (11.57% transitions and 1.14% transversions) while comparing the four taxa. All the three mitochondrial segments clearly differentiated the genus Addax from Oryx using the BA or UPGMA models. The topologies of all the gamma-corrected Bayesian trees were identical irrespective of the marker type. The UPGMA trees resulting from 16S rRNA and d-loop sequences were also identical (Oryx dammah grouped with Oryx leucoryx) to Bayesian trees except that the UPGMA tree based on cyt-b showed a slightly different phylogeny (Oryx dammah grouped with Oryx gazella) with a low bootstrap support. However, the MP model failed to differentiate the genus Addax from Oryx. These findings demonstrate the efficiency and robustness of BA and UPGMA methods for phylogenetic analysis of antelopes using mitochondrial markers.
Using Approximate Bayesian Computation to infer sex ratios from acoustic data.
Lehnen, Lisa; Schorcht, Wigbert; Karst, Inken; Biedermann, Martin; Kerth, Gerald; Puechmaille, Sebastien J
2018-01-01
Population sex ratios are of high ecological relevance, but are challenging to determine in species lacking conspicuous external cues indicating their sex. Acoustic sexing is an option if vocalizations differ between sexes, but is precluded by overlapping distributions of the values of male and female vocalizations in many species. A method allowing the inference of sex ratios despite such an overlap will therefore greatly increase the information extractable from acoustic data. To meet this demand, we developed a novel approach using Approximate Bayesian Computation (ABC) to infer the sex ratio of populations from acoustic data. Additionally, parameters characterizing the male and female distribution of acoustic values (mean and standard deviation) are inferred. This information is then used to probabilistically assign a sex to a single acoustic signal. We furthermore develop a simpler means of sex ratio estimation based on the exclusion of calls from the overlap zone. Applying our methods to simulated data demonstrates that sex ratio and acoustic parameter characteristics of males and females are reliably inferred by the ABC approach. Applying both the ABC and the exclusion method to empirical datasets (echolocation calls recorded in colonies of lesser horseshoe bats, Rhinolophus hipposideros) provides similar sex ratios as molecular sexing. Our methods aim to facilitate evidence-based conservation, and to benefit scientists investigating ecological or conservation questions related to sex- or group specific behaviour across a wide range of organisms emitting acoustic signals. The developed methodology is non-invasive, low-cost and time-efficient, thus allowing the study of many sites and individuals. We provide an R-script for the easy application of the method and discuss potential future extensions and fields of applications. The script can be easily adapted to account for numerous biological systems by adjusting the type and number of groups to be
Bayesian electron density inference from JET lithium beam emission spectra using Gaussian processes
Kwak, Sehyun; Svensson, J.; Brix, M.; Ghim, Y.-C.; Contributors, JET
2017-03-01
A Bayesian model to infer edge electron density profiles is developed for the JET lithium beam emission spectroscopy (Li-BES) system, measuring Li I (2p-2s) line radiation using 26 channels with ∼1 cm spatial resolution and 10∼ 20 ms temporal resolution. The density profile is modelled using a Gaussian process prior, and the uncertainty of the density profile is calculated by a Markov Chain Monte Carlo (MCMC) scheme. From the spectra measured by the transmission grating spectrometer, the Li I line intensities are extracted, and modelled as a function of the plasma density by a multi-state model which describes the relevant processes between neutral lithium beam atoms and plasma particles. The spectral model fully takes into account interference filter and instrument effects, that are separately estimated, again using Gaussian processes. The line intensities are inferred based on a spectral model consistent with the measured spectra within their uncertainties, which includes photon statistics and electronic noise. Our newly developed method to infer JET edge electron density profiles has the following advantages in comparison to the conventional method: (i) providing full posterior distributions of edge density profiles, including their associated uncertainties, (ii) the available radial range for density profiles is increased to the full observation range (∼26 cm), (iii) an assumption of monotonic electron density profile is not necessary, (iv) the absolute calibration factor of the diagnostic system is automatically estimated overcoming the limitation of the conventional technique and allowing us to infer the electron density profiles for all pulses without preprocessing the data or an additional boundary condition, and (v) since the full spectrum is modelled, the procedure of modulating the beam to measure the background signal is only necessary for the case of overlapping of the Li I line with impurity lines.
Yu, Bin; Xu, Jia-Meng; Li, Shan; Chen, Cheng; Chen, Rui-Xin; Wang, Lei; Zhang, Yan; Wang, Ming-Hui
2017-10-06
Gene regulatory networks (GRNs) research reveals complex life phenomena from the perspective of gene interaction, which is an important research field in systems biology. Traditional Bayesian networks have a high computational complexity, and the network structure scoring model has a single feature. Information-based approaches cannot identify the direction of regulation. In order to make up for the shortcomings of the above methods, this paper presents a novel hybrid learning method (DBNCS) based on dynamic Bayesian network (DBN) to construct the multiple time-delayed GRNs for the first time, combining the comprehensive score (CS) with the DBN model. DBNCS algorithm first uses CMI2NI (conditional mutual inclusive information-based network inference) algorithm for network structure profiles learning, namely the construction of search space. Then the redundant regulations are removed by using the recursive optimization algorithm (RO), thereby reduce the false positive rate. Secondly, the network structure profiles are decomposed into a set of cliques without loss, which can significantly reduce the computational complexity. Finally, DBN model is used to identify the direction of gene regulation within the cliques and search for the optimal network structure. The performance of DBNCS algorithm is evaluated by the benchmark GRN datasets from DREAM challenge as well as the SOS DNA repair network in Escherichia coli , and compared with other state-of-the-art methods. The experimental results show the rationality of the algorithm design and the outstanding performance of the GRNs.
Bayesian inference for the distribution of grams of marijuana in a joint.
Ridgeway, Greg; Kilmer, Beau
2016-08-01
The average amount of marijuana in a joint is unknown, yet this figure is a critical quantity for creating credible measures of marijuana consumption. It is essential for projecting tax revenues post-legalization, estimating the size of illicit marijuana markets, and learning about how much marijuana users are consuming in order to understand health and behavioral consequences. Arrestee Drug Abuse Monitoring data collected between 2000 and 2010 contain relevant information on 10,628 marijuana transactions, joints and loose marijuana purchases, including the city in which the purchase occurred and the price paid for the marijuana. Using the Brown-Silverman drug pricing model to link marijuana price and weight, we are able to infer the distribution of grams of marijuana in a joint and provide a Bayesian posterior distribution for the mean weight of marijuana in a joint. We estimate that the mean weight of marijuana in a joint is 0.32g (95% Bayesian posterior interval: 0.30-0.35). Our estimate of the mean weight of marijuana in a joint is lower than figures commonly used to make estimates of marijuana consumption. These estimates can be incorporated into drug policy discussions to produce better understanding about illicit marijuana markets, the size of potential legalized marijuana markets, and health and behavior outcomes. Copyright © 2016 Elsevier Ireland Ltd. All rights reserved.
Walter, G.
2015-01-01
In the Bayesian approach to statistical inference, possibly subjective knowledge on model parameters can be expressed by so-called prior distributions. A prior distribution is updated, via Bayes’ Rule, to the so-called posterior distribution, which combines prior information and information from
Bayesian inference for heterogeneous caprock permeability based on above zone pressure monitoring
Namhata, Argha; Small, Mitchell J.; Dilmore, Robert M.; Nakles, David V.; King, Seth
2017-02-01
The presence of faults/ fractures or highly permeable zones in the primary sealing caprock of a CO2 storage reservoir can result in leakage of CO2. Monitoring of leakage requires the capability to detect and resolve the onset, location, and volume of leakage in a systematic and timely manner. Pressure-based monitoring possesses such capabilities. This study demonstrates a basis for monitoring network design based on the characterization of CO2 leakage scenarios through an assessment of the integrity and permeability of the caprock inferred from above zone pressure measurements. Four representative heterogeneous fractured seal types are characterized to demonstrate seal permeability ranging from highly permeable to impermeable. Based on Bayesian classification theory, the probability of each fractured caprock scenario given above zone pressure measurements with measurement error is inferred. The sensitivity to injection rate and caprock thickness is also evaluated and the probability of proper classification is calculated. The time required to distinguish between above zone pressure outcomes and the associated leakage scenarios is also computed.
Louzoun, Yoram; Alter, Idan; Gragert, Loren; Albrecht, Mark; Maiers, Martin
2018-05-01
Regardless of sampling depth, accurate genotype imputation is limited in regions of high polymorphism which often have a heavy-tailed haplotype frequency distribution. Many rare haplotypes are thus unobserved. Statistical methods to improve imputation by extending reference haplotype distributions using linkage disequilibrium patterns that relate allele and haplotype frequencies have not yet been explored. In the field of unrelated stem cell transplantation, imputation of highly polymorphic human leukocyte antigen (HLA) genes has an important application in identifying the best-matched stem cell donor when searching large registries totaling over 28,000,000 donors worldwide. Despite these large registry sizes, a significant proportion of searched patients present novel HLA haplotypes. Supporting this observation, HLA population genetic models have indicated that many extant HLA haplotypes remain unobserved. The absent haplotypes are a significant cause of error in haplotype matching. We have applied a Bayesian inference methodology for extending haplotype frequency distributions, using a model where new haplotypes are created by recombination of observed alleles. Applications of this joint probability model offer significant improvement in frequency distribution estimates over the best existing alternative methods, as we illustrate using five-locus HLA frequency data from the National Marrow Donor Program registry. Transplant matching algorithms and disease association studies involving phasing and imputation of rare variants may benefit from this statistical inference framework.
Bayesian nonparametric generative models for causal inference with missing at random covariates.
Roy, Jason; Lum, Kirsten J; Zeldow, Bret; Dworkin, Jordan D; Re, Vincent Lo; Daniels, Michael J
2018-03-26
We propose a general Bayesian nonparametric (BNP) approach to causal inference in the point treatment setting. The joint distribution of the observed data (outcome, treatment, and confounders) is modeled using an enriched Dirichlet process. The combination of the observed data model and causal assumptions allows us to identify any type of causal effect-differences, ratios, or quantile effects, either marginally or for subpopulations of interest. The proposed BNP model is well-suited for causal inference problems, as it does not require parametric assumptions about the distribution of confounders and naturally leads to a computationally efficient Gibbs sampling algorithm. By flexibly modeling the joint distribution, we are also able to impute (via data augmentation) values for missing covariates within the algorithm under an assumption of ignorable missingness, obviating the need to create separate imputed data sets. This approach for imputing the missing covariates has the additional advantage of guaranteeing congeniality between the imputation model and the analysis model, and because we use a BNP approach, parametric models are avoided for imputation. The performance of the method is assessed using simulation studies. The method is applied to data from a cohort study of human immunodeficiency virus/hepatitis C virus co-infected patients. © 2018, The International Biometric Society.
Optimal Mortgage Refinancing: A Closed Form Solution.
Agarwal, Sumit; Driscoll, John C; Laibson, David I
2013-06-01
We derive the first closed-form optimal refinancing rule: Refinance when the current mortgage interest rate falls below the original rate by at least [Formula: see text] In this formula W (.) is the Lambert W -function, [Formula: see text] ρ is the real discount rate, λ is the expected real rate of exogenous mortgage repayment, σ is the standard deviation of the mortgage rate, κ/M is the ratio of the tax-adjusted refinancing cost and the remaining mortgage value, and τ is the marginal tax rate. This expression is derived by solving a tractable class of refinancing problems. Our quantitative results closely match those reported by researchers using numerical methods.
Optimal Mortgage Refinancing: A Closed Form Solution
Agarwal, Sumit; Driscoll, John C.; Laibson, David I.
2013-01-01
We derive the first closed-form optimal refinancing rule: Refinance when the current mortgage interest rate falls below the original rate by at least 1ψ[ϕ+W(−exp(−ϕ))]. In this formula W(.) is the Lambert W-function, ψ=2(ρ+λ)σ,ϕ=1+ψ(ρ+λ)κ∕M(1−τ), ρ is the real discount rate, λ is the expected real rate of exogenous mortgage repayment, σ is the standard deviation of the mortgage rate, κ/M is the ratio of the tax-adjusted refinancing cost and the remaining mortgage value, and τ is the marginal tax rate. This expression is derived by solving a tractable class of refinancing problems. Our quantitative results closely match those reported by researchers using numerical methods. PMID:25843977
Izquierdo, K.; Lekic, V.; Montesi, L.
2017-12-01
Gravity inversions are especially important for planetary applications since measurements of the variations in gravitational acceleration are often the only constraint available to map out lateral density variations in the interiors of planets and other Solar system objects. Currently, global gravity data is available for the terrestrial planets and the Moon. Although several methods for inverting these data have been developed and applied, the non-uniqueness of global density models that fit the data has not yet been fully characterized. We make use of Bayesian inference and a Reversible Jump Markov Chain Monte Carlo (RJMCMC) approach to develop a Trans-dimensional Hierarchical Bayesian (THB) inversion algorithm that yields a large sample of models that fit a gravity field. From this group of models, we can determine the most likely value of parameters of a global density model and a measure of the non-uniqueness of each parameter when the number of anomalies describing the gravity field is not fixed a priori. We explore the use of a parallel tempering algorithm and fast multipole method to reduce the number of iterations and computing time needed. We applied this method to a synthetic gravity field of the Moon and a long wavelength synthetic model of density anomalies in the Earth's lower mantle. We obtained a good match between the given gravity field and the gravity field produced by the most likely model in each inversion. The number of anomalies of the models showed parsimony of the algorithm, the value of the noise variance of the input data was retrieved, and the non-uniqueness of the models was quantified. Our results show that the ability to constrain the latitude and longitude of density anomalies, which is excellent at shallow locations (information about the overall density distribution of celestial bodies even when there is no other geophysical data available.
The R Package MitISEM: Efficient and Robust Simulation Procedures for Bayesian Inference
Nalan Baştürk
2017-07-01
Full Text Available This paper presents the R package MitISEM (mixture of t by importance sampling weighted expectation maximization which provides an automatic and flexible two-stage method to approximate a non-elliptical target density kernel - typically a posterior density kernel - using an adaptive mixture of Student t densities as approximating density. In the first stage a mixture of Student t densities is fitted to the target using an expectation maximization algorithm where each step of the optimization procedure is weighted using importance sampling. In the second stage this mixture density is a candidate density for efficient and robust application of importance sampling or the Metropolis-Hastings (MH method to estimate properties of the target distribution. The package enables Bayesian inference and prediction on model parameters and probabilities, in particular, for models where densities have multi-modal or other non-elliptical shapes like curved ridges. These shapes occur in research topics in several scientific fields. For instance, analysis of DNA data in bio-informatics, obtaining loans in the banking sector by heterogeneous groups in financial economics and analysis of education's effect on earned income in labor economics. The package MitISEM provides also an extended algorithm, 'sequential MitISEM', which substantially decreases computation time when the target density has to be approximated for increasing data samples. This occurs when the posterior or predictive density is updated with new observations and/or when one computes model probabilities using predictive likelihoods. We illustrate the MitISEM algorithm using three canonical statistical and econometric models that are characterized by several types of non-elliptical posterior shapes and that describe well-known data patterns in econometrics and finance. We show that MH using the candidate density obtained by MitISEM outperforms, in terms of numerical efficiency, MH using a simpler
qPR: An adaptive partial-report procedure based on Bayesian inference.
Baek, Jongsoo; Lesmes, Luis Andres; Lu, Zhong-Lin
2016-08-01
Iconic memory is best assessed with the partial report procedure in which an array of letters appears briefly on the screen and a poststimulus cue directs the observer to report the identity of the cued letter(s). Typically, 6-8 cue delays or 600-800 trials are tested to measure the iconic memory decay function. Here we develop a quick partial report, or qPR, procedure based on a Bayesian adaptive framework to estimate the iconic memory decay function with much reduced testing time. The iconic memory decay function is characterized by an exponential function and a joint probability distribution of its three parameters. Starting with a prior of the parameters, the method selects the stimulus to maximize the expected information gain in the next test trial. It then updates the posterior probability distribution of the parameters based on the observer's response using Bayesian inference. The procedure is reiterated until either the total number of trials or the precision of the parameter estimates reaches a certain criterion. Simulation studies showed that only 100 trials were necessary to reach an average absolute bias of 0.026 and a precision of 0.070 (both in terms of probability correct). A psychophysical validation experiment showed that estimates of the iconic memory decay function obtained with 100 qPR trials exhibited good precision (the half width of the 68.2% credible interval = 0.055) and excellent agreement with those obtained with 1,600 trials of the conventional method of constant stimuli procedure (RMSE = 0.063). Quick partial-report relieves the data collection burden in characterizing iconic memory and makes it possible to assess iconic memory in clinical populations.
Radial anisotropy of Northeast Asia inferred from Bayesian inversions of ambient noise data
Lee, S. J.; Kim, S.; Rhie, J.
2017-12-01
The eastern margin of the Eurasia plate exhibits complex tectonic settings due to interactions with the subducting Pacific and Philippine Sea plates and the colliding India plate. Distributed extensional basins and intraplate volcanoes, and their heterogeneous features in the region are not easily explained with a simple mechanism. Observations of radial anisotropy in the entire lithosphere and the part of the asthenosphere provide the most effective evidence for the deformation of the lithosphere and the associated variation of the lithosphere-asthenosphere boundary (LAB). To infer anisotropic structures of crustal and upper-mantle in this region, radial anisotropy is measured using ambient noise data. In a continuation of previous Rayleigh wave tomography study in Northeast Asia, we conduct Love wave tomography to determine radial anisotropy using the Bayesian inversion techniques. Continuous seismic noise recordings of 237 broad-band seismic stations are used and more than 55,000 group and phase velocities of fundamental mode are measured for periods of 5-60 s. Total 8 different types of dispersion maps of Love wave from this study (period 10-60 s), Rayleigh wave from previous tomographic study (Kim et al., 2016; period 8-70 s) and longer period data (period 70-200 s) from a global model (Ekstrom, 2011) are jointly inverted using a hierarchical and transdimensional Bayesian technique. For each grid-node, boundary depths, velocities and anisotropy parameters of layers are sampled simultaneously on the assumption of the layered half-space model. The constructed 3-D radial anisotropy model provides much more details about the crust and upper mantle anisotropic structures, and about the complex undulation of the LAB.
Thomas, D.L.; Johnson, D.; Griffith, B.
2006-01-01
Bayesian hierarchical discrete-choice model for resource selection can provide managers with 2 components of population-level inference: average population selection and variability of selection. Both components are necessary to make sound management decisions based on animal selection.
Comments on "A closed-form solution to Tensor voting: theory and applications"
Maggiori, Emmanuel; Lotito, Pablo Andres; Manterola, Hugo Luis; del Fresno, Mariana
2017-01-01
We comment on a paper that describes a closed-form formulation to Tensor Voting, a technique to perceptually group clouds of points, usually applied to infer features in images. The authors proved an analytic solution to the technique, a highly relevant contribution considering that the original formulation required numerical integration, a time-consuming task. Their work constitutes the first closed-form expression for the Tensor Voting framework. In this work we first observe that the propo...
How does aging affect recognition-based inference? A hierarchical Bayesian modeling approach.
Horn, Sebastian S; Pachur, Thorsten; Mata, Rui
2015-01-01
The recognition heuristic (RH) is a simple strategy for probabilistic inference according to which recognized objects are judged to score higher on a criterion than unrecognized objects. In this article, a hierarchical Bayesian extension of the multinomial r-model is applied to measure use of the RH on the individual participant level and to re-evaluate differences between younger and older adults' strategy reliance across environments. Further, it is explored how individual r-model parameters relate to alternative measures of the use of recognition and other knowledge, such as adherence rates and indices from signal-detection theory (SDT). Both younger and older adults used the RH substantially more often in an environment with high than low recognition validity, reflecting adaptivity in strategy use across environments. In extension of previous analyses (based on adherence rates), hierarchical modeling revealed that in an environment with low recognition validity, (a) older adults had a stronger tendency than younger adults to rely on the RH and (b) variability in RH use between individuals was larger than in an environment with high recognition validity; variability did not differ between age groups. Further, the r-model parameters correlated moderately with an SDT measure expressing how well people can discriminate cases where the RH leads to a correct vs. incorrect inference; this suggests that the r-model and the SDT measures may offer complementary insights into the use of recognition in decision making. In conclusion, younger and older adults are largely adaptive in their application of the RH, but cognitive aging may be associated with an increased tendency to rely on this strategy. Copyright © 2014 Elsevier B.V. All rights reserved.
Aeschbacher, S; Futschik, A; Beaumont, M A
2013-02-01
We propose a two-step procedure for estimating multiple migration rates in an approximate Bayesian computation (ABC) framework, accounting for global nuisance parameters. The approach is not limited to migration, but generally of interest for inference problems with multiple parameters and a modular structure (e.g. independent sets of demes or loci). We condition on a known, but complex demographic model of a spatially subdivided population, motivated by the reintroduction of Alpine ibex (Capra ibex) into Switzerland. In the first step, the global parameters ancestral mutation rate and male mating skew have been estimated for the whole population in Aeschbacher et al. (Genetics 2012; 192: 1027). In the second step, we estimate in this study the migration rates independently for clusters of demes putatively connected by migration. For large clusters (many migration rates), ABC faces the problem of too many summary statistics. We therefore assess by simulation if estimation per pair of demes is a valid alternative. We find that the trade-off between reduced dimensionality for the pairwise estimation on the one hand and lower accuracy due to the assumption of pairwise independence on the other depends on the number of migration rates to be inferred: the accuracy of the pairwise approach increases with the number of parameters, relative to the joint estimation approach. To distinguish between low and zero migration, we perform ABC-type model comparison between a model with migration and one without. Applying the approach to microsatellite data from Alpine ibex, we find no evidence for substantial gene flow via migration, except for one pair of demes in one direction. © 2013 Blackwell Publishing Ltd.
Elsheikh, Ahmed H.; Hoteit, Ibrahim; Wheeler, Mary Fanett
2014-01-01
An efficient Bayesian calibration method based on the nested sampling (NS) algorithm and non-intrusive polynomial chaos method is presented. Nested sampling is a Bayesian sampling algorithm that builds a discrete representation of the posterior
Barham, Barbara J.; Barham, Peter J.; Campbell, Kate J.; Crawford, Robert J. M.; Grigg, Jennifer; Horswill, Cat; Morris, Taryn L.; Pichegru, Lorien; Steinfurth, Antje; Weller, Florian; Winker, Henning
2018-01-01
Global forage-fish landings are increasing, with potentially grave consequences for marine ecosystems. Predators of forage fish may be influenced by this harvest, but the nature of these effects is contentious. Experimental fishery manipulations offer the best solution to quantify population-level impacts, but are rare. We used Bayesian inference to examine changes in chick survival, body condition and population growth rate of endangered African penguins Spheniscus demersus in response to 8 years of alternating time–area closures around two pairs of colonies. Our results demonstrate that fishing closures improved chick survival and condition, after controlling for changing prey availability. However, this effect was inconsistent across sites and years, highlighting the difficultly of assessing management interventions in marine ecosystems. Nevertheless, modelled increases in population growth rates exceeded 1% at one colony; i.e. the threshold considered biologically meaningful by fisheries management in South Africa. Fishing closures evidently can improve the population trend of a forage-fish-dependent predator—we therefore recommend they continue in South Africa and support their application elsewhere. However, detecting demographic gains for mobile marine predators from small no-take zones requires experimental time frames and scales that will often exceed those desired by decision makers. PMID:29343602
A dynamic discretization method for reliability inference in Dynamic Bayesian Networks
Zhu, Jiandao; Collette, Matthew
2015-01-01
The material and modeling parameters that drive structural reliability analysis for marine structures are subject to a significant uncertainty. This is especially true when time-dependent degradation mechanisms such as structural fatigue cracking are considered. Through inspection and monitoring, information such as crack location and size can be obtained to improve these parameters and the corresponding reliability estimates. Dynamic Bayesian Networks (DBNs) are a powerful and flexible tool to model dynamic system behavior and update reliability and uncertainty analysis with life cycle data for problems such as fatigue cracking. However, a central challenge in using DBNs is the need to discretize certain types of continuous random variables to perform network inference while still accurately tracking low-probability failure events. Most existing discretization methods focus on getting the overall shape of the distribution correct, with less emphasis on the tail region. Therefore, a novel scheme is presented specifically to estimate the likelihood of low-probability failure events. The scheme is an iterative algorithm which dynamically partitions the discretization intervals at each iteration. Through applications to two stochastic crack-growth example problems, the algorithm is shown to be robust and accurate. Comparisons are presented between the proposed approach and existing methods for the discretization problem. - Highlights: • A dynamic discretization method is developed for low-probability events in DBNs. • The method is compared to existing approaches on two crack growth problems. • The method is shown to improve on existing methods for low-probability events
Characteristics of SiC neutron sensor spectrum unfolding process based on Bayesian inference
Cetnar, Jerzy; Krolikowski, Igor [Faculty of Energy and Fuels AGH - University of Science and Technology, Al. Mickiewicza 30, 30-059 Krakow (Poland); Ottaviani, L. [IM2NP, UMR CNRS 7334, Aix-Marseille University, Case 231 -13397 Marseille Cedex 20 (France); Lyoussi, A. [CEA, DEN, DER, Instrumentation Sensors and Dosimetry Laboratory, Cadarache, F-13108 St-Paul-Lez-Durance (France)
2015-07-01
This paper deals with SiC detector signal interpretation in neutron radiation measurements in mixed neutron gamma radiation fields, which is called the detector inverse problem or the spectrum unfolding, and it aims in finding a representation of the primary radiation, based on the measured detector signals. In our novel methodology we resort to Bayesian inference approach. In the developed procedure the resultant spectra is unfolded form detector channels reading, where the estimated neutron fluence in a group structure is obtained with its statistical characteristic comprising of standard deviation and correlation matrix. In the paper we present results of unfolding process for case of D-T neutron source in neutron moderating environment. Discussions of statistical properties of obtained results are presented as well as of the physical meaning of obtained correlation matrix of estimated group fluence. The presented works has been carried out within the I-SMART project, which is part of the KIC InnoEnergy R and D program. (authors)
Bayesian Predictive Inference of a Proportion Under a Twofold Small-Area Model
Nandram Balgobin
2016-03-01
Full Text Available We extend the twofold small-area model of Stukel and Rao (1997; 1999 to accommodate binary data. An example is the Third International Mathematics and Science Study (TIMSS, in which pass-fail data for mathematics of students from US schools (clusters are available at the third grade by regions and communities (small areas. We compare the finite population proportions of these small areas. We present a hierarchical Bayesian model in which the firststage binary responses have independent Bernoulli distributions, and each subsequent stage is modeled using a beta distribution, which is parameterized by its mean and a correlation coefficient. This twofold small-area model has an intracluster correlation at the first stage and an intercluster correlation at the second stage. The final-stage mean and all correlations are assumed to be noninformative independent random variables. We show how to infer the finite population proportion of each area. We have applied our models to synthetic TIMSS data to show that the twofold model is preferred over a onefold small-area model that ignores the clustering within areas. We further compare these models using a simulation study, which shows that the intracluster correlation is particularly important.
Dario Cuevas Rivera
2015-10-01
Full Text Available The olfactory information that is received by the insect brain is encoded in the form of spatiotemporal patterns in the projection neurons of the antennal lobe. These dense and overlapping patterns are transformed into a sparse code in Kenyon cells in the mushroom body. Although it is clear that this sparse code is the basis for rapid categorization of odors, it is yet unclear how the sparse code in Kenyon cells is computed and what information it represents. Here we show that this computation can be modeled by sequential firing rate patterns using Lotka-Volterra equations and Bayesian online inference. This new model can be understood as an 'intelligent coincidence detector', which robustly and dynamically encodes the presence of specific odor features. We found that the model is able to qualitatively reproduce experimentally observed activity in both the projection neurons and the Kenyon cells. In particular, the model explains mechanistically how sparse activity in the Kenyon cells arises from the dense code in the projection neurons. The odor classification performance of the model proved to be robust against noise and time jitter in the observed input sequences. As in recent experimental results, we found that recognition of an odor happened very early during stimulus presentation in the model. Critically, by using the model, we found surprising but simple computational explanations for several experimental phenomena.
Schmit, C. J.; Pritchard, J. R.
2018-03-01
Next generation radio experiments such as LOFAR, HERA, and SKA are expected to probe the Epoch of Reionization (EoR) and claim a first direct detection of the cosmic 21cm signal within the next decade. Data volumes will be enormous and can thus potentially revolutionize our understanding of the early Universe and galaxy formation. However, numerical modelling of the EoR can be prohibitively expensive for Bayesian parameter inference and how to optimally extract information from incoming data is currently unclear. Emulation techniques for fast model evaluations have recently been proposed as a way to bypass costly simulations. We consider the use of artificial neural networks as a blind emulation technique. We study the impact of training duration and training set size on the quality of the network prediction and the resulting best-fitting values of a parameter search. A direct comparison is drawn between our emulation technique and an equivalent analysis using 21CMMC. We find good predictive capabilities of our network using training sets of as low as 100 model evaluations, which is within the capabilities of fully numerical radiative transfer codes.
George, J.S.; Schmidt, D.M.; Wood, C.C.
1999-01-01
We have developed a Bayesian approach to the analysis of neural electromagnetic (MEG/EEG) data that can incorporate or fuse information from other imaging modalities and addresses the ill-posed inverse problem by sarnpliig the many different solutions which could have produced the given data. From these samples one can draw probabilistic inferences about regions of activation. Our source model assumes a variable number of variable size cortical regions of stimulus-correlated activity. An active region consists of locations on the cortical surf ace, within a sphere centered on some location in cortex. The number and radi of active regions can vary to defined maximum values. The goal of the analysis is to determine the posterior probability distribution for the set of parameters that govern the number, location, and extent of active regions. Markov Chain Monte Carlo is used to generate a large sample of sets of parameters distributed according to the posterior distribution. This sample is representative of the many different source distributions that could account for given data, and allows identification of probable (i.e. consistent) features across solutions. Examples of the use of this analysis technique with both simulated and empirical MEG data are presented
Antonio Canale
2017-06-01
Full Text Available msBP is an R package that implements a new method to perform Bayesian multiscale nonparametric inference introduced by Canale and Dunson (2016. The method, based on mixtures of multiscale beta dictionary densities, overcomes the drawbacks of Pólya trees and inherits many of the advantages of Dirichlet process mixture models. The key idea is that an infinitely-deep binary tree is introduced, with a beta dictionary density assigned to each node of the tree. Using a multiscale stick-breaking characterization, stochastically decreasing weights are assigned to each node. The result is an infinite mixture model. The package msBP implements a series of basic functions to deal with this family of priors such as random densities and numbers generation, creation and manipulation of binary tree objects, and generic functions to plot and print the results. In addition, it implements the Gibbs samplers for posterior computation to perform multiscale density estimation and multiscale testing of group differences described in Canale and Dunson (2016.
Bayesian inference of the heat transfer properties of a wall using experimental data
Iglesias, Marco
2016-01-06
A hierarchical Bayesian inference method is developed to estimate the thermal resistance and volumetric heat capacity of a wall. We apply our methodology to a real case study where measurements are recorded each minute from two temperature probes and two heat flux sensors placed on both sides of a solid brick wall along a period of almost five days. We model the heat transfer through the wall by means of the one-dimensional heat equation with Dirichlet boundary conditions. The initial/boundary conditions for the temperature are approximated by piecewise linear functions. We assume that temperature and heat flux measurements have independent Gaussian noise and derive the joint likelihood of the wall parameters and the initial/boundary conditions. Under the model assumptions, the boundary conditions are marginalized analytically from the joint likelihood. ApproximatedGaussian posterior distributions for the wall parameters and the initial condition parameter are obtained using the Laplace method, after incorporating the available prior information. The information gain is estimated under different experimental setups, to determine the best allocation of resources.
Duggento, Andrea; Stankovski, Tomislav; McClintock, Peter V. E.; Stefanovska, Aneta
2012-12-01
Living systems have time-evolving interactions that, until recently, could not be identified accurately from recorded time series in the presence of noise. Stankovski [Phys. Rev. Lett.PRLTAO0031-900710.1103/PhysRevLett.109.024101 109, 024101 (2012)] introduced a method based on dynamical Bayesian inference that facilitates the simultaneous detection of time-varying synchronization, directionality of influence, and coupling functions. It can distinguish unsynchronized dynamics from noise-induced phase slips. The method is based on phase dynamics, with Bayesian inference of the time-evolving parameters being achieved by shaping the prior densities to incorporate knowledge of previous samples. We now present the method in detail using numerically generated data, data from an analog electronic circuit, and cardiorespiratory data. We also generalize the method to encompass networks of interacting oscillators and thus demonstrate its applicability to small-scale networks.
Ali Mohammad-Djafari
2015-06-01
Full Text Available The main content of this review article is first to review the main inference tools using Bayes rule, the maximum entropy principle (MEP, information theory, relative entropy and the Kullback–Leibler (KL divergence, Fisher information and its corresponding geometries. For each of these tools, the precise context of their use is described. The second part of the paper is focused on the ways these tools have been used in data, signal and image processing and in the inverse problems, which arise in different physical sciences and engineering applications. A few examples of the applications are described: entropy in independent components analysis (ICA and in blind source separation, Fisher information in data model selection, different maximum entropy-based methods in time series spectral estimation and in linear inverse problems and, finally, the Bayesian inference for general inverse problems. Some original materials concerning the approximate Bayesian computation (ABC and, in particular, the variational Bayesian approximation (VBA methods are also presented. VBA is used for proposing an alternative Bayesian computational tool to the classical Markov chain Monte Carlo (MCMC methods. We will also see that VBA englobes joint maximum a posteriori (MAP, as well as the different expectation-maximization (EM algorithms as particular cases.
Hero Alfred
2010-11-01
Full Text Available Abstract Background Nonparametric Bayesian techniques have been developed recently to extend the sophistication of factor models, allowing one to infer the number of appropriate factors from the observed data. We consider such techniques for sparse factor analysis, with application to gene-expression data from three virus challenge studies. Particular attention is placed on employing the Beta Process (BP, the Indian Buffet Process (IBP, and related sparseness-promoting techniques to infer a proper number of factors. The posterior density function on the model parameters is computed using Gibbs sampling and variational Bayesian (VB analysis. Results Time-evolving gene-expression data are considered for respiratory syncytial virus (RSV, Rhino virus, and influenza, using blood samples from healthy human subjects. These data were acquired in three challenge studies, each executed after receiving institutional review board (IRB approval from Duke University. Comparisons are made between several alternative means of per-forming nonparametric factor analysis on these data, with comparisons as well to sparse-PCA and Penalized Matrix Decomposition (PMD, closely related non-Bayesian approaches. Conclusions Applying the Beta Process to the factor scores, or to the singular values of a pseudo-SVD construction, the proposed algorithms infer the number of factors in gene-expression data. For real data the "true" number of factors is unknown; in our simulations we consider a range of noise variances, and the proposed Bayesian models inferred the number of factors accurately relative to other methods in the literature, such as sparse-PCA and PMD. We have also identified a "pan-viral" factor of importance for each of the three viruses considered in this study. We have identified a set of genes associated with this pan-viral factor, of interest for early detection of such viruses based upon the host response, as quantified via gene-expression data.
Chen, Bo; Chen, Minhua; Paisley, John; Zaas, Aimee; Woods, Christopher; Ginsburg, Geoffrey S; Hero, Alfred; Lucas, Joseph; Dunson, David; Carin, Lawrence
2010-11-09
Nonparametric Bayesian techniques have been developed recently to extend the sophistication of factor models, allowing one to infer the number of appropriate factors from the observed data. We consider such techniques for sparse factor analysis, with application to gene-expression data from three virus challenge studies. Particular attention is placed on employing the Beta Process (BP), the Indian Buffet Process (IBP), and related sparseness-promoting techniques to infer a proper number of factors. The posterior density function on the model parameters is computed using Gibbs sampling and variational Bayesian (VB) analysis. Time-evolving gene-expression data are considered for respiratory syncytial virus (RSV), Rhino virus, and influenza, using blood samples from healthy human subjects. These data were acquired in three challenge studies, each executed after receiving institutional review board (IRB) approval from Duke University. Comparisons are made between several alternative means of per-forming nonparametric factor analysis on these data, with comparisons as well to sparse-PCA and Penalized Matrix Decomposition (PMD), closely related non-Bayesian approaches. Applying the Beta Process to the factor scores, or to the singular values of a pseudo-SVD construction, the proposed algorithms infer the number of factors in gene-expression data. For real data the "true" number of factors is unknown; in our simulations we consider a range of noise variances, and the proposed Bayesian models inferred the number of factors accurately relative to other methods in the literature, such as sparse-PCA and PMD. We have also identified a "pan-viral" factor of importance for each of the three viruses considered in this study. We have identified a set of genes associated with this pan-viral factor, of interest for early detection of such viruses based upon the host response, as quantified via gene-expression data.
La Russa, D [The Ottawa Hospital Cancer Centre, Ottawa, ON (Canada)
2015-06-15
Purpose: The purpose of this project is to develop a robust method of parameter estimation for a Poisson-based TCP model using Bayesian inference. Methods: Bayesian inference was performed using the PyMC3 probabilistic programming framework written in Python. A Poisson-based TCP regression model that accounts for clonogen proliferation was fit to observed rates of local relapse as a function of equivalent dose in 2 Gy fractions for a population of 623 stage-I non-small-cell lung cancer patients. The Slice Markov Chain Monte Carlo sampling algorithm was used to sample the posterior distributions, and was initiated using the maximum of the posterior distributions found by optimization. The calculation of TCP with each sample step required integration over the free parameter α, which was performed using an adaptive 24-point Gauss-Legendre quadrature. Convergence was verified via inspection of the trace plot and posterior distribution for each of the fit parameters, as well as with comparisons of the most probable parameter values with their respective maximum likelihood estimates. Results: Posterior distributions for α, the standard deviation of α (σ), the average tumour cell-doubling time (Td), and the repopulation delay time (Tk), were generated assuming α/β = 10 Gy, and a fixed clonogen density of 10{sup 7} cm−{sup 3}. Posterior predictive plots generated from samples from these posterior distributions are in excellent agreement with the observed rates of local relapse used in the Bayesian inference. The most probable values of the model parameters also agree well with maximum likelihood estimates. Conclusion: A robust method of performing Bayesian inference of TCP data using a complex TCP model has been established.
Kim, Daesang; El Gharamti, Iman; Hantouche, Mireille; Elwardani, Ahmed Elsaid; Farooq, Aamir; Bisetti, Fabrizio; Knio, Omar
2017-01-01
We developed a novel two-step hierarchical method for the Bayesian inference of the rate parameters of a target reaction from time-resolved concentration measurements in shock tubes. The method was applied to the calibration of the parameters
Multi-scale inference of interaction rules in animal groups using Bayesian model selection.
Richard P Mann
Full Text Available Inference of interaction rules of animals moving in groups usually relies on an analysis of large scale system behaviour. Models are tuned through repeated simulation until they match the observed behaviour. More recent work has used the fine scale motions of animals to validate and fit the rules of interaction of animals in groups. Here, we use a Bayesian methodology to compare a variety of models to the collective motion of glass prawns (Paratya australiensis. We show that these exhibit a stereotypical 'phase transition', whereby an increase in density leads to the onset of collective motion in one direction. We fit models to this data, which range from: a mean-field model where all prawns interact globally; to a spatial Markovian model where prawns are self-propelled particles influenced only by the current positions and directions of their neighbours; up to non-Markovian models where prawns have 'memory' of previous interactions, integrating their experiences over time when deciding to change behaviour. We show that the mean-field model fits the large scale behaviour of the system, but does not capture the observed locality of interactions. Traditional self-propelled particle models fail to capture the fine scale dynamics of the system. The most sophisticated model, the non-Markovian model, provides a good match to the data at both the fine scale and in terms of reproducing global dynamics, while maintaining a biologically plausible perceptual range. We conclude that prawns' movements are influenced by not just the current direction of nearby conspecifics, but also those encountered in the recent past. Given the simplicity of prawns as a study system our research suggests that self-propelled particle models of collective motion should, if they are to be realistic at multiple biological scales, include memory of previous interactions and other non-Markovian effects.
Kang, Seongkeun; Seong, Poong Hyun [Korea Advanced Institute of Science and Technology, Daejeon (Korea, Republic of)
2014-05-15
The purpose of this paper is to confirm if Bayesian inference can properly reflect the situation awareness of real human operators, and find the difference between the situation of ideal and practical operators, and investigate the factors which contributes to those difference. As a results, human can not think like computer. If human can memorize all the information, and their thinking process is same to the CPU of computer, the results of these two experiments come out more than 99%. However the probability of finding right malfunction by humans are only 64.52% in simple experiment, and 51.61% in complex experiment. Cognition is the mental processing that includes the attention of working memory, comprehending and producing language, calculating, reasoning, problem solving, and decision making. There are many reasons why human thinking process is different with computer, but in this experiment, we suggest that the working memory is the most important factor. Humans have limited working memory which has only seven chunks capacity. These seven chunks are called magic number. If there are more than seven sequential information, people start to forget the previous information because their working memory capacity is running over. We can check how much working memory affects to the result through the simple experiment. Then what if we neglect the effect of working memory? The total number of subjects who have incorrect memory is 7 (subject 3, 5, 6, 7, 8, 15, 25). They could find the right malfunction if the memory hadn't changed because of lack of working memory. Then the probability of find correct malfunction will be increased to 87.10% from 64.52%. Complex experiment has similar result. In this case, eight subjects(1, 5, 8, 9, 15, 17, 18, 30) had changed the memory, and it affects to find the right malfunction. Considering it, then the probability would be (16+8)/31 = 77.42%.
Palacios, Julia A; Minin, Vladimir N
2013-03-01
Changes in population size influence genetic diversity of the population and, as a result, leave a signature of these changes in individual genomes in the population. We are interested in the inverse problem of reconstructing past population dynamics from genomic data. We start with a standard framework based on the coalescent, a stochastic process that generates genealogies connecting randomly sampled individuals from the population of interest. These genealogies serve as a glue between the population demographic history and genomic sequences. It turns out that only the times of genealogical lineage coalescences contain information about population size dynamics. Viewing these coalescent times as a point process, estimating population size trajectories is equivalent to estimating a conditional intensity of this point process. Therefore, our inverse problem is similar to estimating an inhomogeneous Poisson process intensity function. We demonstrate how recent advances in Gaussian process-based nonparametric inference for Poisson processes can be extended to Bayesian nonparametric estimation of population size dynamics under the coalescent. We compare our Gaussian process (GP) approach to one of the state-of-the-art Gaussian Markov random field (GMRF) methods for estimating population trajectories. Using simulated data, we demonstrate that our method has better accuracy and precision. Next, we analyze two genealogies reconstructed from real sequences of hepatitis C and human Influenza A viruses. In both cases, we recover more believed aspects of the viral demographic histories than the GMRF approach. We also find that our GP method produces more reasonable uncertainty estimates than the GMRF method. Copyright © 2013, The International Biometric Society.
Koskela, J. J.; Croke, B. W. F.; Koivusalo, H.; Jakeman, A. J.; Kokkonen, T.
2012-11-01
Bayesian inference is used to study the effect of precipitation and model structural uncertainty on estimates of model parameters and confidence limits of predictive variables in a conceptual rainfall-runoff model in the snow-fed Rudbäck catchment (142 ha) in southern Finland. The IHACRES model is coupled with a simple degree day model to account for snow accumulation and melt. The posterior probability distribution of the model parameters is sampled by using the Differential Evolution Adaptive Metropolis (DREAM(ZS)) algorithm and the generalized likelihood function. Precipitation uncertainty is taken into account by introducing additional latent variables that were used as multipliers for individual storm events. Results suggest that occasional snow water equivalent (SWE) observations together with daily streamflow observations do not contain enough information to simultaneously identify model parameters, precipitation uncertainty and model structural uncertainty in the Rudbäck catchment. The addition of an autoregressive component to account for model structure error and latent variables having uniform priors to account for input uncertainty lead to dubious posterior distributions of model parameters. Thus our hypothesis that informative priors for latent variables could be replaced by additional SWE data could not be confirmed. The model was found to work adequately in 1-day-ahead simulation mode, but the results were poor in the simulation batch mode. This was caused by the interaction of parameters that were used to describe different sources of uncertainty. The findings may have lessons for other cases where parameterizations are similarly high in relation to available prior information.
Hallo, Miroslav; Asano, Kimiyuki; Gallovič, František
2017-09-01
On April 16, 2016, Kumamoto prefecture in Kyushu region, Japan, was devastated by a shallow M JMA7.3 earthquake. The series of foreshocks started by M JMA6.5 foreshock 28 h before the mainshock. They have originated in Hinagu fault zone intersecting the mainshock Futagawa fault zone; hence, the tectonic background for this earthquake sequence is rather complex. Here we infer centroid moment tensors (CMTs) for 11 events with M JMA between 4.8 and 6.5, using strong motion records of the K-NET, KiK-net and F-net networks. We use upgraded Bayesian full-waveform inversion code ISOLA-ObsPy, which takes into account uncertainty of the velocity model. Such an approach allows us to reliably assess uncertainty of the CMT parameters including the centroid position. The solutions show significant systematic spatial and temporal variations throughout the sequence. Foreshocks are right-lateral steeply dipping strike-slip events connected to the NE-SW shear zone. Those located close to the intersection of the Hinagu and Futagawa fault zones are dipping slightly to ESE, while those in the southern area are dipping to WNW. Contrarily, aftershocks are mostly normal dip-slip events, being related to the N-S extensional tectonic regime. Most of the deviatoric moment tensors contain only minor CLVD component, which can be attributed to the velocity model uncertainty. Nevertheless, two of the CMTs involve a significant CLVD component, which may reflect complex rupture process. Decomposition of those moment tensors into two pure shear moment tensors suggests combined right-lateral strike-slip and normal dip-slip mechanisms, consistent with the tectonic settings of the intersection of the Hinagu and Futagawa fault zones.[Figure not available: see fulltext.
Kang, Seongkeun; Seong, Poong Hyun
2014-01-01
The purpose of this paper is to confirm if Bayesian inference can properly reflect the situation awareness of real human operators, and find the difference between the situation of ideal and practical operators, and investigate the factors which contributes to those difference. As a results, human can not think like computer. If human can memorize all the information, and their thinking process is same to the CPU of computer, the results of these two experiments come out more than 99%. However the probability of finding right malfunction by humans are only 64.52% in simple experiment, and 51.61% in complex experiment. Cognition is the mental processing that includes the attention of working memory, comprehending and producing language, calculating, reasoning, problem solving, and decision making. There are many reasons why human thinking process is different with computer, but in this experiment, we suggest that the working memory is the most important factor. Humans have limited working memory which has only seven chunks capacity. These seven chunks are called magic number. If there are more than seven sequential information, people start to forget the previous information because their working memory capacity is running over. We can check how much working memory affects to the result through the simple experiment. Then what if we neglect the effect of working memory? The total number of subjects who have incorrect memory is 7 (subject 3, 5, 6, 7, 8, 15, 25). They could find the right malfunction if the memory hadn't changed because of lack of working memory. Then the probability of find correct malfunction will be increased to 87.10% from 64.52%. Complex experiment has similar result. In this case, eight subjects(1, 5, 8, 9, 15, 17, 18, 30) had changed the memory, and it affects to find the right malfunction. Considering it, then the probability would be (16+8)/31 = 77.42%
Spatial variability of coastal wetland resilience to sea-level rise using Bayesian inference
Hardy, T.; Wu, W.
2017-12-01
The coastal wetlands in the Northern Gulf of Mexico (NGOM) account for 40% of coastal wetland area in the United States and provide various ecosystem services to the region and broader areas. Increasing rates of relative sea-level rise (RSLR), and reduced sediment input have increased coastal wetland loss in the NGOM, accounting for 80% of coastal wetland loss in the nation. Traditional models for predicting the impact of RSLR on coastal wetlands in the NGOM have focused on coastal erosion driven by geophysical variables only, and/or at small spatial extents. Here we developed a model in Bayesian inference to make probabilistic prediction of wetland loss in the entire NGOM as a function of vegetation productivity and geophysical attributes. We also studied how restoration efforts help maintain the area of coastal wetlands. Vegetation productivity contributes organic matter to wetland sedimentation and was approximated using the remotely sensed normalized difference moisture index (NDMI). The geophysical variables include RSLR, tidal range, river discharge, coastal slope, and wave height. We found a significantly positive relation between wetland loss and RSLR, which varied significantly at different river discharge regimes. There also existed a significantly negative relation between wetland loss and NDMI, indicating that in-situ vegetation productivity contributed to wetland resilience to RSLR. This relation did not vary significantly between river discharge regimes. The spatial relation revealed three areas of high RSLR but relatively low wetland loss; these areas were associated with wetland restoration projects in coastal Louisiana. Two projects were breakwater projects, where hard materials were placed off-shore to reduce wave action and promote sedimentation. And one project was a vegetation planting project used to promote sedimentation and wetland stabilization. We further developed an interactive web tool that allows stakeholders to develop similar wetland
Multi-scale inference of interaction rules in animal groups using Bayesian model selection.
Richard P Mann
2012-01-01
Full Text Available Inference of interaction rules of animals moving in groups usually relies on an analysis of large scale system behaviour. Models are tuned through repeated simulation until they match the observed behaviour. More recent work has used the fine scale motions of animals to validate and fit the rules of interaction of animals in groups. Here, we use a Bayesian methodology to compare a variety of models to the collective motion of glass prawns (Paratya australiensis. We show that these exhibit a stereotypical 'phase transition', whereby an increase in density leads to the onset of collective motion in one direction. We fit models to this data, which range from: a mean-field model where all prawns interact globally; to a spatial Markovian model where prawns are self-propelled particles influenced only by the current positions and directions of their neighbours; up to non-Markovian models where prawns have 'memory' of previous interactions, integrating their experiences over time when deciding to change behaviour. We show that the mean-field model fits the large scale behaviour of the system, but does not capture fine scale rules of interaction, which are primarily mediated by physical contact. Conversely, the Markovian self-propelled particle model captures the fine scale rules of interaction but fails to reproduce global dynamics. The most sophisticated model, the non-Markovian model, provides a good match to the data at both the fine scale and in terms of reproducing global dynamics. We conclude that prawns' movements are influenced by not just the current direction of nearby conspecifics, but also those encountered in the recent past. Given the simplicity of prawns as a study system our research suggests that self-propelled particle models of collective motion should, if they are to be realistic at multiple biological scales, include memory of previous interactions and other non-Markovian effects.
A new Bayesian Inference-based Phase Associator for Earthquake Early Warning
Meier, Men-Andrin; Heaton, Thomas; Clinton, John; Wiemer, Stefan
2013-04-01
State of the art network-based Earthquake Early Warning (EEW) systems can provide warnings for large magnitude 7+ earthquakes. Although regions in the direct vicinity of the epicenter will not receive warnings prior to damaging shaking, real-time event characterization is available before the destructive S-wave arrival across much of the strongly affected region. In contrast, in the case of the more frequent medium size events, such as the devastating 1994 Mw6.7 Northridge, California, earthquake, providing timely warning to the smaller damage zone is more difficult. For such events the "blind zone" of current systems (e.g. the CISN ShakeAlert system in California) is similar in size to the area over which severe damage occurs. We propose a faster and more robust Bayesian inference-based event associator, that in contrast to the current standard associators (e.g. Earthworm Binder), is tailored to EEW and exploits information other than only phase arrival times. In particular, the associator potentially allows for reliable automated event association with as little as two observations, which, compared to the ShakeAlert system, would speed up the real-time characterizations by about ten seconds and thus reduce the blind zone area by up to 80%. We compile an extensive data set of regional and teleseismic earthquake and noise waveforms spanning a wide range of earthquake magnitudes and tectonic regimes. We pass these waveforms through a causal real-time filterbank with passband filters between 0.1 and 50Hz, and, updating every second from the event detection, extract the maximum amplitudes in each frequency band. Using this dataset, we define distributions of amplitude maxima in each passband as a function of epicentral distance and magnitude. For the real-time data, we pass incoming broadband and strong motion waveforms through the same filterbank and extract an evolving set of maximum amplitudes in each passband. We use the maximum amplitude distributions to check
Huang, Yi-Fei; Golding, G Brian
2015-02-15
A number of statistical phylogenetic methods have been developed to infer conserved functional sites or regions in proteins. Many methods, e.g. Rate4Site, apply the standard phylogenetic models to infer site-specific substitution rates and totally ignore the spatial correlation of substitution rates in protein tertiary structures, which may reduce their power to identify conserved functional patches in protein tertiary structures when the sequences used in the analysis are highly similar. The 3D sliding window method has been proposed to infer conserved functional patches in protein tertiary structures, but the window size, which reflects the strength of the spatial correlation, must be predefined and is not inferred from data. We recently developed GP4Rate to solve these problems under the Bayesian framework. Unfortunately, GP4Rate is computationally slow. Here, we present an intuitive web server, FuncPatch, to perform a fast approximate Bayesian inference of conserved functional patches in protein tertiary structures. Both simulations and four case studies based on empirical data suggest that FuncPatch is a good approximation to GP4Rate. However, FuncPatch is orders of magnitudes faster than GP4Rate. In addition, simulations suggest that FuncPatch is potentially a useful tool complementary to Rate4Site, but the 3D sliding window method is less powerful than FuncPatch and Rate4Site. The functional patches predicted by FuncPatch in the four case studies are supported by experimental evidence, which corroborates the usefulness of FuncPatch. The software FuncPatch is freely available at the web site, http://info.mcmaster.ca/yifei/FuncPatch golding@mcmaster.ca Supplementary data are available at Bioinformatics online. © The Author 2014. Published by Oxford University Press. All rights reserved. For Permissions, please e-mail: journals.permissions@oup.com.
Raithel, Carolyn A.; Özel, Feryal; Psaltis, Dimitrios
2017-08-01
One of the key goals of observing neutron stars is to infer the equation of state (EoS) of the cold, ultradense matter in their interiors. Here, we present a Bayesian statistical method of inferring the pressures at five fixed densities, from a sample of mock neutron star masses and radii. We show that while five polytropic segments are needed for maximum flexibility in the absence of any prior knowledge of the EoS, regularizers are also necessary to ensure that simple underlying EoS are not over-parameterized. For ideal data with small measurement uncertainties, we show that the pressure at roughly twice the nuclear saturation density, {ρ }{sat}, can be inferred to within 0.3 dex for many realizations of potential sources of uncertainties. The pressures of more complicated EoS with significant phase transitions can also be inferred to within ˜30%. We also find that marginalizing the multi-dimensional parameter space of pressure to infer a mass-radius relation can lead to biases of nearly 1 km in radius, toward larger radii. Using the full, five-dimensional posterior likelihoods avoids this bias.
Systematic validation of non-equilibrium thermochemical models using Bayesian inference
Miki, Kenji; Panesi, Marco; Prudhomme, Serge
2015-01-01
and Treanor [3], and Park [4]. Up to 16 uncertain parameters are estimated using Bayesian updating based on the latest absolute volumetric radiance data collected at the Electric Arc Shock Tube (EAST) installed inside the NASA Ames Research Center. Following
Hooghoudt, Jan Otto; Barroso, Margarida; Waagepetersen, Rasmus Plenge
2017-01-01
Főrster resonance energy transfer (FRET) is a quantum-physical phenomenon where energy may be transferred from one molecule to a neighbour molecule if the molecules are close enough. Using fluorophore molecule marking of proteins in a cell it is possible to measure in microscopic images to what....... In this paper we propose a new likelihood-based approach to statistical inference for FRET microscopic data. The likelihood function is obtained from a detailed modeling of the FRET data generating mechanism conditional on a protein configuration. We next follow a Bayesian approach and introduce a spatial point...
E. Laloy
2017-07-01
Full Text Available The rate at which low-lying sandy areas in temperate regions, such as the Campine Plateau (NE Belgium, have been eroding during the Quaternary is a matter of debate. Current knowledge on the average pace of landscape evolution in the Campine area is largely based on geological inferences and modern analogies. We performed a Bayesian inversion of an in situ-produced 10Be concentration depth profile to infer the average long-term erosion rate together with two other parameters: the surface exposure age and the inherited 10Be concentration. Compared to the latest advances in probabilistic inversion of cosmogenic radionuclide (CRN data, our approach has the following two innovative components: it (1 uses Markov chain Monte Carlo (MCMC sampling and (2 accounts (under certain assumptions for the contribution of model errors to posterior uncertainty. To investigate to what extent our approach differs from the state of the art in practice, a comparison against the Bayesian inversion method implemented in the CRONUScalc program is made. Both approaches identify similar maximum a posteriori (MAP parameter values, but posterior parameter and predictive uncertainty derived using the method taken in CRONUScalc is moderately underestimated. A simple way for producing more consistent uncertainty estimates with the CRONUScalc-like method in the presence of model errors is therefore suggested. Our inferred erosion rate of 39 ± 8. 9 mm kyr−1 (1σ is relatively large in comparison with landforms that erode under comparable (paleo-climates elsewhere in the world. We evaluate this value in the light of the erodibility of the substrate and sudden base level lowering during the Middle Pleistocene. A denser sampling scheme of a two-nuclide concentration depth profile would allow for better inferred erosion rate resolution, and including more uncertain parameters in the MCMC inversion.
Laloy, Eric; Beerten, Koen; Vanacker, Veerle; Christl, Marcus; Rogiers, Bart; Wouters, Laurent
2017-07-01
The rate at which low-lying sandy areas in temperate regions, such as the Campine Plateau (NE Belgium), have been eroding during the Quaternary is a matter of debate. Current knowledge on the average pace of landscape evolution in the Campine area is largely based on geological inferences and modern analogies. We performed a Bayesian inversion of an in situ-produced 10Be concentration depth profile to infer the average long-term erosion rate together with two other parameters: the surface exposure age and the inherited 10Be concentration. Compared to the latest advances in probabilistic inversion of cosmogenic radionuclide (CRN) data, our approach has the following two innovative components: it (1) uses Markov chain Monte Carlo (MCMC) sampling and (2) accounts (under certain assumptions) for the contribution of model errors to posterior uncertainty. To investigate to what extent our approach differs from the state of the art in practice, a comparison against the Bayesian inversion method implemented in the CRONUScalc program is made. Both approaches identify similar maximum a posteriori (MAP) parameter values, but posterior parameter and predictive uncertainty derived using the method taken in CRONUScalc is moderately underestimated. A simple way for producing more consistent uncertainty estimates with the CRONUScalc-like method in the presence of model errors is therefore suggested. Our inferred erosion rate of 39 ± 8. 9 mm kyr-1 (1σ) is relatively large in comparison with landforms that erode under comparable (paleo-)climates elsewhere in the world. We evaluate this value in the light of the erodibility of the substrate and sudden base level lowering during the Middle Pleistocene. A denser sampling scheme of a two-nuclide concentration depth profile would allow for better inferred erosion rate resolution, and including more uncertain parameters in the MCMC inversion.
Bayesian inference – a way to combine statistical data and semantic analysis meaningfully
Eila Lindfors
2011-11-01
Full Text Available This article focuses on presenting the possibilities of Bayesian modelling (Finite Mixture Modelling in the semantic analysis of statistically modelled data. The probability of a hypothesis in relation to the data available is an important question in inductive reasoning. Bayesian modelling allows the researcher to use many models at a time and provides tools to evaluate the goodness of different models. The researcher should always be aware that there is no such thing as the exact probability of an exact event. This is the reason for using probabilistic models. Each model presents a different perspective on the phenomenon in focus, and the researcher has to choose the most probable model with a view to previous research and the knowledge available.The idea of Bayesian modelling is illustrated here by presenting two different sets of data, one from craft science research (n=167 and the other (n=63 from educational research (Lindfors, 2007, 2002. The principles of how to build models and how to combine different profiles are described in the light of the research mentioned.Bayesian modelling is an analysis based on calculating probabilities in relation to a specific set of quantitative data. It is a tool for handling data and interpreting it semantically. The reliability of the analysis arises from an argumentation of which model can be selected from the model space as the basis for an interpretation, and on which arguments.Keywords: method, sloyd, Bayesian modelling, student teachersURN:NBN:no-29959
Yu, Jianbo
2015-12-01
Prognostics is much efficient to achieve zero-downtime performance, maximum productivity and proactive maintenance of machines. Prognostics intends to assess and predict the time evolution of machine health degradation so that machine failures can be predicted and prevented. A novel prognostics system is developed based on the data-model-fusion scheme using the Bayesian inference-based self-organizing map (SOM) and an integration of logistic regression (LR) and high-order particle filtering (HOPF). In this prognostics system, a baseline SOM is constructed to model the data distribution space of healthy machine under an assumption that predictable fault patterns are not available. Bayesian inference-based probability (BIP) derived from the baseline SOM is developed as a quantification indication of machine health degradation. BIP is capable of offering failure probability for the monitored machine, which has intuitionist explanation related to health degradation state. Based on those historic BIPs, the constructed LR and its modeling noise constitute a high-order Markov process (HOMP) to describe machine health propagation. HOPF is used to solve the HOMP estimation to predict the evolution of the machine health in the form of a probability density function (PDF). An on-line model update scheme is developed to adapt the Markov process changes to machine health dynamics quickly. The experimental results on a bearing test-bed illustrate the potential applications of the proposed system as an effective and simple tool for machine health prognostics.
Zhou, X.; Albertson, J. D.
2016-12-01
Natural gas is considered as a bridge fuel towards clean energy due to its potential lower greenhouse gas emission comparing with other fossil fuels. Despite numerous efforts, an efficient and cost-effective approach to monitor fugitive methane emissions along the natural gas production-supply chain has not been developed yet. Recently, mobile methane measurement has been introduced which applies a Bayesian approach to probabilistically infer methane emission rates and update estimates recursively when new measurements become available. However, the likelihood function, especially the error term which determines the shape of the estimate uncertainty, is not rigorously defined and evaluated with field data. To address this issue, we performed a series of near-source (using a specialized vehicle mounted with fast response methane analyzers and a GPS unit. Methane concentrations were measured at two different heights along mobile traversals downwind of the sources, and concurrent wind and temperature data are recorded by nearby 3-D sonic anemometers. With known methane release rates, the measurements were used to determine the functional form and the parameterization of the likelihood function in the Bayesian inference scheme under different meteorological conditions.
Scliar, Marilia O; Gouveia, Mateus H; Benazzo, Andrea; Ghirotto, Silvia; Fagundes, Nelson J R; Leal, Thiago P; Magalhães, Wagner C S; Pereira, Latife; Rodrigues, Maira R; Soares-Souza, Giordano B; Cabrera, Lilia; Berg, Douglas E; Gilman, Robert H; Bertorelle, Giorgio; Tarazona-Santos, Eduardo
2014-09-30
Archaeology reports millenary cultural contacts between Peruvian Coast-Andes and the Amazon Yunga, a rainforest transitional region between Andes and Lower Amazonia. To clarify the relationships between cultural and biological evolution of these populations, in particular between Amazon Yungas and Andeans, we used DNA-sequence data, a model-based Bayesian approach and several statistical validations to infer a set of demographic parameters. We found that the genetic diversity of the Shimaa (an Amazon Yunga population) is a subset of that of Quechuas from Central-Andes. Using the Isolation-with-Migration population genetics model, we inferred that the Shimaa ancestors were a small subgroup that split less than 5300 years ago (after the development of complex societies) from an ancestral Andean population. After the split, the most plausible scenario compatible with our results is that the ancestors of Shimaas moved toward the Peruvian Amazon Yunga and incorporated the culture and language of some of their neighbors, but not a substantial amount of their genes. We validated our results using Approximate Bayesian Computations, posterior predictive tests and the analysis of pseudo-observed datasets. We presented a case study in which model-based Bayesian approaches, combined with necessary statistical validations, shed light into the prehistoric demographic relationship between Andeans and a population from the Amazon Yunga. Our results offer a testable model for the peopling of this large transitional environmental region between the Andes and the Lower Amazonia. However, studies on larger samples and involving more populations of these regions are necessary to confirm if the predominant Andean biological origin of the Shimaas is the rule, and not the exception.
M. Subbiah
2017-01-01
Full Text Available Extensive statistical practice has shown the importance and relevance of the inferential problem of estimating probability parameters in a binomial experiment; especially on the issues of competing intervals from frequentist, Bayesian, and Bootstrap approaches. The package written in the free R environment and presented in this paper tries to take care of the issues just highlighted, by pooling a number of widely available and well-performing methods and apporting on them essential variations. A wide range of functions helps users with differing skills to estimate, evaluate, summarize, numerically and graphically, various measures adopting either the frequentist or the Bayesian paradigm.
Fernandes, R.; Eley, Y.; Brabec, Marek; Lucquin, A.; Millard, A.; Craig, O.E.
2018-01-01
Roč. 117, March (2018), s. 31-42 ISSN 0146-6380 Institutional support: RVO:67985807 Keywords : Fatty acids * carbon isotopes * pottery use * Bayesian mixing models * FRUITS Subject RIV: BB - Applied Statistics, Operational Research Impact factor: 3.081, year: 2016
Adaptive Bayesian inference on the mean of an infinite-dimensional normal distribution
Belitser, E.; Ghosal, S.
2003-01-01
We consider the problem of estimating the mean of an infinite-break dimensional normal distribution from the Bayesian perspective. Under the assumption that the unknown true mean satisfies a "smoothness condition," we first derive the convergence rate of the posterior distribution for a prior that
Blanc, Guillermo A.; Kewley, Lisa; Vogt, Frédéric P. A.; Dopita, Michael A.
2015-01-01
We present a new method for inferring the metallicity (Z) and ionization parameter (q) of H II regions and star-forming galaxies using strong nebular emission lines (SELs). We use Bayesian inference to derive the joint and marginalized posterior probability density functions for Z and q given a set of observed line fluxes and an input photoionization model. Our approach allows the use of arbitrary sets of SELs and the inclusion of flux upper limits. The method provides a self-consistent way of determining the physical conditions of ionized nebulae that is not tied to the arbitrary choice of a particular SEL diagnostic and uses all the available information. Unlike theoretically calibrated SEL diagnostics, the method is flexible and not tied to a particular photoionization model. We describe our algorithm, validate it against other methods, and present a tool that implements it called IZI. Using a sample of nearby extragalactic H II regions, we assess the performance of commonly used SEL abundance diagnostics. We also use a sample of 22 local H II regions having both direct and recombination line (RL) oxygen abundance measurements in the literature to study discrepancies in the abundance scale between different methods. We find that oxygen abundances derived through Bayesian inference using currently available photoionization models in the literature can be in good (∼30%) agreement with RL abundances, although some models perform significantly better than others. We also confirm that abundances measured using the direct method are typically ∼0.2 dex lower than both RL and photoionization-model-based abundances
Blanc, Guillermo A. [Observatories of the Carnegie Institution for Science, 813 Santa Barbara Street, Pasadena, CA 91101 (United States); Kewley, Lisa; Vogt, Frédéric P. A.; Dopita, Michael A. [Research School of Astronomy and Astrophysics, Australian National University, Cotter Road, Weston, ACT 2611 (Australia)
2015-01-10
We present a new method for inferring the metallicity (Z) and ionization parameter (q) of H II regions and star-forming galaxies using strong nebular emission lines (SELs). We use Bayesian inference to derive the joint and marginalized posterior probability density functions for Z and q given a set of observed line fluxes and an input photoionization model. Our approach allows the use of arbitrary sets of SELs and the inclusion of flux upper limits. The method provides a self-consistent way of determining the physical conditions of ionized nebulae that is not tied to the arbitrary choice of a particular SEL diagnostic and uses all the available information. Unlike theoretically calibrated SEL diagnostics, the method is flexible and not tied to a particular photoionization model. We describe our algorithm, validate it against other methods, and present a tool that implements it called IZI. Using a sample of nearby extragalactic H II regions, we assess the performance of commonly used SEL abundance diagnostics. We also use a sample of 22 local H II regions having both direct and recombination line (RL) oxygen abundance measurements in the literature to study discrepancies in the abundance scale between different methods. We find that oxygen abundances derived through Bayesian inference using currently available photoionization models in the literature can be in good (∼30%) agreement with RL abundances, although some models perform significantly better than others. We also confirm that abundances measured using the direct method are typically ∼0.2 dex lower than both RL and photoionization-model-based abundances.
Multi-model polynomial chaos surrogate dictionary for Bayesian inference in elasticity problems
Contreras, Andres A.; Le Maî tre, Olivier P.; Aquino, Wilkins; Knio, Omar
2016-01-01
of stiff inclusions embedded in a soft matrix, mimicking tumors in soft tissues. We rely on a polynomial chaos (PC) surrogate to accelerate the inference process. The PC surrogate predicts the dependence of the displacements field with the random elastic
From least squares to multilevel modeling: A graphical introduction to Bayesian inference
Loredo, Thomas J.
2016-01-01
This tutorial presentation will introduce some of the key ideas and techniques involved in applying Bayesian methods to problems in astrostatistics. The focus will be on the big picture: understanding the foundations (interpreting probability, Bayes's theorem, the law of total probability and marginalization), making connections to traditional methods (propagation of errors, least squares, chi-squared, maximum likelihood, Monte Carlo simulation), and highlighting problems where a Bayesian approach can be particularly powerful (Poisson processes, density estimation and curve fitting with measurement error). The "graphical" component of the title reflects an emphasis on pictorial representations of some of the math, but also on the use of graphical models (multilevel or hierarchical models) for analyzing complex data. Code for some examples from the talk will be available to participants, in Python and in the Stan probabilistic programming language.
Iglesias, Juan Eugenio; Sabuncu, Mert Rory; Van Leemput, Koen
2013-01-01
Many segmentation algorithms in medical image analysis use Bayesian modeling to augment local image appearance with prior anatomical knowledge. Such methods often contain a large number of free parameters that are first estimated and then kept fixed during the actual segmentation process. However...... in an Alzheimer’s disease classification task. As an additional benefit, the technique also allows one to compute informative “error bars” on the volume estimates of individual structures....
Inferring the most probable maps of underground utilities using Bayesian mapping model
Bilal, Muhammad; Khan, Wasiq; Muggleton, Jennifer; Rustighi, Emiliano; Jenks, Hugo; Pennock, Steve R.; Atkins, Phil R.; Cohn, Anthony
2018-03-01
Mapping the Underworld (MTU), a major initiative in the UK, is focused on addressing social, environmental and economic consequences raised from the inability to locate buried underground utilities (such as pipes and cables) by developing a multi-sensor mobile device. The aim of MTU device is to locate different types of buried assets in real time with the use of automated data processing techniques and statutory records. The statutory records, even though typically being inaccurate and incomplete, provide useful prior information on what is buried under the ground and where. However, the integration of information from multiple sensors (raw data) with these qualitative maps and their visualization is challenging and requires the implementation of robust machine learning/data fusion approaches. An approach for automated creation of revised maps was developed as a Bayesian Mapping model in this paper by integrating the knowledge extracted from sensors raw data and available statutory records. The combination of statutory records with the hypotheses from sensors was for initial estimation of what might be found underground and roughly where. The maps were (re)constructed using automated image segmentation techniques for hypotheses extraction and Bayesian classification techniques for segment-manhole connections. The model consisting of image segmentation algorithm and various Bayesian classification techniques (segment recognition and expectation maximization (EM) algorithm) provided robust performance on various simulated as well as real sites in terms of predicting linear/non-linear segments and constructing refined 2D/3D maps.
Hagemann, M. W.; Gleason, C. J.; Durand, M. T.
2017-11-01
The forthcoming Surface Water and Ocean Topography (SWOT) NASA satellite mission will measure water surface width, height, and slope of major rivers worldwide. The resulting data could provide an unprecedented account of river discharge at continental scales, but reliable methods need to be identified prior to launch. Here we present a novel algorithm for discharge estimation from only remotely sensed stream width, slope, and height at multiple locations along a mass-conserved river segment. The algorithm, termed the Bayesian AMHG-Manning (BAM) algorithm, implements a Bayesian formulation of streamflow uncertainty using a combination of Manning's equation and at-many-stations hydraulic geometry (AMHG). Bayesian methods provide a statistically defensible approach to generating discharge estimates in a physically underconstrained system but rely on prior distributions that quantify the a priori uncertainty of unknown quantities including discharge and hydraulic equation parameters. These were obtained from literature-reported values and from a USGS data set of acoustic Doppler current profiler (ADCP) measurements at USGS stream gauges. A data set of simulated widths, slopes, and heights from 19 rivers was used to evaluate the algorithms using a set of performance metrics. Results across the 19 rivers indicate an improvement in performance of BAM over previously tested methods and highlight a path forward in solving discharge estimation using solely satellite remote sensing.
Safner, T.; Miller, M.P.; McRae, B.H.; Fortin, M.-J.; Manel, S.
2011-01-01
Recently, techniques available for identifying clusters of individuals or boundaries between clusters using genetic data from natural populations have expanded rapidly. Consequently, there is a need to evaluate these different techniques. We used spatially-explicit simulation models to compare three spatial Bayesian clustering programs and two edge detection methods. Spatially-structured populations were simulated where a continuous population was subdivided by barriers. We evaluated the ability of each method to correctly identify boundary locations while varying: (i) time after divergence, (ii) strength of isolation by distance, (iii) level of genetic diversity, and (iv) amount of gene flow across barriers. To further evaluate the methods' effectiveness to detect genetic clusters in natural populations, we used previously published data on North American pumas and a European shrub. Our results show that with simulated and empirical data, the Bayesian spatial clustering algorithms outperformed direct edge detection methods. All methods incorrectly detected boundaries in the presence of strong patterns of isolation by distance. Based on this finding, we support the application of Bayesian spatial clustering algorithms for boundary detection in empirical datasets, with necessary tests for the influence of isolation by distance. ?? 2011 by the authors; licensee MDPI, Basel, Switzerland.
Allen Rodrigo
2006-01-01
Full Text Available Using the structured serial coalescent with Bayesian MCMC and serial samples, we estimate population size when some demes are not sampled or are hidden, ie ghost demes. It is found that even with the presence of a ghost deme, accurate inference was possible if the parameters are estimated with the true model. However with an incorrect model, estimates were biased and can be positively misleading. We extend these results to the case where there are sequences from the ghost at the last time sample. This case can arise in HIV patients, when some tissue samples and viral sequences only become available after death. When some sequences from the ghost deme are available at the last sampling time, estimation bias is reduced and accurate estimation of parameters associated with the ghost deme is possible despite sampling bias. Migration rates for this case are also shown to be good estimates when migration values are low.
Furtado-Junior, I; Abrunhosa, F A; Holanda, F C A F; Tavares, M C S
2016-06-01
Fishing selectivity of the mangrove crab Ucides cordatus in the north coast of Brazil can be defined as the fisherman's ability to capture and select individuals from a certain size or sex (or a combination of these factors) which suggests an empirical selectivity. Considering this hypothesis, we calculated the selectivity curves for males and females crabs using the logit function of the logistic model in the formulation. The Bayesian inference consisted of obtaining the posterior distribution by applying the Markov chain Monte Carlo (MCMC) method to software R using the OpenBUGS, BRugs, and R2WinBUGS libraries. The estimated results of width average carapace selection for males and females compared with previous studies reporting the average width of the carapace of sexual maturity allow us to confirm the hypothesis that most mature individuals do not suffer from fishing pressure; thus, ensuring their sustainability.
Goodlet, Brent R.; Mills, Leah; Bales, Ben; Charpagne, Marie-Agathe; Murray, Sean P.; Lenthe, William C.; Petzold, Linda; Pollock, Tresa M.
2018-06-01
Bayesian inference is employed to precisely evaluate single crystal elastic properties of novel γ -γ ' Co- and CoNi-based superalloys from simple and non-destructive resonant ultrasound spectroscopy (RUS) measurements. Nine alloys from three Co-, CoNi-, and Ni-based alloy classes were evaluated in the fully aged condition, with one alloy per class also evaluated in the solution heat-treated condition. Comparisons are made between the elastic properties of the three alloy classes and among the alloys of a single class, with the following trends observed. A monotonic rise in the c_{44} (shear) elastic constant by a total of 12 pct is observed between the three alloy classes as Co is substituted for Ni. Elastic anisotropy ( A) is also increased, with a large majority of the nearly 13 pct increase occurring after Co becomes the dominant constituent. Together the five CoNi alloys, with Co:Ni ratios from 1:1 to 1.5:1, exhibited remarkably similar properties with an average A 1.8 pct greater than the Ni-based alloy CMSX-4. Custom code demonstrating a substantial advance over previously reported methods for RUS inversion is also reported here for the first time. CmdStan-RUS is built upon the open-source probabilistic programing language of Stan and formulates the inverse problem using Bayesian methods. Bayesian posterior distributions are efficiently computed with Hamiltonian Monte Carlo (HMC), while initial parameterization is randomly generated from weakly informative prior distributions. Remarkably robust convergence behavior is demonstrated across multiple independent HMC chains in spite of initial parameterization often very far from actual parameter values. Experimental procedures are substantially simplified by allowing any arbitrary misorientation between the specimen and crystal axes, as elastic properties and misorientation are estimated simultaneously.
Ponciano, José Miguel
2017-11-22
Using a nonparametric Bayesian approach Palacios and Minin (2013) dramatically improved the accuracy, precision of Bayesian inference of population size trajectories from gene genealogies. These authors proposed an extension of a Gaussian Process (GP) nonparametric inferential method for the intensity function of non-homogeneous Poisson processes. They found that not only the statistical properties of the estimators were improved with their method, but also, that key aspects of the demographic histories were recovered. The authors' work represents the first Bayesian nonparametric solution to this inferential problem because they specify a convenient prior belief without a particular functional form on the population trajectory. Their approach works so well and provides such a profound understanding of the biological process, that the question arises as to how truly "biology-free" their approach really is. Using well-known concepts of stochastic population dynamics, here I demonstrate that in fact, Palacios and Minin's GP model can be cast as a parametric population growth model with density dependence and environmental stochasticity. Making this link between population genetics and stochastic population dynamics modeling provides novel insights into eliciting biologically meaningful priors for the trajectory of the effective population size. The results presented here also bring novel understanding of GP as models for the evolution of a trait. Thus, the ecological principles foundation of Palacios and Minin (2013)'s prior adds to the conceptual and scientific value of these authors' inferential approach. I conclude this note by listing a series of insights brought about by this connection with Ecology. Copyright © 2017 The Author. Published by Elsevier Inc. All rights reserved.
Underwood, Kristen L.; Rizzo, Donna M.; Schroth, Andrew W.; Dewoolkar, Mandar M.
2017-12-01
Given the variable biogeochemical, physical, and hydrological processes driving fluvial sediment and nutrient export, the water science and management communities need data-driven methods to identify regions prone to production and transport under variable hydrometeorological conditions. We use Bayesian analysis to segment concentration-discharge linear regression models for total suspended solids (TSS) and particulate and dissolved phosphorus (PP, DP) using 22 years of monitoring data from 18 Lake Champlain watersheds. Bayesian inference was leveraged to estimate segmented regression model parameters and identify threshold position. The identified threshold positions demonstrated a considerable range below and above the median discharge—which has been used previously as the default breakpoint in segmented regression models to discern differences between pre and post-threshold export regimes. We then applied a Self-Organizing Map (SOM), which partitioned the watersheds into clusters of TSS, PP, and DP export regimes using watershed characteristics, as well as Bayesian regression intercepts and slopes. A SOM defined two clusters of high-flux basins, one where PP flux was predominantly episodic and hydrologically driven; and another in which the sediment and nutrient sourcing and mobilization were more bimodal, resulting from both hydrologic processes at post-threshold discharges and reactive processes (e.g., nutrient cycling or lateral/vertical exchanges of fine sediment) at prethreshold discharges. A separate DP SOM defined two high-flux clusters exhibiting a bimodal concentration-discharge response, but driven by differing land use. Our novel framework shows promise as a tool with broad management application that provides insights into landscape drivers of riverine solute and sediment export.
Bayesian inference for data assimilation using Least-Squares Finite Element methods
Dwight, Richard P
2010-01-01
It has recently been observed that Least-Squares Finite Element methods (LS-FEMs) can be used to assimilate experimental data into approximations of PDEs in a natural way, as shown by Heyes et al. in the case of incompressible Navier-Stokes flow. The approach was shown to be effective without regularization terms, and can handle substantial noise in the experimental data without filtering. Of great practical importance is that - unlike other data assimilation techniques - it is not significantly more expensive than a single physical simulation. However the method as presented so far in the literature is not set in the context of an inverse problem framework, so that for example the meaning of the final result is unclear. In this paper it is shown that the method can be interpreted as finding a maximum a posteriori (MAP) estimator in a Bayesian approach to data assimilation, with normally distributed observational noise, and a Bayesian prior based on an appropriate norm of the governing equations. In this setting the method may be seen to have several desirable properties: most importantly discretization and modelling error in the simulation code does not affect the solution in limit of complete experimental information, so these errors do not have to be modelled statistically. Also the Bayesian interpretation better justifies the choice of the method, and some useful generalizations become apparent. The technique is applied to incompressible Navier-Stokes flow in a pipe with added velocity data, where its effectiveness, robustness to noise, and application to inverse problems is demonstrated.
Bayesian inference in a discrete shock model using confounded common cause data
Kvam, Paul H.; Martz, Harry F.
1995-01-01
We consider redundant systems of identical components for which reliability is assessed statistically using only demand-based failures and successes. Direct assessment of system reliability can lead to gross errors in estimation if there exist external events in the working environment that cause two or more components in the system to fail in the same demand period which have not been included in the reliability model. We develop a simple Bayesian model for estimating component reliability and the corresponding probability of common cause failure in operating systems for which the data is confounded; that is, the common cause failures cannot be distinguished from multiple independent component failures in the narrative event descriptions
Bayesian inference for spatio-temporal spike-and-slab priors
Andersen, Michael Riis; Vehtari, Aki; Winther, Ole
2017-01-01
a transformed Gaussian process on the spike-and-slab probabilities. An expectation propagation (EP) algorithm for posterior inference under the proposed model is derived. For large scale problems, the standard EP algorithm can be prohibitively slow. We therefore introduce three different approximation schemes...
A cost minimisation and Bayesian inference model predicts startle reflex modulation across species.
Bach, Dominik R
2015-04-07
In many species, rapid defensive reflexes are paramount to escaping acute danger. These reflexes are modulated by the state of the environment. This is exemplified in fear-potentiated startle, a more vigorous startle response during conditioned anticipation of an unrelated threatening event. Extant explanations of this phenomenon build on descriptive models of underlying psychological states, or neural processes. Yet, they fail to predict invigorated startle during reward anticipation and instructed attention, and do not explain why startle reflex modulation evolved. Here, we fill this lacuna by developing a normative cost minimisation model based on Bayesian optimality principles. This model predicts the observed pattern of startle modification by rewards, punishments, instructed attention, and several other states. Moreover, the mathematical formalism furnishes predictions that can be tested experimentally. Comparing the model with existing data suggests a specific neural implementation of the underlying computations which yields close approximations to the optimal solution under most circumstances. This analysis puts startle modification into the framework of Bayesian decision theory and predictive coding, and illustrates the importance of an adaptive perspective to interpret defensive behaviour across species. Copyright © 2015 The Author. Published by Elsevier Ltd.. All rights reserved.
Rajaona, Harizo; Septier, François; Armand, Patrick; Delignon, Yves; Olry, Christophe; Albergel, Armand; Moussafir, Jacques
2015-12-01
In the eventuality of an accidental or intentional atmospheric release, the reconstruction of the source term using measurements from a set of sensors is an important and challenging inverse problem. A rapid and accurate estimation of the source allows faster and more efficient action for first-response teams, in addition to providing better damage assessment. This paper presents a Bayesian probabilistic approach to estimate the location and the temporal emission profile of a pointwise source. The release rate is evaluated analytically by using a Gaussian assumption on its prior distribution, and is enhanced with a positivity constraint to improve the estimation. The source location is obtained by the means of an advanced iterative Monte-Carlo technique called Adaptive Multiple Importance Sampling (AMIS), which uses a recycling process at each iteration to accelerate its convergence. The proposed methodology is tested using synthetic and real concentration data in the framework of the Fusion Field Trials 2007 (FFT-07) experiment. The quality of the obtained results is comparable to those coming from the Markov Chain Monte Carlo (MCMC) algorithm, a popular Bayesian method used for source estimation. Moreover, the adaptive processing of the AMIS provides a better sampling efficiency by reusing all the generated samples.
Mariana Inés Pocovi
2015-06-01
Full Text Available Understanding the population structure and genetic diversity in sugarcane (Saccharum officinarum L. accessions from INTA germplasm bank (Argentina will be of great importance for germplasm collection and breeding improvement as it will identify diverse parental combinations to create segregating progenies with maximum genetic variability for further selection. A Bayesian approach, ordination methods (PCoA, Principal Coordinate Analysis and clustering analysis (UPGMA, Unweighted Pair Group Method with Arithmetic Mean were applied to this purpose. Sixty three INTA sugarcane hybrids were genotyped for 107 Simple Sequence Repeat (SSR and 136 Amplified Fragment Length Polymorphism (AFLP loci. Given the low probability values found with AFLP for individual assignment (4.7%, microsatellites seemed to perform better (54% for STRUCTURE analysis that revealed the germplasm to exist in five optimum groups with partly corresponding to their origin. However clusters shown high degree of admixture, F ST values confirmed the existence of differences among groups. Dissimilarity coefficients ranged from 0.079 to 0.651. PCoA separated sugarcane in groups that did not agree with those identified by STRUCTURE. The clustering including all genotypes neither showed resemblance to populations find by STRUCTURE, but clustering performed considering only individuals displaying a proportional membership > 0.6 in their primary population obtained with STRUCTURE showed close similarities. The Bayesian method indubitably brought more information on cultivar origins than classical PCoA and hierarchical clustering method.
Bayesian inference in mass flow simulations - from back calculation to prediction
Kofler, Andreas; Fischer, Jan-Thomas; Hellweger, Valentin; Huber, Andreas; Mergili, Martin; Pudasaini, Shiva; Fellin, Wolfgang; Oberguggenberger, Michael
2017-04-01
Mass flow simulations are an integral part of hazard assessment. Determining the hazard potential requires a multidisciplinary approach, including different scientific fields such as geomorphology, meteorology, physics, civil engineering and mathematics. An important task in snow avalanche simulation is to predict process intensities (runout, flow velocity and depth, ...). The application of probabilistic methods allows one to develop a comprehensive simulation concept, ranging from back to forward calculation and finally to prediction of mass flow events. In this context optimized parameter sets for the used simulation model or intensities of the modeled mass flow process (e.g. runout distances) are represented by probability distributions. Existing deterministic flow models, in particular with respect to snow avalanche dynamics, contain several parameters (e.g. friction). Some of these parameters are more conceptual than physical and their direct measurement in the field is hardly possible. Hence, parameters have to be optimized by matching simulation results to field observations. This inverse problem can be solved by a Bayesian approach (Markov chain Monte Carlo). The optimization process yields parameter distributions, that can be utilized for probabilistic reconstruction and prediction of avalanche events. Arising challenges include the limited amount of observations, correlations appearing in model parameters or observed avalanche characteristics (e.g. velocity and runout) and the accurate handling of ensemble simulations, always taking into account the related uncertainties. Here we present an operational Bayesian simulation framework with r.avaflow, the open source GIS simulation model for granular avalanches and debris flows.
Bayesian inference in genetic parameter estimation of visual scores in Nellore beef-cattle
2009-01-01
The aim of this study was to estimate the components of variance and genetic parameters for the visual scores which constitute the Morphological Evaluation System (MES), such as body structure (S), precocity (P) and musculature (M) in Nellore beef-cattle at the weaning and yearling stages, by using threshold Bayesian models. The information used for this was gleaned from visual scores of 5,407 animals evaluated at the weaning and 2,649 at the yearling stages. The genetic parameters for visual score traits were estimated through two-trait analysis, using the threshold animal model, with Bayesian statistics methodology and MTGSAM (Multiple Trait Gibbs Sampler for Animal Models) threshold software. Heritability estimates for S, P and M were 0.68, 0.65 and 0.62 (at weaning) and 0.44, 0.38 and 0.32 (at the yearling stage), respectively. Heritability estimates for S, P and M were found to be high, and so it is expected that these traits should respond favorably to direct selection. The visual scores evaluated at the weaning and yearling stages might be used in the composition of new selection indexes, as they presented sufficient genetic variability to promote genetic progress in such morphological traits. PMID:21637450
Elsheikh, Ahmed H.
2014-02-01
An efficient Bayesian calibration method based on the nested sampling (NS) algorithm and non-intrusive polynomial chaos method is presented. Nested sampling is a Bayesian sampling algorithm that builds a discrete representation of the posterior distributions by iteratively re-focusing a set of samples to high likelihood regions. NS allows representing the posterior probability density function (PDF) with a smaller number of samples and reduces the curse of dimensionality effects. The main difficulty of the NS algorithm is in the constrained sampling step which is commonly performed using a random walk Markov Chain Monte-Carlo (MCMC) algorithm. In this work, we perform a two-stage sampling using a polynomial chaos response surface to filter out rejected samples in the Markov Chain Monte-Carlo method. The combined use of nested sampling and the two-stage MCMC based on approximate response surfaces provides significant computational gains in terms of the number of simulation runs. The proposed algorithm is applied for calibration and model selection of subsurface flow models. © 2013.
Bayesian inference of nonlinear unsteady aerodynamics from aeroelastic limit cycle oscillations
Sandhu, Rimple [Department of Civil and Environmental Engineering, Carleton University, Ottawa, Ontario (Canada); Poirel, Dominique [Department of Mechanical and Aerospace Engineering, Royal Military College of Canada, Kingston, Ontario (Canada); Pettit, Chris [Department of Aerospace Engineering, United States Naval Academy, Annapolis, MD (United States); Khalil, Mohammad [Department of Civil and Environmental Engineering, Carleton University, Ottawa, Ontario (Canada); Sarkar, Abhijit, E-mail: abhijit.sarkar@carleton.ca [Department of Civil and Environmental Engineering, Carleton University, Ottawa, Ontario (Canada)
2016-07-01
A Bayesian model selection and parameter estimation algorithm is applied to investigate the influence of nonlinear and unsteady aerodynamic loads on the limit cycle oscillation (LCO) of a pitching airfoil in the transitional Reynolds number regime. At small angles of attack, laminar boundary layer trailing edge separation causes negative aerodynamic damping leading to the LCO. The fluid–structure interaction of the rigid, but elastically mounted, airfoil and nonlinear unsteady aerodynamics is represented by two coupled nonlinear stochastic ordinary differential equations containing uncertain parameters and model approximation errors. Several plausible aerodynamic models with increasing complexity are proposed to describe the aeroelastic system leading to LCO. The likelihood in the posterior parameter probability density function (pdf) is available semi-analytically using the extended Kalman filter for the state estimation of the coupled nonlinear structural and unsteady aerodynamic model. The posterior parameter pdf is sampled using a parallel and adaptive Markov Chain Monte Carlo (MCMC) algorithm. The posterior probability of each model is estimated using the Chib–Jeliazkov method that directly uses the posterior MCMC samples for evidence (marginal likelihood) computation. The Bayesian algorithm is validated through a numerical study and then applied to model the nonlinear unsteady aerodynamic loads using wind-tunnel test data at various Reynolds numbers.
Marzouk, Youssef; Fast P. (Lawrence Livermore National Laboratory, Livermore, CA); Kraus, M. (Peterson AFB, CO); Ray, J. P.
2006-01-01
Terrorist attacks using an aerosolized pathogen preparation have gained credibility as a national security concern after the anthrax attacks of 2001. The ability to characterize such attacks, i.e., to estimate the number of people infected, the time of infection, and the average dose received, is important when planning a medical response. We address this question of characterization by formulating a Bayesian inverse problem predicated on a short time-series of diagnosed patients exhibiting symptoms. To be of relevance to response planning, we limit ourselves to 3-5 days of data. In tests performed with anthrax as the pathogen, we find that these data are usually sufficient, especially if the model of the outbreak used in the inverse problem is an accurate one. In some cases the scarcity of data may initially support outbreak characterizations at odds with the true one, but with sufficient data the correct inferences are recovered; in other words, the inverse problem posed and its solution methodology are consistent. We also explore the effect of model error-situations for which the model used in the inverse problem is only a partially accurate representation of the outbreak; here, the model predictions and the observations differ by more than a random noise. We find that while there is a consistent discrepancy between the inferred and the true characterizations, they are also close enough to be of relevance when planning a response.
Sraj, Ihab
2016-08-26
The authors present a polynomial chaos (PC)-based Bayesian inference method for quantifying the uncertainties of the K-profile parameterization (KPP) within the MIT general circulation model (MITgcm) of the tropical Pacific. The inference of the uncertain parameters is based on a Markov chain Monte Carlo (MCMC) scheme that utilizes a newly formulated test statistic taking into account the different components representing the structures of turbulent mixing on both daily and seasonal time scales in addition to the data quality, and filters for the effects of parameter perturbations over those as a result of changes in the wind. To avoid the prohibitive computational cost of integrating the MITgcm model at each MCMC iteration, a surrogate model for the test statistic using the PC method is built. Because of the noise in the model predictions, a basis-pursuit-denoising (BPDN) compressed sensing approach is employed to determine the PC coefficients of a representative surrogate model. The PC surrogate is then used to evaluate the test statistic in the MCMC step for sampling the posterior of the uncertain parameters. Results of the posteriors indicate good agreement with the default values for two parameters of the KPP model, namely the critical bulk and gradient Richardson numbers; while the posteriors of the remaining parameters were barely informative. © 2016 American Meteorological Society.
Prudhomme, Serge
2015-01-07
The need for surrogate models and adaptive methods can be best appreciated if one is interested in parameter estimation using a Bayesian calibration procedure for validation purposes. We extend here our latest work on error decomposition and adaptive refinement for response surfaces to the development of surrogate models that can be substituted for the full models to estimate the parameters of Reynolds-averaged Navier-Stokes models. The error estimates and adaptive schemes are driven here by a quantity of interest and are thus based on the approximation of an adjoint problem. We will focus in particular to the accurate estimation of evidences to facilitate model selection. The methodology will be illustrated on the Spalart-Allmaras RANS model for turbulence simulation.
Galliano, Frédéric
2018-05-01
This article presents a new dust spectral energy distribution (SED) model, named HerBIE, aimed at eliminating the noise-induced correlations and large scatter obtained when performing least-squares fits. The originality of this code is to apply the hierarchical Bayesian approach to full dust models, including realistic optical properties, stochastic heating, and the mixing of physical conditions in the observed regions. We test the performances of our model by applying it to synthetic observations. We explore the impact on the recovered parameters of several effects: signal-to-noise ratio, SED shape, sample size, the presence of intrinsic correlations, the wavelength coverage, and the use of different SED model components. We show that this method is very efficient: the recovered parameters are consistently distributed around their true values. We do not find any clear bias, even for the most degenerate parameters, or with extreme signal-to-noise ratios.
Prudhomme, Serge
2015-01-01
The need for surrogate models and adaptive methods can be best appreciated if one is interested in parameter estimation using a Bayesian calibration procedure for validation purposes. We extend here our latest work on error decomposition and adaptive refinement for response surfaces to the development of surrogate models that can be substituted for the full models to estimate the parameters of Reynolds-averaged Navier-Stokes models. The error estimates and adaptive schemes are driven here by a quantity of interest and are thus based on the approximation of an adjoint problem. We will focus in particular to the accurate estimation of evidences to facilitate model selection. The methodology will be illustrated on the Spalart-Allmaras RANS model for turbulence simulation.
Partial inversion of elliptic operator to speed up computation of likelihood in Bayesian inference
Litvinenko, Alexander
2017-08-09
In this paper, we speed up the solution of inverse problems in Bayesian settings. By computing the likelihood, the most expensive part of the Bayesian formula, one compares the available measurement data with the simulated data. To get simulated data, repeated solution of the forward problem is required. This could be a great challenge. Often, the available measurement is a functional $F(u)$ of the solution $u$ or a small part of $u$. Typical examples of $F(u)$ are the solution in a point, solution on a coarser grid, in a small subdomain, the mean value in a subdomain. It is a waste of computational resources to evaluate, first, the whole solution and then compute a part of it. In this work, we compute the functional $F(u)$ direct, without computing the full inverse operator and without computing the whole solution $u$. The main ingredients of the developed approach are the hierarchical domain decomposition technique, the finite element method and the Schur complements. To speed up computations and to reduce the storage cost, we approximate the forward operator and the Schur complement in the hierarchical matrix format. Applying the hierarchical matrix technique, we reduced the computing cost to $\\\\mathcal{O}(k^2n \\\\log^2 n)$, where $k\\\\ll n$ and $n$ is the number of degrees of freedom. Up to the $\\\\H$-matrix accuracy, the computation of the functional $F(u)$ is exact. To reduce the computational resources further, we can approximate $F(u)$ on, for instance, multiple coarse meshes. The offered method is well suited for solving multiscale problems. A disadvantage of this method is the assumption that one has to have access to the discretisation and to the procedure of assembling the Galerkin matrix.
Fukuda, J.; Johnson, K. M.
2009-12-01
Studies utilizing inversions of geodetic data for the spatial distribution of coseismic slip on faults typically present the result as a single fault plane and slip distribution. Commonly the geometry of the fault plane is assumed to be known a priori and the data are inverted for slip. However, sometimes there is not strong a priori information on the geometry of the fault that produced the earthquake and the data is not always strong enough to completely resolve the fault geometry. We develop a method to solve for the full posterior probability distribution of fault slip and fault geometry parameters in a Bayesian framework using Monte Carlo methods. The slip inversion problem is particularly challenging because it often involves multiple data sets with unknown relative weights (e.g. InSAR, GPS), model parameters that are related linearly (slip) and nonlinearly (fault geometry) through the theoretical model to surface observations, prior information on model parameters, and a regularization prior to stabilize the inversion. We present the theoretical framework and solution method for a Bayesian inversion that can handle all of these aspects of the problem. The method handles the mixed linear/nonlinear nature of the problem through combination of both analytical least-squares solutions and Monte Carlo methods. We first illustrate and validate the inversion scheme using synthetic data sets. We then apply the method to inversion of geodetic data from the 2003 M6.6 San Simeon, California earthquake. We show that the uncertainty in strike and dip of the fault plane is over 20 degrees. We characterize the uncertainty in the slip estimate with a volume around the mean fault solution in which the slip most likely occurred. Slip likely occurred somewhere in a volume that extends 5-10 km in either direction normal to the fault plane. We implement slip inversions with both traditional, kinematic smoothing constraints on slip and a simple physical condition of uniform stress
Wang, L.; Davis, J. L.; Tamisiea, M. E.
2017-12-01
The Antarctic ice sheet (AIS) holds about 60% of all fresh water on the Earth, an amount equivalent to about 58 m of sea-level rise. Observation of AIS mass change is thus essential in determining and predicting its contribution to sea level. While the ice mass loss estimates for West Antarctica (WA) and the Antarctic Peninsula (AP) are in good agreement, what the mass balance over East Antarctica (EA) is, and whether or not it compensates for the mass loss is under debate. Besides the different error sources and sensitivities of different measurement types, complex spatial and temporal variabilities would be another factor complicating the accurate estimation of the AIS mass balance. Therefore, a model that allows for variabilities in both melting rate and seasonal signals would seem appropriate in the estimation of present-day AIS melting. We present a stochastic filter technique, which enables the Bayesian separation of the systematic stripe noise and mass signal in decade-length GRACE monthly gravity series, and allows the estimation of time-variable seasonal and inter-annual components in the signals. One of the primary advantages of this Bayesian method is that it yields statistically rigorous uncertainty estimates reflecting the inherent spatial resolution of the data. By applying the stochastic filter to the decade-long GRACE observations, we present the temporal variabilities of the AIS mass balance at basin scale, particularly over East Antarctica, and decipher the EA mass variations in the past decade, and their role in affecting overall AIS mass balance and sea level.
Exploring the Connection Between Sampling Problems in Bayesian Inference and Statistical Mechanics
Pohorille, Andrew
2006-01-01
The Bayesian and statistical mechanical communities often share the same objective in their work - estimating and integrating probability distribution functions (pdfs) describing stochastic systems, models or processes. Frequently, these pdfs are complex functions of random variables exhibiting multiple, well separated local minima. Conventional strategies for sampling such pdfs are inefficient, sometimes leading to an apparent non-ergodic behavior. Several recently developed techniques for handling this problem have been successfully applied in statistical mechanics. In the multicanonical and Wang-Landau Monte Carlo (MC) methods, the correct pdfs are recovered from uniform sampling of the parameter space by iteratively establishing proper weighting factors connecting these distributions. Trivial generalizations allow for sampling from any chosen pdf. The closely related transition matrix method relies on estimating transition probabilities between different states. All these methods proved to generate estimates of pdfs with high statistical accuracy. In another MC technique, parallel tempering, several random walks, each corresponding to a different value of a parameter (e.g. "temperature"), are generated and occasionally exchanged using the Metropolis criterion. This method can be considered as a statistically correct version of simulated annealing. An alternative approach is to represent the set of independent variables as a Hamiltonian system. Considerab!e progress has been made in understanding how to ensure that the system obeys the equipartition theorem or, equivalently, that coupling between the variables is correctly described. Then a host of techniques developed for dynamical systems can be used. Among them, probably the most powerful is the Adaptive Biasing Force method, in which thermodynamic integration and biased sampling are combined to yield very efficient estimates of pdfs. The third class of methods deals with transitions between states described
Bayesian inference in an item response theory model with a generalized student t link function
Azevedo, Caio L. N.; Migon, Helio S.
2012-10-01
In this paper we introduce a new item response theory (IRT) model with a generalized Student t-link function with unknown degrees of freedom (df), named generalized t-link (GtL) IRT model. In this model we consider only the difficulty parameter in the item response function. GtL is an alternative to the two parameter logit and probit models, since the degrees of freedom (df) play a similar role to the discrimination parameter. However, the behavior of the curves of the GtL is different from those of the two parameter models and the usual Student t link, since in GtL the curve obtained from different df's can cross the probit curves in more than one latent trait level. The GtL model has similar proprieties to the generalized linear mixed models, such as the existence of sufficient statistics and easy parameter interpretation. Also, many techniques of parameter estimation, model fit assessment and residual analysis developed for that models can be used for the GtL model. We develop fully Bayesian estimation and model fit assessment tools through a Metropolis-Hastings step within Gibbs sampling algorithm. We consider a prior sensitivity choice concerning the degrees of freedom. The simulation study indicates that the algorithm recovers all parameters properly. In addition, some Bayesian model fit assessment tools are considered. Finally, a real data set is analyzed using our approach and other usual models. The results indicate that our model fits the data better than the two parameter models.
Closed Form Solution of Synchronous Machine Short Circuit Transients
Gibson H.M. Sianipar
2010-05-01
Full Text Available This paper presents the closed form solution of the synchronous machine transients undergoing short circuit. That analytic formulation has been derived based on linearity and balanced conditions of the fault. Even though restrictive, the proposed method will serve somehow or other as a new resource for EMTP productivity. Indisputably superior, the closed-form formulation has some features inimitable by discretization such as continuity, accuracy and absolute numerical stability. Moreover, it enables us to calculate states at one specific instant independent of previous states or a snapshot, which any discretization methods cannot do.
Lucka, Felix
2012-01-01
Sparsity has become a key concept for solving of high-dimensional inverse problems using variational regularization techniques. Recently, using similar sparsity-constraints in the Bayesian framework for inverse problems by encoding them in the prior distribution has attracted attention. Important questions about the relation between regularization theory and Bayesian inference still need to be addressed when using sparsity promoting inversion. A practical obstacle for these examinations is the lack of fast posterior sampling algorithms for sparse, high-dimensional Bayesian inversion. Accessing the full range of Bayesian inference methods requires being able to draw samples from the posterior probability distribution in a fast and efficient way. This is usually done using Markov chain Monte Carlo (MCMC) sampling algorithms. In this paper, we develop and examine a new implementation of a single component Gibbs MCMC sampler for sparse priors relying on L1-norms. We demonstrate that the efficiency of our Gibbs sampler increases when the level of sparsity or the dimension of the unknowns is increased. This property is contrary to the properties of the most commonly applied Metropolis–Hastings (MH) sampling schemes. We demonstrate that the efficiency of MH schemes for L1-type priors dramatically decreases when the level of sparsity or the dimension of the unknowns is increased. Practically, Bayesian inversion for L1-type priors using MH samplers is not feasible at all. As this is commonly believed to be an intrinsic feature of MCMC sampling, the performance of our Gibbs sampler also challenges common beliefs about the applicability of sample based Bayesian inference. (paper)
Niwayama, Ritsuya; Nagao, Hiromichi; Kitajima, Tomoya S; Hufnagel, Lars; Shinohara, Kyosuke; Higuchi, Tomoyuki; Ishikawa, Takuji; Kimura, Akatsuki
2016-01-01
Cellular structures are hydrodynamically interconnected, such that force generation in one location can move distal structures. One example of this phenomenon is cytoplasmic streaming, whereby active forces at the cell cortex induce streaming of the entire cytoplasm. However, it is not known how the spatial distribution and magnitude of these forces move distant objects within the cell. To address this issue, we developed a computational method that used cytoplasm hydrodynamics to infer the spatial distribution of shear stress at the cell cortex induced by active force generators from experimentally obtained flow field of cytoplasmic streaming. By applying this method, we determined the shear-stress distribution that quantitatively reproduces in vivo flow fields in Caenorhabditis elegans embryos and mouse oocytes during meiosis II. Shear stress in mouse oocytes were predicted to localize to a narrower cortical region than that with a high cortical flow velocity and corresponded with the localization of the cortical actin cap. The predicted patterns of pressure gradient in both species were consistent with species-specific cytoplasmic streaming functions. The shear-stress distribution inferred by our method can contribute to the characterization of active force generation driving biological streaming.
Estimation of Ship Motions Using Closed-Form Expressions
Jensen, Jørgen Juncher; Mansour, A.E.; Olsen, Anders Smærup
2004-01-01
A semi-analytical approach is used to derive frequency response functions for the wave-induced motions for monohull ships. The results are given as closed-form expressions and the required input information for the procedure is restricted to the main dimensions: Length, breadth, draught, block...
On Closed Form Calculation of Line Spectral Frequencies (LSF)
Dalsgaard, Paul; Andersen, Ove
2014-01-01
of characteristic polynomial zeros. The theoretical analysis is based on decomposition of sequences into symmetric and anti-symmetric polynomials defined as a series expansion of reduced Chebyshev polynomials of the first kind. Two variants of closed form functions are presented — each characterised by using...
Closed form fourier-based transmit beamforming for MIMO radar
Lipor, John J.; Ahmed, Sajid; Alouini, Mohamed-Slim
2014-01-01
-pattern, current research uses iterative algorithms, first to synthesize the waveform covariance matrix, R, then to design the actual waveforms to realize R. In contrast to this, we present a closed form method to design R that exploits discrete Fourier transform
Yildiz, Izzet B; von Kriegstein, Katharina; Kiebel, Stefan J
2013-01-01
Our knowledge about the computational mechanisms underlying human learning and recognition of sound sequences, especially speech, is still very limited. One difficulty in deciphering the exact means by which humans recognize speech is that there are scarce experimental findings at a neuronal, microscopic level. Here, we show that our neuronal-computational understanding of speech learning and recognition may be vastly improved by looking at an animal model, i.e., the songbird, which faces the same challenge as humans: to learn and decode complex auditory input, in an online fashion. Motivated by striking similarities between the human and songbird neural recognition systems at the macroscopic level, we assumed that the human brain uses the same computational principles at a microscopic level and translated a birdsong model into a novel human sound learning and recognition model with an emphasis on speech. We show that the resulting Bayesian model with a hierarchy of nonlinear dynamical systems can learn speech samples such as words rapidly and recognize them robustly, even in adverse conditions. In addition, we show that recognition can be performed even when words are spoken by different speakers and with different accents-an everyday situation in which current state-of-the-art speech recognition models often fail. The model can also be used to qualitatively explain behavioral data on human speech learning and derive predictions for future experiments.
Izzet B Yildiz
Full Text Available Our knowledge about the computational mechanisms underlying human learning and recognition of sound sequences, especially speech, is still very limited. One difficulty in deciphering the exact means by which humans recognize speech is that there are scarce experimental findings at a neuronal, microscopic level. Here, we show that our neuronal-computational understanding of speech learning and recognition may be vastly improved by looking at an animal model, i.e., the songbird, which faces the same challenge as humans: to learn and decode complex auditory input, in an online fashion. Motivated by striking similarities between the human and songbird neural recognition systems at the macroscopic level, we assumed that the human brain uses the same computational principles at a microscopic level and translated a birdsong model into a novel human sound learning and recognition model with an emphasis on speech. We show that the resulting Bayesian model with a hierarchy of nonlinear dynamical systems can learn speech samples such as words rapidly and recognize them robustly, even in adverse conditions. In addition, we show that recognition can be performed even when words are spoken by different speakers and with different accents-an everyday situation in which current state-of-the-art speech recognition models often fail. The model can also be used to qualitatively explain behavioral data on human speech learning and derive predictions for future experiments.
Systematic validation of non-equilibrium thermochemical models using Bayesian inference
Miki, Kenji
2015-10-01
© 2015 Elsevier Inc. The validation process proposed by Babuška et al. [1] is applied to thermochemical models describing post-shock flow conditions. In this validation approach, experimental data is involved only in the calibration of the models, and the decision process is based on quantities of interest (QoIs) predicted on scenarios that are not necessarily amenable experimentally. Moreover, uncertainties present in the experimental data, as well as those resulting from an incomplete physical model description, are propagated to the QoIs. We investigate four commonly used thermochemical models: a one-temperature model (which assumes thermal equilibrium among all inner modes), and two-temperature models developed by Macheret et al. [2], Marrone and Treanor [3], and Park [4]. Up to 16 uncertain parameters are estimated using Bayesian updating based on the latest absolute volumetric radiance data collected at the Electric Arc Shock Tube (EAST) installed inside the NASA Ames Research Center. Following the solution of the inverse problems, the forward problems are solved in order to predict the radiative heat flux, QoI, and examine the validity of these models. Our results show that all four models are invalid, but for different reasons: the one-temperature model simply fails to reproduce the data while the two-temperature models exhibit unacceptably large uncertainties in the QoI predictions.
Park, Taeyoung; Jeong, Jong-Hyeon; Lee, Jae Won
2012-08-15
There is often an interest in estimating a residual life function as a summary measure of survival data. For ease in presentation of the potential therapeutic effect of a new drug, investigators may summarize survival data in terms of the remaining life years of patients. Under heavy right censoring, however, some reasonably high quantiles (e.g., median) of a residual lifetime distribution cannot be always estimated via a popular nonparametric approach on the basis of the Kaplan-Meier estimator. To overcome the difficulties in dealing with heavily censored survival data, this paper develops a Bayesian nonparametric approach that takes advantage of a fully model-based but highly flexible probabilistic framework. We use a Dirichlet process mixture of Weibull distributions to avoid strong parametric assumptions on the unknown failure time distribution, making it possible to estimate any quantile residual life function under heavy censoring. Posterior computation through Markov chain Monte Carlo is straightforward and efficient because of conjugacy properties and partial collapse. We illustrate the proposed methods by using both simulated data and heavily censored survival data from a recent breast cancer clinical trial conducted by the National Surgical Adjuvant Breast and Bowel Project. Copyright © 2012 John Wiley & Sons, Ltd.
Baur, Brittany; Bozdag, Serdar
2015-04-01
One of the challenging and important computational problems in systems biology is to infer gene regulatory networks (GRNs) of biological systems. Several methods that exploit gene expression data have been developed to tackle this problem. In this study, we propose the use of copy number and DNA methylation data to infer GRNs. We developed an algorithm that scores regulatory interactions between genes based on canonical correlation analysis. In this algorithm, copy number or DNA methylation variables are treated as potential regulator variables, and expression variables are treated as potential target variables. We first validated that the canonical correlation analysis method is able to infer true interactions in high accuracy. We showed that the use of DNA methylation or copy number datasets leads to improved inference over steady-state expression. Our results also showed that epigenetic and structural information could be used to infer directionality of regulatory interactions. Additional improvements in GRN inference can be gleaned from incorporating the result in an informative prior in a dynamic Bayesian algorithm. This is the first study that incorporates copy number and DNA methylation into an informative prior in dynamic Bayesian framework. By closely examining top-scoring interactions with different sources of epigenetic or structural information, we also identified potential novel regulatory interactions.
Hernández, Mario R.; Francés, Félix
2015-04-01
One phase of the hydrological models implementation process, significantly contributing to the hydrological predictions uncertainty, is the calibration phase in which values of the unknown model parameters are tuned by optimizing an objective function. An unsuitable error model (e.g. Standard Least Squares or SLS) introduces noise into the estimation of the parameters. The main sources of this noise are the input errors and the hydrological model structural deficiencies. Thus, the biased calibrated parameters cause the divergence model phenomenon, where the errors variance of the (spatially and temporally) forecasted flows far exceeds the errors variance in the fitting period, and provoke the loss of part or all of the physical meaning of the modeled processes. In other words, yielding a calibrated hydrological model which works well, but not for the right reasons. Besides, an unsuitable error model yields a non-reliable predictive uncertainty assessment. Hence, with the aim of prevent all these undesirable effects, this research focuses on the Bayesian joint inference (BJI) of both the hydrological and error model parameters, considering a general additive (GA) error model that allows for correlation, non-stationarity (in variance and bias) and non-normality of model residuals. As hydrological model, it has been used a conceptual distributed model called TETIS, with a particular split structure of the effective model parameters. Bayesian inference has been performed with the aid of a Markov Chain Monte Carlo (MCMC) algorithm called Dream-ZS. MCMC algorithm quantifies the uncertainty of the hydrological and error model parameters by getting the joint posterior probability distribution, conditioned on the observed flows. The BJI methodology is a very powerful and reliable tool, but it must be used correctly this is, if non-stationarity in errors variance and bias is modeled, the Total Laws must be taken into account. The results of this research show that the
Bayesian inference for dynamic transcriptional regulation; the Hes1 system as a case study.
Heron, Elizabeth A; Finkenstädt, Bärbel; Rand, David A
2007-10-01
In this study, we address the problem of estimating the parameters of regulatory networks and provide the first application of Markov chain Monte Carlo (MCMC) methods to experimental data. As a case study, we consider a stochastic model of the Hes1 system expressed in terms of stochastic differential equations (SDEs) to which rigorous likelihood methods of inference can be applied. When fitting continuous-time stochastic models to discretely observed time series the lengths of the sampling intervals are important, and much of our study addresses the problem when the data are sparse. We estimate the parameters of an autoregulatory network providing results both for simulated and real experimental data from the Hes1 system. We develop an estimation algorithm using MCMC techniques which are flexible enough to allow for the imputation of latent data on a finer time scale and the presence of prior information about parameters which may be informed from other experiments as well as additional measurement error.
FPGA Acceleration of the phylogenetic likelihood function for Bayesian MCMC inference methods
Bakos Jason D
2010-04-01
Full Text Available Abstract Background Likelihood (ML-based phylogenetic inference has become a popular method for estimating the evolutionary relationships among species based on genomic sequence data. This method is used in applications such as RAxML, GARLI, MrBayes, PAML, and PAUP. The Phylogenetic Likelihood Function (PLF is an important kernel computation for this method. The PLF consists of a loop with no conditional behavior or dependencies between iterations. As such it contains a high potential for exploiting parallelism using micro-architectural techniques. In this paper, we describe a technique for mapping the PLF and supporting logic onto a Field Programmable Gate Array (FPGA-based co-processor. By leveraging the FPGA's on-chip DSP modules and the high-bandwidth local memory attached to the FPGA, the resultant co-processor can accelerate ML-based methods and outperform state-of-the-art multi-core processors. Results We use the MrBayes 3 tool as a framework for designing our co-processor. For large datasets, we estimate that our accelerated MrBayes, if run on a current-generation FPGA, achieves a 10× speedup relative to software running on a state-of-the-art server-class microprocessor. The FPGA-based implementation achieves its performance by deeply pipelining the likelihood computations, performing multiple floating-point operations in parallel, and through a natural log approximation that is chosen specifically to leverage a deeply pipelined custom architecture. Conclusions Heterogeneous computing, which combines general-purpose processors with special-purpose co-processors such as FPGAs and GPUs, is a promising approach for high-performance phylogeny inference as shown by the growing body of literature in this field. FPGAs in particular are well-suited for this task because of their low power consumption as compared to many-core processors and Graphics Processor Units (GPUs 1.
Rapid molecular evolution of human bocavirus revealed by Bayesian coalescent inference.
Zehender, Gianguglielmo; De Maddalena, Chiara; Canuti, Marta; Zappa, Alessandra; Amendola, Antonella; Lai, Alessia; Galli, Massimo; Tanzi, Elisabetta
2010-03-01
Human bocavirus (HBoV) is a linear single-stranded DNA virus belonging to the Parvoviridae family that has recently been isolated from the upper respiratory tract of children with acute respiratory infection. All of the strains observed so far segregate into two genotypes (1 and 2) with a low level of polymorphism. Given the recent description of the infection and the lack of epidemiological and molecular data, we estimated the virus's rates of molecular evolution and population dynamics. A dataset of forty-nine dated VP2 sequences, including also eight new isolates obtained from pharyngeal swabs of Italian patients with acute respiratory tract infections, was submitted to phylogenetic analysis. The model parameters, evolutionary rates and population dynamics were co-estimated using a Bayesian Markov Chain Monte Carlo approach, and site-specific positive and negative selection was also investigated. Recombination was investigated by seven different methods and one suspected recombinant strain was excluded from further analysis. The estimated mean evolutionary rate of HBoV was 8.6x10(-4)subs/site/year, and that of the 1st+2nd codon positions was more than 15 times less than that of the 3rd codon position. Viral population dynamics analysis revealed that the two known genotypes diverged recently (mean tMRCA: 24 years), and that the epidemic due to HBoV genotype 2 grew exponentially at a rate of 1.01year(-1). Selection analysis of the partial VP2 showed that 8.5% of sites were under significant negative pressure and the absence of positive selection. Our results show that, like other parvoviruses, HBoV is characterised by a rapid evolution. The low level of polymorphism is probably due to a relatively recent divergence between the circulating genotypes and strong purifying selection acting on viral antigens.
Pablo Fresia
Full Text Available Insect pest phylogeography might be shaped both by biogeographic events and by human influence. Here, we conducted an approximate Bayesian computation (ABC analysis to investigate the phylogeography of the New World screwworm fly, Cochliomyia hominivorax, with the aim of understanding its population history and its order and time of divergence. Our ABC analysis supports that populations spread from North to South in the Americas, in at least two different moments. The first split occurred between the North/Central American and South American populations in the end of the Last Glacial Maximum (15,300-19,000 YBP. The second split occurred between the North and South Amazonian populations in the transition between the Pleistocene and the Holocene eras (9,100-11,000 YBP. The species also experienced population expansion. Phylogenetic analysis likewise suggests this north to south colonization and Maxent models suggest an increase in the number of suitable areas in South America from the past to present. We found that the phylogeographic patterns observed in C. hominivorax cannot be explained only by climatic oscillations and can be connected to host population histories. Interestingly we found these patterns are very coincident with general patterns of ancient human movements in the Americas, suggesting that humans might have played a crucial role in shaping the distribution and population structure of this insect pest. This work presents the first hypothesis test regarding the processes that shaped the current phylogeographic structure of C. hominivorax and represents an alternate perspective on investigating the problem of insect pests.
Final Report: Large-Scale Optimization for Bayesian Inference in Complex Systems
Ghattas, Omar [The University of Texas at Austin
2013-10-15
The SAGUARO (Scalable Algorithms for Groundwater Uncertainty Analysis and Robust Optimiza- tion) Project focuses on the development of scalable numerical algorithms for large-scale Bayesian inversion in complex systems that capitalize on advances in large-scale simulation-based optimiza- tion and inversion methods. Our research is directed in three complementary areas: efficient approximations of the Hessian operator, reductions in complexity of forward simulations via stochastic spectral approximations and model reduction, and employing large-scale optimization concepts to accelerate sampling. Our efforts are integrated in the context of a challenging testbed problem that considers subsurface reacting flow and transport. The MIT component of the SAGUARO Project addresses the intractability of conventional sampling methods for large-scale statistical inverse problems by devising reduced-order models that are faithful to the full-order model over a wide range of parameter values; sampling then employs the reduced model rather than the full model, resulting in very large computational savings. Results indicate little effect on the computed posterior distribution. On the other hand, in the Texas-Georgia Tech component of the project, we retain the full-order model, but exploit inverse problem structure (adjoint-based gradients and partial Hessian information of the parameter-to- observation map) to implicitly extract lower dimensional information on the posterior distribution; this greatly speeds up sampling methods, so that fewer sampling points are needed. We can think of these two approaches as "reduce then sample" and "sample then reduce." In fact, these two approaches are complementary, and can be used in conjunction with each other. Moreover, they both exploit deterministic inverse problem structure, in the form of adjoint-based gradient and Hessian information of the underlying parameter-to-observation map, to achieve their speedups.
Davis, A. D.; Huan, X.; Heimbach, P.; Marzouk, Y.
2017-12-01
Borehole data are essential for calibrating ice sheet models. However, field expeditions for acquiring borehole data are often time-consuming, expensive, and dangerous. It is thus essential to plan the best sampling locations that maximize the value of data while minimizing costs and risks. We present an uncertainty quantification (UQ) workflow based on rigorous probability framework to achieve these objectives. First, we employ an optimal experimental design (OED) procedure to compute borehole locations that yield the highest expected information gain. We take into account practical considerations of location accessibility (e.g., proximity to research sites, terrain, and ice velocity may affect feasibility of drilling) and robustness (e.g., real-time constraints such as weather may force researchers to drill at sub-optimal locations near those originally planned), by incorporating a penalty reflecting accessibility as well as sensitivity to deviations from the optimal locations. Next, we extract vertical temperature profiles from these boreholes and formulate a Bayesian inverse problem to reconstruct past surface temperatures. Using a model of temperature advection/diffusion, the top boundary condition (corresponding to surface temperatures) is calibrated via efficient Markov chain Monte Carlo (MCMC). The overall procedure can then be iterated to choose new optimal borehole locations for the next expeditions.Through this work, we demonstrate powerful UQ methods for designing experiments, calibrating models, making predictions, and assessing sensitivity--all performed under an uncertain environment. We develop a theoretical framework as well as practical software within an intuitive workflow, and illustrate their usefulness for combining data and models for environmental and climate research.
Mario A Pardo
Full Text Available We inferred the population densities of blue whales (Balaenoptera musculus and short-beaked common dolphins (Delphinus delphis in the Northeast Pacific Ocean as functions of the water-column's physical structure by implementing hierarchical models in a Bayesian framework. This approach allowed us to propagate the uncertainty of the field observations into the inference of species-habitat relationships and to generate spatially explicit population density predictions with reduced effects of sampling heterogeneity. Our hypothesis was that the large-scale spatial distributions of these two cetacean species respond primarily to ecological processes resulting from shoaling and outcropping of the pycnocline in regions of wind-forced upwelling and eddy-like circulation. Physically, these processes affect the thermodynamic balance of the water column, decreasing its volume and thus the height of the absolute dynamic topography (ADT. Biologically, they lead to elevated primary productivity and persistent aggregation of low-trophic-level prey. Unlike other remotely sensed variables, ADT provides information about the structure of the entire water column and it is also routinely measured at high spatial-temporal resolution by satellite altimeters with uniform global coverage. Our models provide spatially explicit population density predictions for both species, even in areas where the pycnocline shoals but does not outcrop (e.g. the Costa Rica Dome and the North Equatorial Countercurrent thermocline ridge. Interannual variations in distribution during El Niño anomalies suggest that the population density of both species decreases dramatically in the Equatorial Cold Tongue and the Costa Rica Dome, and that their distributions retract to particular areas that remain productive, such as the more oceanic waters in the central California Current System, the northern Gulf of California, the North Equatorial Countercurrent thermocline ridge, and the more
Weyant, Anja; Wood-Vasey, W. Michael [Pittsburgh Particle Physics, Astrophysics, and Cosmology Center (PITT PACC), Physics and Astronomy Department, University of Pittsburgh, Pittsburgh, PA 15260 (United States); Schafer, Chad, E-mail: anw19@pitt.edu [Department of Statistics, Carnegie Mellon University, Pittsburgh, PA 15213 (United States)
2013-02-20
Cosmological inference becomes increasingly difficult when complex data-generating processes cannot be modeled by simple probability distributions. With the ever-increasing size of data sets in cosmology, there is an increasing burden placed on adequate modeling; systematic errors in the model will dominate where previously these were swamped by statistical errors. For example, Gaussian distributions are an insufficient representation for errors in quantities like photometric redshifts. Likewise, it can be difficult to quantify analytically the distribution of errors that are introduced in complex fitting codes. Without a simple form for these distributions, it becomes difficult to accurately construct a likelihood function for the data as a function of parameters of interest. Approximate Bayesian computation (ABC) provides a means of probing the posterior distribution when direct calculation of a sufficiently accurate likelihood is intractable. ABC allows one to bypass direct calculation of the likelihood but instead relies upon the ability to simulate the forward process that generated the data. These simulations can naturally incorporate priors placed on nuisance parameters, and hence these can be marginalized in a natural way. We present and discuss ABC methods in the context of supernova cosmology using data from the SDSS-II Supernova Survey. Assuming a flat cosmology and constant dark energy equation of state, we demonstrate that ABC can recover an accurate posterior distribution. Finally, we show that ABC can still produce an accurate posterior distribution when we contaminate the sample with Type IIP supernovae.
Weyant, Anja; Wood-Vasey, W. Michael; Schafer, Chad
2013-01-01
Cosmological inference becomes increasingly difficult when complex data-generating processes cannot be modeled by simple probability distributions. With the ever-increasing size of data sets in cosmology, there is an increasing burden placed on adequate modeling; systematic errors in the model will dominate where previously these were swamped by statistical errors. For example, Gaussian distributions are an insufficient representation for errors in quantities like photometric redshifts. Likewise, it can be difficult to quantify analytically the distribution of errors that are introduced in complex fitting codes. Without a simple form for these distributions, it becomes difficult to accurately construct a likelihood function for the data as a function of parameters of interest. Approximate Bayesian computation (ABC) provides a means of probing the posterior distribution when direct calculation of a sufficiently accurate likelihood is intractable. ABC allows one to bypass direct calculation of the likelihood but instead relies upon the ability to simulate the forward process that generated the data. These simulations can naturally incorporate priors placed on nuisance parameters, and hence these can be marginalized in a natural way. We present and discuss ABC methods in the context of supernova cosmology using data from the SDSS-II Supernova Survey. Assuming a flat cosmology and constant dark energy equation of state, we demonstrate that ABC can recover an accurate posterior distribution. Finally, we show that ABC can still produce an accurate posterior distribution when we contaminate the sample with Type IIP supernovae.
Karras, D A; Mertzios, G B
2009-01-01
A novel approach is presented in this paper for improving anisotropic diffusion PDE models, based on the Perona–Malik equation. A solution is proposed from an engineering perspective to adaptively estimate the parameters of the regularizing function in this equation. The goal of such a new adaptive diffusion scheme is to better preserve edges when the anisotropic diffusion PDE models are applied to image enhancement tasks. The proposed adaptive parameter estimation in the anisotropic diffusion PDE model involves self-organizing maps and Bayesian inference to define edge probabilities accurately. The proposed modifications attempt to capture not only simple edges but also difficult textural edges and incorporate their probability in the anisotropic diffusion model. In the context of the application of PDE models to image processing such adaptive schemes are closely related to the discrete image representation problem and the investigation of more suitable discretization algorithms using constraints derived from image processing theory. The proposed adaptive anisotropic diffusion model illustrates these concepts when it is numerically approximated by various discretization schemes in a database of magnetic resonance images (MRI), where it is shown to be efficient in image filtering and restoration applications
Xing, Junliang; Ai, Haizhou; Liu, Liwei; Lao, Shihong
2011-06-01
Multiple object tracking (MOT) is a very challenging task yet of fundamental importance for many practical applications. In this paper, we focus on the problem of tracking multiple players in sports video which is even more difficult due to the abrupt movements of players and their complex interactions. To handle the difficulties in this problem, we present a new MOT algorithm which contributes both in the observation modeling level and in the tracking strategy level. For the observation modeling, we develop a progressive observation modeling process that is able to provide strong tracking observations and greatly facilitate the tracking task. For the tracking strategy, we propose a dual-mode two-way Bayesian inference approach which dynamically switches between an offline general model and an online dedicated model to deal with single isolated object tracking and multiple occluded object tracking integrally by forward filtering and backward smoothing. Extensive experiments on different kinds of sports videos, including football, basketball, as well as hockey, demonstrate the effectiveness and efficiency of the proposed method.
Höhna, Sebastian; May, Michael R; Moore, Brian R
2016-03-01
Many fundamental questions in evolutionary biology entail estimating rates of lineage diversification (speciation-extinction) that are modeled using birth-death branching processes. We leverage recent advances in branching-process theory to develop a flexible Bayesian framework for specifying diversification models-where rates are constant, vary continuously, or change episodically through time-and implement numerical methods to estimate parameters of these models from molecular phylogenies, even when species sampling is incomplete. We enable both statistical inference and efficient simulation under these models. We also provide robust methods for comparing the relative and absolute fit of competing branching-process models to a given tree, thereby providing rigorous tests of biological hypotheses regarding patterns and processes of lineage diversification. The source code for TESS is freely available at http://cran.r-project.org/web/packages/TESS/ CONTACT: Sebastian.Hoehna@gmail.com. © The Author 2015. Published by Oxford University Press. All rights reserved. For Permissions, please e-mail: journals.permissions@oup.com.
von Hansen, Yann; Mehlich, Alexander; Pelz, Benjamin; Rief, Matthias; Netz, Roland R
2012-09-01
The thermal fluctuations of micron-sized beads in dual trap optical tweezer experiments contain complete dynamic information about the viscoelastic properties of the embedding medium and-if present-macromolecular constructs connecting the two beads. To quantitatively interpret the spectral properties of the measured signals, a detailed understanding of the instrumental characteristics is required. To this end, we present a theoretical description of the signal processing in a typical dual trap optical tweezer experiment accounting for polarization crosstalk and instrumental noise and discuss the effect of finite statistics. To infer the unknown parameters from experimental data, a maximum likelihood method based on the statistical properties of the stochastic signals is derived. In a first step, the method can be used for calibration purposes: We propose a scheme involving three consecutive measurements (both traps empty, first one occupied and second empty, and vice versa), by which all instrumental and physical parameters of the setup are determined. We test our approach for a simple model system, namely a pair of unconnected, but hydrodynamically interacting spheres. The comparison to theoretical predictions based on instantaneous as well as retarded hydrodynamics emphasizes the importance of hydrodynamic retardation effects due to vorticity diffusion in the fluid. For more complex experimental scenarios, where macromolecular constructs are tethered between the two beads, the same maximum likelihood method in conjunction with dynamic deconvolution theory will in a second step allow one to determine the viscoelastic properties of the tethered element connecting the two beads.
Closed-form summations of Dowker's and related trigonometric sums
Cvijović, Djurdje; Srivastava, H M
2012-01-01
Through a unified and relatively simple approach which uses complex contour integrals, particularly convenient integration contours and calculus of residues, closed-form summation formulas for 12 very general families of trigonometric sums are deduced. One of them is a family of cosecant sums which was first summed in closed form in a series of papers by Dowker (1987 Phys. Rev. D 36 3095–101; 1989 J. Math. Phys. 30 770–3; 1992 J. Phys. A: Math. Gen. 25 2641–8), whose method has inspired our work in this area. All of the formulas derived here involve the higher-order Bernoulli polynomials. This article is part of a special issue of Journal of Physics A: Mathematical and Theoretical in honour of Stuart Dowker's 75th birthday devoted to ‘Applications of zeta functions and other spectral functions in mathematics and physics’. (paper)
Inverse Kinematics With Closed Form Solution For Denso Robot Manipulator
Ikhsan Eka Prasetia
2015-03-01
Full Text Available In this paper, the forward kinematics and inverse kinematics used on the Denso robot manipulator which has a 6-DOF. The forward kinematics will result in the desired position by end-effector, while inverse kinematics produce angel on each joint. Inverse kinematics problem are very difficult, therefor to obtain the solution of inverse kinematics using closed form solution with geometry approach. The simulation result obtained from forward kinematics and inverse kinematics is determining desired position by Denso robot manipulator. Forward kinematics produce the desired position by the end-effector. Inverse kinematics produce joint angle, where the inverse kinematics produce eight conditions obtained from closed form solution with geometry approach to reach the desired position by the end-effector.
Closed-form summations of Dowker's and related trigonometric sums
Cvijović, Djurdje; Srivastava, H. M.
2012-09-01
Through a unified and relatively simple approach which uses complex contour integrals, particularly convenient integration contours and calculus of residues, closed-form summation formulas for 12 very general families of trigonometric sums are deduced. One of them is a family of cosecant sums which was first summed in closed form in a series of papers by Dowker (1987 Phys. Rev. D 36 3095-101 1989 J. Math. Phys. 30 770-3 1992 J. Phys. A: Math. Gen. 25 2641-8), whose method has inspired our work in this area. All of the formulas derived here involve the higher-order Bernoulli polynomials. This article is part of a special issue of Journal of Physics A: Mathematical and Theoretical in honour of Stuart Dowker's 75th birthday devoted to ‘Applications of zeta functions and other spectral functions in mathematics and physics’.
Inverse Kinematics With Closed Form Solution For Denso Robot Manipulator
Ikhsan Eka Prasetia; Trihastuti Agustinah
2015-01-01
In this paper, the forward kinematics and inverse kinematics used on the Denso robot manipulator which has a 6-DOF. The forward kinematics will result in the desired position by end-effector, while inverse kinematics produce angel on each joint. Inverse kinematics problem are very difficult, therefor to obtain the solution of inverse kinematics using closed form solution with geometry approach. The simulation result obtained from forward kinematics and inverse kinematics is determining desire...
A Closed Form Solution for an Unorthodox Trigonometric Integral
Wu, Yan
2009-01-01
A closed form solution for the trigonometric integral [integral]sec[superscript 2k+1]xdx, k=0,1,2,..., is presented in this article. The result will fill the gap in another trigonometric integral [integral]sec[superscript 2m+1] x tan[superscript 2n]xdx, which is neglected by most of the calculus textbooks due to its foreseeable unorthodox solution…
Bayesian Predictive Models for Rayleigh Wind Speed
Shahirinia, Amir; Hajizadeh, Amin; Yu, David C
2017-01-01
predictive model of the wind speed aggregates the non-homogeneous distributions into a single continuous distribution. Therefore, the result is able to capture the variation among the probability distributions of the wind speeds at the turbines’ locations in a wind farm. More specifically, instead of using...... a wind speed distribution whose parameters are known or estimated, the parameters are considered as random whose variations are according to probability distributions. The Bayesian predictive model for a Rayleigh which only has a single model scale parameter has been proposed. Also closed-form posterior...... and predictive inferences under different reasonable choices of prior distribution in sensitivity analysis have been presented....
Liu, Fang; Eugenio, Evercita C
2018-04-01
Beta regression is an increasingly popular statistical technique in medical research for modeling of outcomes that assume values in (0, 1), such as proportions and patient reported outcomes. When outcomes take values in the intervals [0,1), (0,1], or [0,1], zero-or-one-inflated beta (zoib) regression can be used. We provide a thorough review on beta regression and zoib regression in the modeling, inferential, and computational aspects via the likelihood-based and Bayesian approaches. We demonstrate the statistical and practical importance of correctly modeling the inflation at zero/one rather than ad hoc replacing them with values close to zero/one via simulation studies; the latter approach can lead to biased estimates and invalid inferences. We show via simulation studies that the likelihood-based approach is computationally faster in general than MCMC algorithms used in the Bayesian inferences, but runs the risk of non-convergence, large biases, and sensitivity to starting values in the optimization algorithm especially with clustered/correlated data, data with sparse inflation at zero and one, and data that warrant regularization of the likelihood. The disadvantages of the regular likelihood-based approach make the Bayesian approach an attractive alternative in these cases. Software packages and tools for fitting beta and zoib regressions in both the likelihood-based and Bayesian frameworks are also reviewed.
Møller, Jesper
(This text written by Jesper Møller, Aalborg University, is submitted for the collection ‘Stochastic Geometry: Highlights, Interactions and New Perspectives', edited by Wilfrid S. Kendall and Ilya Molchanov, to be published by ClarendonPress, Oxford, and planned to appear as Section 4.1 with the ......(This text written by Jesper Møller, Aalborg University, is submitted for the collection ‘Stochastic Geometry: Highlights, Interactions and New Perspectives', edited by Wilfrid S. Kendall and Ilya Molchanov, to be published by ClarendonPress, Oxford, and planned to appear as Section 4.......1 with the title ‘Inference'.) This contribution concerns statistical inference for parametric models used in stochastic geometry and based on quick and simple simulation free procedures as well as more comprehensive methods using Markov chain Monte Carlo (MCMC) simulations. Due to space limitations the focus...
Comments on "A Closed-Form Solution to Tensor Voting: Theory and Applications".
Maggiori, Emmanuel; Lotito, Pablo; Manterola, Hugo Luis; del Fresno, Mariana
2014-12-01
We comment on a paper that describes a closed-form formulation to Tensor Voting, a technique to perceptually group clouds of points, usually applied to infer features in images. The authors proved an analytic solution to the technique, a highly relevant contribution considering that the original formulation required numerical integration, a time-consuming task. Their work constitutes the first closed-form expression for the Tensor Voting framework. In this work we first observe that the proposed formulation leads to unexpected results which do not satisfy the constraints for a Tensor Voting output, hence they cannot be interpreted. Given that the closed-form expression is said to be an analytic equivalent solution, unexpected outputs should not be encountered unless there are flaws in the proof. We analyzed the underlying math to find which were the causes of these unexpected results. In this commentary we show that their proposal does not in fact provide a proper analytic solution to Tensor Voting and we indicate the flaws in the proof.
Kim, Daesang
2016-01-06
A new Bayesian inference method has been developed and applied to Furan shock tube experimental data for efficient statistical inferences of the Arrhenius parameters of two OH radical consumption reactions. The collected experimental data, which consist of time series signals of OH radical concentrations of 14 shock tube experiments, may require several days for MCMC computations even with the support of a fast surrogate of the combustion simulation model, while the new method reduces it to several hours by splitting the process into two steps of MCMC: the first inference of rate constants and the second inference of the Arrhenius parameters. Each step has low dimensional parameter spaces and the second step does not need the executions of the combustion simulation. Furthermore, the new approach has more flexibility in choosing the ranges of the inference parameters, and the higher speed and flexibility enable the more accurate inferences and the analyses of the propagation of errors in the measured temperatures and the alignment of the experimental time to the inference results.
Choi, Sang-Hyeon; Lee, Ikjin; Jeong, Cheol-Ho
2016-01-01
Sabine absorption coefficient is a widely used one deduced from reverberation time measurements via the Sabine equation. First- and second-level Bayesian analysis are used to estimate the flow resistivity of a sound absorber and the influences of the test chambers from Sabine absorption...... coefficients measured in 13 different reverberation chambers. The first-level Bayesian analysis is more general than the second-level Bayesian analysis. Sharper posterior distribution can be acquired by the second-level Bayesian analysis than the one by the first-level Bayesian analysis because more data...... are used to set more reliable prior distribution. The estimated room’s influences by the first- and the second-level Bayesian analyses are similar to the estimated results by the mean absolute error minimization....
Simon Boitard
2016-03-01
Full Text Available Inferring the ancestral dynamics of effective population size is a long-standing question in population genetics, which can now be tackled much more accurately thanks to the massive genomic data available in many species. Several promising methods that take advantage of whole-genome sequences have been recently developed in this context. However, they can only be applied to rather small samples, which limits their ability to estimate recent population size history. Besides, they can be very sensitive to sequencing or phasing errors. Here we introduce a new approximate Bayesian computation approach named PopSizeABC that allows estimating the evolution of the effective population size through time, using a large sample of complete genomes. This sample is summarized using the folded allele frequency spectrum and the average zygotic linkage disequilibrium at different bins of physical distance, two classes of statistics that are widely used in population genetics and can be easily computed from unphased and unpolarized SNP data. Our approach provides accurate estimations of past population sizes, from the very first generations before present back to the expected time to the most recent common ancestor of the sample, as shown by simulations under a wide range of demographic scenarios. When applied to samples of 15 or 25 complete genomes in four cattle breeds (Angus, Fleckvieh, Holstein and Jersey, PopSizeABC revealed a series of population declines, related to historical events such as domestication or modern breed creation. We further highlight that our approach is robust to sequencing errors, provided summary statistics are computed from SNPs with common alleles.
Gogoshin, Grigoriy; Boerwinkle, Eric; Rodin, Andrei S
2017-04-01
Bayesian network (BN) reconstruction is a prototypical systems biology data analysis approach that has been successfully used to reverse engineer and model networks reflecting different layers of biological organization (ranging from genetic to epigenetic to cellular pathway to metabolomic). It is especially relevant in the context of modern (ongoing and prospective) studies that generate heterogeneous high-throughput omics datasets. However, there are both theoretical and practical obstacles to the seamless application of BN modeling to such big data, including computational inefficiency of optimal BN structure search algorithms, ambiguity in data discretization, mixing data types, imputation and validation, and, in general, limited scalability in both reconstruction and visualization of BNs. To overcome these and other obstacles, we present BNOmics, an improved algorithm and software toolkit for inferring and analyzing BNs from omics datasets. BNOmics aims at comprehensive systems biology-type data exploration, including both generating new biological hypothesis and testing and validating the existing ones. Novel aspects of the algorithm center around increasing scalability and applicability to varying data types (with different explicit and implicit distributional assumptions) within the same analysis framework. An output and visualization interface to widely available graph-rendering software is also included. Three diverse applications are detailed. BNOmics was originally developed in the context of genetic epidemiology data and is being continuously optimized to keep pace with the ever-increasing inflow of available large-scale omics datasets. As such, the software scalability and usability on the less than exotic computer hardware are a priority, as well as the applicability of the algorithm and software to the heterogeneous datasets containing many data types-single-nucleotide polymorphisms and other genetic/epigenetic/transcriptome variables, metabolite
Introduction to Bayesian statistics
Bolstad, William M
2017-01-01
There is a strong upsurge in the use of Bayesian methods in applied statistical analysis, yet most introductory statistics texts only present frequentist methods. Bayesian statistics has many important advantages that students should learn about if they are going into fields where statistics will be used. In this Third Edition, four newly-added chapters address topics that reflect the rapid advances in the field of Bayesian staistics. The author continues to provide a Bayesian treatment of introductory statistical topics, such as scientific data gathering, discrete random variables, robust Bayesian methods, and Bayesian approaches to inferenfe cfor discrete random variables, bionomial proprotion, Poisson, normal mean, and simple linear regression. In addition, newly-developing topics in the field are presented in four new chapters: Bayesian inference with unknown mean and variance; Bayesian inference for Multivariate Normal mean vector; Bayesian inference for Multiple Linear RegressionModel; and Computati...
Decoupled Closed-Form Solution for Humanoid Lower Limb Kinematics
Alejandro Said
2015-01-01
Full Text Available This paper presents an explicit, omnidirectional, analytical, and decoupled closed-form solution for the lower limb kinematics of the humanoid robot NAO. The paper starts by decoupling the position and orientation analysis from the overall Denavit-Hartenberg (DH transformation matrices. Here, the joint activation sequence for the DH matrices is based on the geometry of a triangle. Furthermore, the implementation of a forward and a reversed kinematic analysis for the support and swing phase equations is developed to avoid matrix inversion. The allocation of constant transformations allows the position and orientation end-coordinate systems to be aligned with each other. Also, the redefinition of the DH transformations and the use of constraints allow decoupling the shared DOF between the legs and the torso. Finally, a geometric approach to avoid the singularities during the walking process is indicated. Numerical data is presented along with an experimental implementation to prove the validity of the analytical results.
Closed form fourier-based transmit beamforming for MIMO radar
Lipor, John J.
2014-05-01
In multiple-input multiple-output (MIMO) radar setting, it is often desirable to design correlated waveforms such that power is transmitted only to a given set of locations, a process known as beampattern design. To design desired beam-pattern, current research uses iterative algorithms, first to synthesize the waveform covariance matrix, R, then to design the actual waveforms to realize R. In contrast to this, we present a closed form method to design R that exploits discrete Fourier transform and Toeplitz matrix. The resulting covariance matrix fulfills the practical constraints and performance is similar to that of iterative methods. Next, we present a radar architecture for the desired beampattern that does not require the synthesis of covariance matrix nor the design of correlated waveforms. © 2014 IEEE.
Closed-Form Expressions for the Matrix Exponential
F. De Zela
2014-04-01
Full Text Available We discuss a method to obtain closed-form expressions of f(A, where f is an analytic function and A a square, diagonalizable matrix. The method exploits the Cayley–Hamilton theorem and has been previously reported using tools that are perhaps not sufficiently appealing to physicists. Here, we derive the results on which the method is based by using tools most commonly employed by physicists. We show the advantages of the method in comparison with standard approaches, especially when dealing with the exponential of low-dimensional matrices. In contrast to other approaches that require, e.g., solving differential equations, the present method only requires the construction of the inverse of the Vandermonde matrix. We show the advantages of the method by applying it to different cases, mostly restricting the calculational effort to the handling of two-by-two matrices.
Some closed form expressions for the generalized secant integrals
Nadarajah, Saralees
2007-01-01
The generalized secant integrals of the form I a (ψ,b)=b a ∫ 0 ψ exp(-bsecθ)(secθ) a dθ for b>0 and 0 a (ψ,b) have been known except when both a and ψ are fixed. In this note, we provide several closed form expressions for I a (ψ,b) applicable for a wide range of values of a and b. We establish their numerical accuracy over the methods presented in Michieli [1998. Point kernel calculations of dose fields from line sources using expanded polynomial form of buildup factor data: generalized secant integral series representations. Radiat. Phys. Chem. 51, 121-128; 2001. Some properties of generalized secant integrals: extended definition and recurrence relations. Radiat. Phys. Chem. 60, 551-554]. Finally, a simple computer program is provided for I a (ψ,b) that could be used widely
Jameel, M. Y.; Brewer, S.; Fiorella, R.; Tipple, B. J.; Bowen, G. J.; Terry, S.
2017-12-01
Public water supply systems (PWSS) are complex distribution systems and critical infrastructure, making them vulnerable to physical disruption and contamination. Exploring the susceptibility of PWSS to such perturbations requires detailed knowledge of the supply system structure and operation. Although the physical structure of supply systems (i.e., pipeline connection) is usually well documented for developed cities, the actual flow patterns of water in these systems are typically unknown or estimated based on hydrodynamic models with limited observational validation. Here, we present a novel method for mapping the flow structure of water in a large, complex PWSS, building upon recent work highlighting the potential of stable isotopes of water (SIW) to document water management practices within complex PWSS. We sampled a major water distribution system of the Salt Lake Valley, Utah, measuring SIW of water sources, treatment facilities, and numerous sites within in the supply system. We then developed a hierarchical Bayesian (HB) isotope mixing model to quantify the proportion of water supplied by different sources at sites within the supply system. Known production volumes and spatial distance effects were used to define the prior probabilities for each source; however, we did not include other physical information about the supply system. Our results were in general agreement with those obtained by hydrodynamic models and provide quantitative estimates of contributions of different water sources to a given site along with robust estimates of uncertainty. Secondary properties of the supply system, such as regions of "static" and "dynamic" source (e.g., regions supplied dominantly by one source vs. those experiencing active mixing between multiple sources), can be inferred from the results. The isotope-based HB isotope mixing model offers a new investigative technique for analyzing PWSS and documenting aspects of supply system structure and operation that are
Single-spin precessing gravitational waveform in closed form
Lundgren, Andrew; O'Shaughnessy, R.
2014-02-01
In coming years, gravitational-wave detectors should find black hole-neutron star (BH-NS) binaries, potentially coincident with astronomical phenomena like short gamma ray bursts. These binaries are expected to precess. Gravitational-wave science requires a tractable model for precessing binaries, to disentangle precession physics from other phenomena like modified strong field gravity, tidal deformability, or Hubble flow; and to measure compact object masses, spins, and alignments. Moreover, current searches for gravitational waves from compact binaries use templates where the binary does not precess and are ill-suited for detection of generic precessing sources. In this paper we provide a closed-form representation of the single-spin precessing waveform in the frequency domain by reorganizing the signal as a sum over harmonics, each of which resembles a nonprecessing waveform. This form enables simple analytic calculations of the Fisher matrix for use in template bank generation and coincidence metrics, and jump proposals to improve the efficiency of Markov chain Monte Carlo sampling. We have verified that for generic BH-NS binaries, our model agrees with the time-domain waveform to 2%. Straightforward extensions of the derivations outlined here (and provided in full online) allow higher accuracy and error estimates.
Delay chemical master equation: direct and closed-form solutions.
Leier, Andre; Marquez-Lago, Tatiana T
2015-07-08
The stochastic simulation algorithm (SSA) describes the time evolution of a discrete nonlinear Markov process. This stochastic process has a probability density function that is the solution of a differential equation, commonly known as the chemical master equation (CME) or forward-Kolmogorov equation. In the same way that the CME gives rise to the SSA, and trajectories of the latter are exact with respect to the former, trajectories obtained from a delay SSA are exact representations of the underlying delay CME (DCME). However, in contrast to the CME, no closed-form solutions have so far been derived for any kind of DCME. In this paper, we describe for the first time direct and closed solutions of the DCME for simple reaction schemes, such as a single-delayed unimolecular reaction as well as chemical reactions for transcription and translation with delayed mRNA maturation. We also discuss the conditions that have to be met such that such solutions can be derived.
Closed Form Aliasing Probability For Q-ary Symmetric Errors
Geetani Edirisooriya
1996-01-01
Full Text Available In Built-In Self-Test (BIST techniques, test data reduction can be achieved using Linear Feedback Shift Registers (LFSRs. A faulty circuit may escape detection due to loss of information inherent to data compaction schemes. This is referred to as aliasing. The probability of aliasing in Multiple-Input Shift-Registers (MISRs has been studied under various bit error models. By modeling the signature analyzer as a Markov process we show that the closed form expression derived for aliasing probability previously, for MISRs with primitive polynomials under q-ary symmetric error model holds for all MISRs irrespective of their feedback polynomials and for group cellular automata signature analyzers as well. If the erroneous behaviour of a circuit can be modelled with q-ary symmetric errors, then the test circuit complexity and propagation delay associated with the signature analyzer can be minimized by using a set of m single bit LFSRs without increasing the probability of aliasing.
Closed form analytic solutions describing glow discharge plasma
Pai, S.T.; Guo, X.M.; Zhou, T.D.
1996-01-01
On the basis of an analytic model developed previously [S. T. Pai, J. Appl. Phys. 71, 5820 (1992)], an improved version of the model for the description of dc glow discharge plasma was successfully developed. A set of closed form solutions was obtained from the governing equations. The two-dimensional, analytic solutions are functional and completely satisfy the governing equations, the actual boundary conditions, and Maxwell equations. They can be readily used to carry out numerical calculations without the necessity of employing any assumed boundary conditions. Results obtained from the model reveal that as the discharge gap spacing or pressure increases the maximum value in the electron density distribution moves toward the cathode. At a sufficiently large value of gap spacing, the positive column phenomenon begins to appear in the discharge region. The model has the capability of treating the positive column and negative glow as a continuous system without the necessity of studying them separately. The model also predicts a sharp rise of the positive ion density near the cathode and field reversal in the anode region. Variation of the electrode radius produces little effect on the axial spatial distribution of physical quantities studied. copyright 1996 American Institute of Physics
Wills Rachael A
2009-05-01
Full Text Available Abstract Background The problem of silent multiple comparisons is one of the most difficult statistical problems faced by scientists. It is a particular problem for investigating a one-off cancer cluster reported to a health department because any one of hundreds, or possibly thousands, of neighbourhoods, schools, or workplaces could have reported a cluster, which could have been for any one of several types of cancer or any one of several time periods. Methods This paper contrasts the frequentist approach with a Bayesian approach for dealing with silent multiple comparisons in the context of a one-off cluster reported to a health department. Two published cluster investigations were re-analysed using the Dunn-Sidak method to adjust frequentist p-values and confidence intervals for silent multiple comparisons. Bayesian methods were based on the Gamma distribution. Results Bayesian analysis with non-informative priors produced results similar to the frequentist analysis, and suggested that both clusters represented a statistical excess. In the frequentist framework, the statistical significance of both clusters was extremely sensitive to the number of silent multiple comparisons, which can only ever be a subjective "guesstimate". The Bayesian approach is also subjective: whether there is an apparent statistical excess depends on the specified prior. Conclusion In cluster investigations, the frequentist approach is just as subjective as the Bayesian approach, but the Bayesian approach is less ambitious in that it treats the analysis as a synthesis of data and personal judgements (possibly poor ones, rather than objective reality. Bayesian analysis is (arguably a useful tool to support complicated decision-making, because it makes the uncertainty associated with silent multiple comparisons explicit.
Bayesian methods for data analysis
Carlin, Bradley P.
2009-01-01
Approaches for statistical inference Introduction Motivating Vignettes Defining the Approaches The Bayes-Frequentist Controversy Some Basic Bayesian Models The Bayes approach Introduction Prior Distributions Bayesian Inference Hierarchical Modeling Model Assessment Nonparametric Methods Bayesian computation Introduction Asymptotic Methods Noniterative Monte Carlo Methods Markov Chain Monte Carlo Methods Model criticism and selection Bayesian Modeling Bayesian Robustness Model Assessment Bayes Factors via Marginal Density Estimation Bayes Factors
Davis, Sergio; Gutiérrez, Gonzalo
2013-01-01
We present a systematic implementation of the recently developed Z-method for computing melting points of solids, augmented by a Bayesian analysis of the data obtained from molecular dynamics simulations. The use of Bayesian inference allows us to extract valuable information from limited data, reducing the computational cost of drawing the isochoric curve. From this Bayesian Z-method we obtain posterior distributions for the melting temperature T m , the critical superheating temperature T LS and the slopes dT/dE of the liquid and solid phases. The method therefore gives full quantification of the errors in the prediction of the melting point. This procedure is applied to the estimation of the melting point of Ti 2 GaN (one of the so-called MAX phases), a complex, laminar material, by density functional theory molecular dynamics, finding an estimate T m of 2591.61 ± 89.61 K, which is in good agreement with melting points of similar ceramics. (paper)
Kim, Daesang
2017-06-22
We developed a novel two-step hierarchical method for the Bayesian inference of the rate parameters of a target reaction from time-resolved concentration measurements in shock tubes. The method was applied to the calibration of the parameters of the reaction of hydroxyl with 2-methylfuran, which is studied experimentally via absorption measurements of the OH radical\\'s concentration following shock-heating. In the first step of the approach, each shock tube experiment is treated independently to infer the posterior distribution of the rate constant and error hyper-parameter that best explains the OH signal. In the second step, these posterior distributions are sampled to calibrate the parameters appearing in the Arrhenius reaction model for the rate constant. Furthermore, the second step is modified and repeated in order to explore alternative rate constant models and to assess the effect of uncertainties in the reflected shock\\'s temperature. Comparisons of the estimates obtained via the proposed methodology against the common least squares approach are presented. The relative merits of the novel Bayesian framework are highlighted, especially with respect to the opportunity to utilize the posterior distributions of the parameters in future uncertainty quantification studies.
Caticha, Ariel
2011-03-01
In this tutorial we review the essential arguments behing entropic inference. We focus on the epistemological notion of information and its relation to the Bayesian beliefs of rational agents. The problem of updating from a prior to a posterior probability distribution is tackled through an eliminative induction process that singles out the logarithmic relative entropy as the unique tool for inference. The resulting method of Maximum relative Entropy (ME), includes as special cases both MaxEnt and Bayes' rule, and therefore unifies the two themes of these workshops—the Maximum Entropy and the Bayesian methods—into a single general inference scheme.
Exact Closed-form Solutions for Lamb's Problem
Feng, X.
2017-12-01
In this work, we report on an exact closedform solution for the displacement at the surfaceof an elastic halfspace elicited by a buried point source that acts at some point underneath thatsurface. This is commonly referred to as the 3D Lamb's problem, for which previous solutionswere restricted to sources and receivers placed at the free surface. By means of the reciprocitytheorem, our solution should also be valid as a means to obtain the displacements at interior pointswhen the source is placed at the free surface. We manage to obtain explicit results by expressingthe solution in terms of elementary algebraic expression as well as elliptic integrals. We anchorour developments on Poissons ratio 0.25 starting from Johnson's numerical, integral transformsolutions. Furthermore, the spatial derivatives of our solutions can be easily acquired in termsof our methods. In the end, our closed-form results agree perfectly with the numerical results ofJohnson, which strongly conrms the correctness of our explicit formulas. It is hoped that in duetime, these formulas may constitute a valuable canonical solution that will serve as a yardstickagainst which other numerical solutions can be compared and measured.In addition, we abstract some terms from our solutions as the generator of the Rayleigh waves.Some basic properties of the Rayleigh waves in the time domain will be indicated in terms of thegenerator. The fareld radiation patterns of P-wave and S-wave elicited by the double-couple forcein the uniform half-space medium could also be acquired from our results.
Qin, H.; Zhou, W.; Zhang, S.
2015-01-01
Stochastic process-based models are developed to characterize the generation and growth of metal-loss corrosion defects on oil and gas steel pipelines. The generation of corrosion defects over time is characterized by the non-homogenous Poisson process, and the growth of depths of individual defects is modeled by the non-homogenous gamma process (NHGP). The defect generation and growth models are formulated in a hierarchical Bayesian framework, whereby the parameters of the models are evaluated from the in-line inspection (ILI) data through the Bayesian updating by accounting for the probability of detection (POD) and measurement errors associated with the ILI data. The Markov Chain Monte Carlo (MCMC) simulation in conjunction with the data augmentation (DA) technique is employed to carry out the Bayesian updating. Numerical examples that involve simulated ILI data are used to illustrate and validate the proposed methodology. - Highlights: • Bayesian updating of growth and generation models of defects on energy pipelines. • Non-homogeneous Poisson process for defect generation. • Non-homogeneous gamma process for defect growth. • Updating based on inspection data with detecting and sizing uncertainties. • MCMC in conjunction with data augmentation technique employed for the updating.
Ilaria A M Marino
Full Text Available A precise inference of past demographic histories including dating of demographic events using bayesian methods can only be achieved with the use of appropriate molecular rates and evolutionary models. Using a set of 596 mitochondrial cytochrome c oxidase I (COI sequences of two sister species of European green crabs of the genus Carcinus (C. maenas and C. aestuarii, our study shows how chronologies of past evolutionary events change significantly with the application of revised molecular rates that incorporate biogeographic events for calibration and appropriate demographic priors. A clear signal of demographic expansion was found for both species, dated between 10,000 and 20,000 years ago, which places the expansions events in a time frame following the Last Glacial Maximum (LGM. In the case of C. aestuarii, a population expansion was only inferred for the Adriatic-Ionian, suggestive of a colonization event following the flooding of the Adriatic Sea (18,000 years ago. For C. maenas, the demographic expansion inferred for the continental populations of West and North Europe might result from a northward recolonization from a southern refugium when the ice sheet retreated after the LGM. Collectively, our results highlight the importance of using adequate calibrations and demographic priors in order to avoid considerable overestimates of evolutionary time scales.
Yuan, Ying; MacKinnon, David P.
2009-01-01
This article proposes Bayesian analysis of mediation effects. Compared to conventional frequentist mediation analysis, the Bayesian approach has several advantages. First, it allows researchers to incorporate prior information into the mediation analysis, thus potentially improving the efficiency of estimates. Second, under the Bayesian mediation analysis, inference is straightforward and exact, which makes it appealing for studies with small samples. Third, the Bayesian approach is conceptua...
Bayesian artificial intelligence
Korb, Kevin B
2010-01-01
Updated and expanded, Bayesian Artificial Intelligence, Second Edition provides a practical and accessible introduction to the main concepts, foundation, and applications of Bayesian networks. It focuses on both the causal discovery of networks and Bayesian inference procedures. Adopting a causal interpretation of Bayesian networks, the authors discuss the use of Bayesian networks for causal modeling. They also draw on their own applied research to illustrate various applications of the technology.New to the Second EditionNew chapter on Bayesian network classifiersNew section on object-oriente
Serang, Oliver
2015-08-01
Observations depending on sums of random variables are common throughout many fields; however, no efficient solution is currently known for performing max-product inference on these sums of general discrete distributions (max-product inference can be used to obtain maximum a posteriori estimates). The limiting step to max-product inference is the max-convolution problem (sometimes presented in log-transformed form and denoted as "infimal convolution," "min-convolution," or "convolution on the tropical semiring"), for which no O(k log(k)) method is currently known. Presented here is an O(k log(k)) numerical method for estimating the max-convolution of two nonnegative vectors (e.g., two probability mass functions), where k is the length of the larger vector. This numerical max-convolution method is then demonstrated by performing fast max-product inference on a convolution tree, a data structure for performing fast inference given information on the sum of n discrete random variables in O(nk log(nk)log(n)) steps (where each random variable has an arbitrary prior distribution on k contiguous possible states). The numerical max-convolution method can be applied to specialized classes of hidden Markov models to reduce the runtime of computing the Viterbi path from nk(2) to nk log(k), and has potential application to the all-pairs shortest paths problem.
McNally, Kevin; Cotton, Richard; Cocker, John; Jones, Kate; Bartels, Mike; Rick, David; Price, Paul; Loizou, George
2012-01-01
There are numerous biomonitoring programs, both recent and ongoing, to evaluate environmental exposure of humans to chemicals. Due to the lack of exposure and kinetic data, the correlation of biomarker levels with exposure concentrations leads to difficulty in utilizing biomonitoring data for biological guidance values. Exposure reconstruction or reverse dosimetry is the retrospective interpretation of external exposure consistent with biomonitoring data. We investigated the integration of physiologically based pharmacokinetic modelling, global sensitivity analysis, Bayesian inference, and Markov chain Monte Carlo simulation to obtain a population estimate of inhalation exposure to m-xylene. We used exhaled breath and venous blood m-xylene and urinary 3-methylhippuric acid measurements from a controlled human volunteer study in order to evaluate the ability of our computational framework to predict known inhalation exposures. We also investigated the importance of model structure and dimensionality with respect to its ability to reconstruct exposure. PMID:22719759
Kevin McNally
2012-01-01
Full Text Available There are numerous biomonitoring programs, both recent and ongoing, to evaluate environmental exposure of humans to chemicals. Due to the lack of exposure and kinetic data, the correlation of biomarker levels with exposure concentrations leads to difficulty in utilizing biomonitoring data for biological guidance values. Exposure reconstruction or reverse dosimetry is the retrospective interpretation of external exposure consistent with biomonitoring data. We investigated the integration of physiologically based pharmacokinetic modelling, global sensitivity analysis, Bayesian inference, and Markov chain Monte Carlo simulation to obtain a population estimate of inhalation exposure to m-xylene. We used exhaled breath and venous blood m-xylene and urinary 3-methylhippuric acid measurements from a controlled human volunteer study in order to evaluate the ability of our computational framework to predict known inhalation exposures. We also investigated the importance of model structure and dimensionality with respect to its ability to reconstruct exposure.
van Lier-Walqui, M.; Morrison, H.; Kumjian, M. R.; Prat, O. P.
2016-12-01
Microphysical parameterization schemes have reached an impressive level of sophistication: numerous prognostic hydrometeor categories, and either size-resolved (bin) particle size distributions, or multiple prognostic moments of the size distribution. Yet, uncertainty in model representation of microphysical processes and the effects of microphysics on numerical simulation of weather has not shown a improvement commensurate with the advanced sophistication of these schemes. We posit that this may be caused by unconstrained assumptions of these schemes, such as ad-hoc parameter value choices and structural uncertainties (e.g. choice of a particular form for the size distribution). We present work on development and observational constraint of a novel microphysical parameterization approach, the Bayesian Observationally-constrained Statistical-physical Scheme (BOSS), which seeks to address these sources of uncertainty. Our framework avoids unnecessary a priori assumptions, and instead relies on observations to provide probabilistic constraint of the scheme structure and sensitivities to environmental and microphysical conditions. We harness the rich microphysical information content of polarimetric radar observations to develop and constrain BOSS within a Bayesian inference framework using a Markov Chain Monte Carlo sampler (see Kumjian et al., this meeting for details on development of an associated polarimetric forward operator). Our work shows how knowledge of microphysical processes is provided by polarimetric radar observations of diverse weather conditions, and which processes remain highly uncertain, even after considering observations.
Zoltán Csörnyei
2010-01-01
Full Text Available Genetic parameters of number of piglets born alive (NBA and gestation length (GL were analyzed for 39798 Hungarian Landrace (HLA, 141397 records and 70356 Hungarian Large White (HLW, 246961 records sows. Bivariate repeatability animal models were used, applying a Bayesian statistics. Estimated and heritabilitie repeatabilities (within brackets, were low for NBA, 0.07 (0.14 for HLA and 0.08 (0.17 for HLW, but somewhat higher for GL, 0.18 (0.27 for HLA and 0.26 (0.35 for HLW. Estimated genetic correlations between NBA and GL were low, -0.08 for HLA and -0.05 for HLW.
Beatty, William; Jay, Chadwick V.; Fischbach, Anthony S.
2016-01-01
State-space models offer researchers an objective approach to modeling complex animal location data sets, and state-space model behavior classifications are often assumed to have a link to animal behavior. In this study, we evaluated the behavioral classification accuracy of a Bayesian state-space model in Pacific walruses using Argos satellite tags with sensors to detect animal behavior in real time. We fit a two-state discrete-time continuous-space Bayesian state-space model to data from 306 Pacific walruses tagged in the Chukchi Sea. We matched predicted locations and behaviors from the state-space model (resident, transient behavior) to true animal behavior (foraging, swimming, hauled out) and evaluated classification accuracy with kappa statistics (κ) and root mean square error (RMSE). In addition, we compared biased random bridge utilization distributions generated with resident behavior locations to true foraging behavior locations to evaluate differences in space use patterns. Results indicated that the two-state model fairly classified true animal behavior (0.06 ≤ κ ≤ 0.26, 0.49 ≤ RMSE ≤ 0.59). Kernel overlap metrics indicated utilization distributions generated with resident behavior locations were generally smaller than utilization distributions generated with true foraging behavior locations. Consequently, we encourage researchers to carefully examine parameters and priors associated with behaviors in state-space models, and reconcile these parameters with the study species and its expected behaviors.
Caticha, Ariel
2010-01-01
In this tutorial we review the essential arguments behing entropic inference. We focus on the epistemological notion of information and its relation to the Bayesian beliefs of rational agents. The problem of updating from a prior to a posterior probability distribution is tackled through an eliminative induction process that singles out the logarithmic relative entropy as the unique tool for inference. The resulting method of Maximum relative Entropy (ME), includes as special cases both MaxEn...
Jeong, Cheol-Ho; Choi, Sang-Hyeon; Lee, Ikjin
2017-01-01
A Bayesian analysis is applied to determine the flow resistivity of a porous sample and the influence of the test chamber based on measured Sabine absorption coefficient data. The Sabine absorption coefficient measured in a reverberation chamber according to ISO 354 is influenced by the test...... chamber significantly, whereas the flow resistivity is a rather reproducible material property, from which the absorptive characteristics can be calculated through reliable models. Using Sabine absorption coefficients measured in 13 European reverberation chambers, the maximum a posteriori...... and the uncertainty of the flow resistivity and the test chamber’s influence are estimated. Inclusion of more than one chamber’s absorption data helps the flow resistivity converge towards a reliable value with a standard deviation below 17%...
Murray, Jessica R.; Minson, Sarah E.; Svarc, Jerry L.
2014-01-01
Fault creep, depending on its rate and spatial extent, is thought to reduce earthquake hazard by releasing tectonic strain aseismically. We use Bayesian inversion and a newly expanded GPS data set to infer the deep slip rates below assigned locking depths on the San Andreas, Maacama, and Bartlett Springs Faults of Northern California and, for the latter two, the spatially variable interseismic creep rate above the locking depth. We estimate deep slip rates of 21.5 ± 0.5, 13.1 ± 0.8, and 7.5 ± 0.7 mm/yr below 16 km, 9 km, and 13 km on the San Andreas, Maacama, and Bartlett Springs Faults, respectively. We infer that on average the Bartlett Springs fault creeps from the Earth's surface to 13 km depth, and below 5 km the creep rate approaches the deep slip rate. This implies that microseismicity may extend below the locking depth; however, we cannot rule out the presence of locked patches in the seismogenic zone that could generate moderate earthquakes. Our estimated Maacama creep rate, while comparable to the inferred deep slip rate at the Earth's surface, decreases with depth, implying a slip deficit exists. The Maacama deep slip rate estimate, 13.1 mm/yr, exceeds long-term geologic slip rate estimates, perhaps due to distributed off-fault strain or the presence of multiple active fault strands. While our creep rate estimates are relatively insensitive to choice of model locking depth, insufficient independent information regarding locking depths is a source of epistemic uncertainty that impacts deep slip rate estimates.
Jakkareddy, Pradeep S.; Balaji, C.
2016-09-01
This paper employs the Bayesian based Metropolis Hasting - Markov Chain Monte Carlo algorithm to solve inverse heat transfer problem of determining the spatially varying heat transfer coefficient from a flat plate with flush mounted discrete heat sources with measured temperatures at the bottom of the plate. The Nusselt number is assumed to be of the form Nu = aReb(x/l)c . To input reasonable values of ’a’ and ‘b’ into the inverse problem, first limited two dimensional conjugate convection simulations were done with Comsol. Based on the guidance from this different values of ‘a’ and ‘b’ are input to a computationally less complex problem of conjugate conduction in the flat plate (15mm thickness) and temperature distributions at the bottom of the plate which is a more convenient location for measuring the temperatures without disturbing the flow were obtained. Since the goal of this work is to demonstrate the eficiacy of the Bayesian approach to accurately retrieve ‘a’ and ‘b’, numerically generated temperatures with known values of ‘a’ and ‘b’ are treated as ‘surrogate’ experimental data. The inverse problem is then solved by repeatedly using the forward solutions together with the MH-MCMC aprroach. To speed up the estimation, the forward model is replaced by an artificial neural network. The mean, maximum-a-posteriori and standard deviation of the estimated parameters ‘a’ and ‘b’ are reported. The robustness of the proposed method is examined, by synthetically adding noise to the temperatures.
Sigeti, David E. [Los Alamos National Laboratory; Pelak, Robert A. [Los Alamos National Laboratory
2012-09-11
We present a Bayesian statistical methodology for identifying improvement in predictive simulations, including an analysis of the number of (presumably expensive) simulations that will need to be made in order to establish with a given level of confidence that an improvement has been observed. Our analysis assumes the ability to predict (or postdict) the same experiments with legacy and new simulation codes and uses a simple binomial model for the probability, {theta}, that, in an experiment chosen at random, the new code will provide a better prediction than the old. This model makes it possible to do statistical analysis with an absolute minimum of assumptions about the statistics of the quantities involved, at the price of discarding some potentially important information in the data. In particular, the analysis depends only on whether or not the new code predicts better than the old in any given experiment, and not on the magnitude of the improvement. We show how the posterior distribution for {theta} may be used, in a kind of Bayesian hypothesis testing, both to decide if an improvement has been observed and to quantify our confidence in that decision. We quantify the predictive probability that should be assigned, prior to taking any data, to the possibility of achieving a given level of confidence, as a function of sample size. We show how this predictive probability depends on the true value of {theta} and, in particular, how there will always be a region around {theta} = 1/2 where it is highly improbable that we will be able to identify an improvement in predictive capability, although the width of this region will shrink to zero as the sample size goes to infinity. We show how the posterior standard deviation may be used, as a kind of 'plan B metric' in the case that the analysis shows that {theta} is close to 1/2 and argue that such a plan B should generally be part of hypothesis testing. All the analysis presented in the paper is done with a
Renner, Susanne S; Zhang, Li-Bing
2004-06-01
Pistia stratiotes (water lettuce) and Lemna (duckweeds) are the only free-floating aquatic Araceae. The geographic origin and phylogenetic placement of these unrelated aroids present long-standing problems because of their highly modified reproductive structures and wide geographical distributions. We sampled chloroplast (trnL-trnF and rpl20-rps12 spacers, trnL intron) and mitochondrial sequences (nad1 b/c intron) for all genera implicated as close relatives of Pistia by morphological, restriction site, and sequencing data, and present a hypothesis about its geographic origin based on the consensus of trees obtained from the combined data, using Bayesian, maximum likelihood, parsimony, and distance analyses. Of the 14 genera closest to Pistia, only Alocasia, Arisaema, and Typhonium are species-rich, and the latter two were studied previously, facilitating the choice of representatives that span the roots of these genera. Results indicate that Pistia and the Seychelles endemic Protarum sechellarum are the basalmost branches in a grade comprising the tribes Colocasieae (Ariopsis, Steudnera, Remusatia, Alocasia, Colocasia), Arisaemateae (Arisaema, Pinellia), and Areae (Arum, Biarum, Dracunculus, Eminium, Helicodiceros, Theriophonum, Typhonium). Unexpectedly, all Areae genera are embedded in Typhonium, which throws new light on the geographic history of Areae. A Bayesian analysis of divergence times that explores the effects of multiple fossil and geological calibration points indicates that the Pistia lineage is 90 to 76 million years (my) old. The oldest fossils of the Pistia clade, though not Pistia itself, are 45-my-old leaves from Germany; the closest outgroup, Peltandreae (comprising a few species in Florida, the Mediterranean, and Madagascar), is known from 60-my-old leaves from Europe, Kazakhstan, North Dakota, and Tennessee. Based on the geographic ranges of close relatives, Pistia likely originated in the Tethys region, with Protarum then surviving on the
Fang, Fang; Chen, Jing; Jiang, Li-Yun; Qu, Yan-Hua; Qiao, Ge-Xia
2018-01-09
Biological invasion is considered one of the most important global environmental problems. Knowledge of the source and dispersal routes of invasion could facilitate the eradication and control of invasive species. Soybean aphid, Aphis glycines Matsumura, is one of the most destructive soybean pests. For effective management of this pest, we conducted genetic analyses and approximate Bayesian computation (ABC) analysis to determine the origins and dispersal of the aphid species, as well as the source of its invasion in the USA, using eight microsatellite loci and the mitochondrial cytochrome c oxidase subunit I (COI) gene. We were able to identify a significant isolation by distance (IBD) pattern and three genetic lineages in the microsatellite data but not in the mtDNA dataset. The genetic structure showed that the USA population has the closest relationship with those from Korea and Japan, indicating that the two latter populations might be the sources of the invasion to the USA. Both population genetic analyses and ABC showed that the northeastern populations in China were the possible sources of the further spread of A. glycines to Indonesia. The dispersal history of this aphid can provide useful information for pest management strategies and can further help predict areas at risk of invasion. This article is protected by copyright. All rights reserved.
Safari, Parviz; Danyali, Syyedeh Fatemeh; Rahimi, Mehdi
2018-06-02
Drought is the main abiotic stress seriously influencing wheat production. Information about the inheritance of drought tolerance is necessary to determine the most appropriate strategy to develop tolerant cultivars and populations. In this study, generation means analysis to identify the genetic effects controlling grain yield inheritance in water deficit and normal conditions was considered as a model selection problem in a Bayesian framework. Stochastic search variable selection (SSVS) was applied to identify the most important genetic effects and the best fitted models using different generations obtained from two crosses applying two water regimes in two growing seasons. The SSVS is used to evaluate the effect of each variable on the dependent variable via posterior variable inclusion probabilities. The model with the highest posterior probability is selected as the best model. In this study, the grain yield was controlled by the main effects (additive and non-additive effects) and epistatic. The results demonstrate that breeding methods such as recurrent selection and subsequent pedigree method and hybrid production can be useful to improve grain yield.
Xing, Dongyuan; Huang, Yangxin; Chen, Henian; Zhu, Yiliang; Dagne, Getachew A; Baldwin, Julie
2017-08-01
Semicontinuous data featured with an excessive proportion of zeros and right-skewed continuous positive values arise frequently in practice. One example would be the substance abuse/dependence symptoms data for which a substantial proportion of subjects investigated may report zero. Two-part mixed-effects models have been developed to analyze repeated measures of semicontinuous data from longitudinal studies. In this paper, we propose a flexible two-part mixed-effects model with skew distributions for correlated semicontinuous alcohol data under the framework of a Bayesian approach. The proposed model specification consists of two mixed-effects models linked by the correlated random effects: (i) a model on the occurrence of positive values using a generalized logistic mixed-effects model (Part I); and (ii) a model on the intensity of positive values using a linear mixed-effects model where the model errors follow skew distributions including skew- t and skew-normal distributions (Part II). The proposed method is illustrated with an alcohol abuse/dependence symptoms data from a longitudinal observational study, and the analytic results are reported by comparing potential models under different random-effects structures. Simulation studies are conducted to assess the performance of the proposed models and method.
Wu Wei; Biber, Patrick D; Peterson, Mark S; Gong Chongfeng
2012-01-01
To study the impact of the Deepwater Horizon oil spill on photosynthesis of coastal salt marsh plants in Mississippi, we developed a hierarchical Bayesian (HB) model based on field measurements collected from July 2010 to November 2011. We sampled three locations in Davis Bayou, Mississippi (30.375°N, 88.790°W) representative of a range of oil spill impacts. Measured photosynthesis was negative (respiration only) at the heavily oiled location in July 2010 only, and rates started to increase by August 2010. Photosynthesis at the medium oiling location was lower than at the control location in July 2010 and it continued to decrease in September 2010. During winter 2010–2011, the contrast between the control and the two impacted locations was not as obvious as in the growing season of 2010. Photosynthesis increased through spring 2011 at the three locations and decreased starting with October at the control location and a month earlier (September) at the impacted locations. Using the field data, we developed an HB model. The model simulations agreed well with the measured photosynthesis, capturing most of the variability of the measured data. On the basis of the posteriors of the parameters, we found that air temperature and photosynthetic active radiation positively influenced photosynthesis whereas the leaf stress level negatively affected photosynthesis. The photosynthesis rates at the heavily impacted location had recovered to the status of the control location about 140 days after the initial impact, while the impact at the medium impact location was never severe enough to make photosynthesis significantly lower than that at the control location over the study period. The uncertainty in modeling photosynthesis rates mainly came from the individual and micro-site scales, and to a lesser extent from the leaf scale. (letter)
Wu, Zhen; Liu, Yong; Liang, Zhongyao; Wu, Sifeng; Guo, Huaicheng
2017-06-01
Lake eutrophication is associated with excessive anthropogenic nutrients (mainly nitrogen (N) and phosphorus (P)) and unobserved internal nutrient cycling. Despite the advances in understanding the role of external loadings, the contribution of internal nutrient cycling is still an open question. A dynamic mass-balance model was developed to simulate and measure the contributions of internal cycling and external loading. It was based on the temporal Bayesian Hierarchical Framework (BHM), where we explored the seasonal patterns in the dynamics of nutrient cycling processes and the limitation of N and P on phytoplankton growth in hyper-eutrophic Lake Dianchi, China. The dynamic patterns of the five state variables (Chla, TP, ammonia, nitrate and organic N) were simulated based on the model. Five parameters (algae growth rate, sediment exchange rate of N and P, nitrification rate and denitrification rate) were estimated based on BHM. The model provided a good fit to observations. Our model results highlighted the role of internal cycling of N and P in Lake Dianchi. The internal cycling processes contributed more than external loading to the N and P changes in the water column. Further insights into the nutrient limitation analysis indicated that the sediment exchange of P determined the P limitation. Allowing for the contribution of denitrification to N removal, N was the more limiting nutrient in most of the time, however, P was the more important nutrient for eutrophication management. For Lake Dianchi, it would not be possible to recover solely by reducing the external watershed nutrient load; the mechanisms of internal cycling should also be considered as an approach to inhibit the release of sediments and to enhance denitrification. Copyright © 2017 Elsevier Ltd. All rights reserved.
Wu, Mengmeng; Lin, Zhixiang; Ma, Shining; Chen, Ting; Jiang, Rui; Wong, Wing Hung
2017-12-01
Although genome-wide association studies (GWAS) have successfully identified thousands of genomic loci associated with hundreds of complex traits in the past decade, the debate about such problems as missing heritability and weak interpretability has been appealing for effective computational methods to facilitate the advanced analysis of the vast volume of existing and anticipated genetic data. Towards this goal, gene-level integrative GWAS analysis with the assumption that genes associated with a phenotype tend to be enriched in biological gene sets or gene networks has recently attracted much attention, due to such advantages as straightforward interpretation, less multiple testing burdens, and robustness across studies. However, existing methods in this category usually exploit non-tissue-specific gene networks and thus lack the ability to utilize informative tissue-specific characteristics. To overcome this limitation, we proposed a Bayesian approach called SIGNET (Simultaneously Inference of GeNEs and Tissues) to integrate GWAS data and multiple tissue-specific gene networks for the simultaneous inference of phenotype-associated genes and relevant tissues. Through extensive simulation studies, we showed the effectiveness of our method in finding both associated genes and relevant tissues for a phenotype. In applications to real GWAS data of 14 complex phenotypes, we demonstrated the power of our method in both deciphering genetic basis and discovering biological insights of a phenotype. With this understanding, we expect to see SIGNET as a valuable tool for integrative GWAS analysis, thereby boosting the prevention, diagnosis, and treatment of human inherited diseases and eventually facilitating precision medicine.
Drilleau, M.; Beucler, E.; Mocquet, A.; Verhoeven, O.; Moebs, G.; Burgos, G.; Montagner, J.
2013-12-01
Mineralogical transformations and matter transfers within the Earth's mantle make the 350-1000 km depth range (considered here as the mantle transition zone) highly heterogeneous and anisotropic. Most of the 3-D global tomographic models are anchored on small perturbations from 1-D models such as PREM, and are secondly interpreted in terms of temperature and composition distributions. However, the degree of heterogeneity in the transition zone can be strong enough so that the concept of a 1-D reference seismic model may be addressed. To avoid the use of any seismic reference model, we developed a Markov chain Monte Carlo algorithm to directly interpret surface wave dispersion curves in terms of temperature and radial anisotropy distributions, considering a given composition of the mantle. These interpretations are based on laboratory measurements of elastic moduli and Birch-Murnaghan equation of state. An originality of the algorithm is its ability to explore both smoothly varying models and first-order discontinuities, using C1-Bézier curves, which interpolate the randomly chosen values for depth, temperature and radial anisotropy. This parameterization is able to generate a self-adapting parameter space exploration while reducing the computing time. Using a Bayesian exploration, the probability distributions on temperature and anisotropy are governed by uncertainties on the data set. The method was successfully applied to both synthetic data and real dispersion curves. Surface wave measurements along the Vanuatu- California path suggest a strong anisotropy above 400 km depth which decreases below, and a monotonous temperature distribution between 350 and 1000 km depth. On the contrary, a negative shear wave anisotropy of about 2 % is found at the top of the transition zone below Eurasia. Considering compositions ranging from piclogite to pyrolite, the overall temperature profile and temperature gradient are higher for the continental path than for the oceanic
Norris, Peter M.; da Silva, Arlindo M.
2018-01-01
A method is presented to constrain a statistical model of sub-gridcolumn moisture variability using high-resolution satellite cloud data. The method can be used for large-scale model parameter estimation or cloud data assimilation. The gridcolumn model includes assumed probability density function (PDF) intra-layer horizontal variability and a copula-based inter-layer correlation model. The observables used in the current study are Moderate Resolution Imaging Spectroradiometer (MODIS) cloud-top pressure, brightness temperature and cloud optical thickness, but the method should be extensible to direct cloudy radiance assimilation for a small number of channels. The algorithm is a form of Bayesian inference with a Markov chain Monte Carlo (MCMC) approach to characterizing the posterior distribution. This approach is especially useful in cases where the background state is clear but cloudy observations exist. In traditional linearized data assimilation methods, a subsaturated background cannot produce clouds via any infinitesimal equilibrium perturbation, but the Monte Carlo approach is not gradient-based and allows jumps into regions of non-zero cloud probability. The current study uses a skewed-triangle distribution for layer moisture. The article also includes a discussion of the Metropolis and multiple-try Metropolis versions of MCMC. PMID:29618847
Norris, Peter M.; Da Silva, Arlindo M.
2016-01-01
A method is presented to constrain a statistical model of sub-gridcolumn moisture variability using high-resolution satellite cloud data. The method can be used for large-scale model parameter estimation or cloud data assimilation. The gridcolumn model includes assumed probability density function (PDF) intra-layer horizontal variability and a copula-based inter-layer correlation model. The observables used in the current study are Moderate Resolution Imaging Spectroradiometer (MODIS) cloud-top pressure, brightness temperature and cloud optical thickness, but the method should be extensible to direct cloudy radiance assimilation for a small number of channels. The algorithm is a form of Bayesian inference with a Markov chain Monte Carlo (MCMC) approach to characterizing the posterior distribution. This approach is especially useful in cases where the background state is clear but cloudy observations exist. In traditional linearized data assimilation methods, a subsaturated background cannot produce clouds via any infinitesimal equilibrium perturbation, but the Monte Carlo approach is not gradient-based and allows jumps into regions of non-zero cloud probability. The current study uses a skewed-triangle distribution for layer moisture. The article also includes a discussion of the Metropolis and multiple-try Metropolis versions of MCMC.
Tamás Petkovits
Full Text Available Although the fungal order Mortierellales constitutes one of the largest classical groups of Zygomycota, its phylogeny is poorly understood and no modern taxonomic revision is currently available. In the present study, 90 type and reference strains were used to infer a comprehensive phylogeny of Mortierellales from the sequence data of the complete ITS region and the LSU and SSU genes with a special attention to the monophyly of the genus Mortierella. Out of 15 alternative partitioning strategies compared on the basis of Bayes factors, the one with the highest number of partitions was found optimal (with mixture models yielding the best likelihood and tree length values, implying a higher complexity of evolutionary patterns in the ribosomal genes than generally recognized. Modeling the ITS1, 5.8S, and ITS2, loci separately improved model fit significantly as compared to treating all as one and the same partition. Further, within-partition mixture models suggests that not only the SSU, LSU and ITS regions evolve under qualitatively and/or quantitatively different constraints, but that significant heterogeneity can be found within these loci also. The phylogenetic analysis indicated that the genus Mortierella is paraphyletic with respect to the genera Dissophora, Gamsiella and Lobosporangium and the resulting phylogeny contradict previous, morphology-based sectional classification of Mortierella. Based on tree structure and phenotypic traits, we recognize 12 major clades, for which we attempt to summarize phenotypic similarities. M. longicollis is closely related to the outgroup taxon Rhizopus oryzae, suggesting that it belongs to the Mucorales. Our results demonstrate that traits used in previous classifications of the Mortierellales are highly homoplastic and that the Mortierellales is in a need of a reclassification, where new, phylogenetically informative phenotypic traits should be identified, with molecular phylogenies playing a decisive role.
Guillermo Amo de Paz
Full Text Available There is a long-standing debate on the extent of vicariance and long-distance dispersal events to explain the current distribution of organisms, especially in those with small diaspores potentially prone to long-distance dispersal. Age estimates of clades play a crucial role in evaluating the impact of these processes. The aim of this study is to understand the evolutionary history of the largest clade of macrolichens, the parmelioid lichens (Parmeliaceae, Lecanoromycetes, Ascomycota by dating the origin of the group and its major lineages. They have a worldwide distribution with centers of distribution in the Neo- and Paleotropics, and semi-arid subtropical regions of the Southern Hemisphere. Phylogenetic analyses were performed using DNA sequences of nuLSU and mtSSU rDNA, and the protein-coding RPB1 gene. The three DNA regions had different evolutionary rates: RPB1 gave a rate two to four times higher than nuLSU and mtSSU. Divergence times of the major clades were estimated with partitioned BEAST analyses allowing different rates for each DNA region and using a relaxed clock model. Three calibrations points were used to date the tree: an inferred age at the stem of Lecanoromycetes, and two dated fossils: Parmelia in the parmelioid group, and Alectoria. Palaeoclimatic conditions and the palaeogeological area cladogram were compared to the dated phylogeny of parmelioid. The parmelioid group diversified around the K/T boundary, and the major clades diverged during the Eocene and Oligocene. The radiation of the genera occurred through globally changing climatic condition of the early Oligocene, Miocene and early Pliocene. The estimated divergence times are consistent with long-distance dispersal events being the major factor to explain the biogeographical distribution patterns of Southern Hemisphere parmelioids, especially for Africa-Australia disjunctions, because the sequential break-up of Gondwana started much earlier than the origin of these
Understanding Computational Bayesian Statistics
Bolstad, William M
2011-01-01
A hands-on introduction to computational statistics from a Bayesian point of view Providing a solid grounding in statistics while uniquely covering the topics from a Bayesian perspective, Understanding Computational Bayesian Statistics successfully guides readers through this new, cutting-edge approach. With its hands-on treatment of the topic, the book shows how samples can be drawn from the posterior distribution when the formula giving its shape is all that is known, and how Bayesian inferences can be based on these samples from the posterior. These ideas are illustrated on common statistic
Closed form solution to a second order boundary value problem and its application in fluid mechanics
Eldabe, N.T.; Elghazy, E.M.; Ebaid, A.
2007-01-01
The Adomian decomposition method is used by many researchers to investigate several scientific models. In this Letter, the modified Adomian decomposition method is applied to construct a closed form solution for a second order boundary value problem with singularity
A Closed-Form Solution to Tensor Voting: Theory and Applications
Wu, Tai-Pang; Yeung, Sai-Kit; Jia, Jiaya; Tang, Chi-Keung; Medioni, Gerard
2016-01-01
We prove a closed-form solution to tensor voting (CFTV): given a point set in any dimensions, our closed-form solution provides an exact, continuous and efficient algorithm for computing a structure-aware tensor that simultaneously achieves salient structure detection and outlier attenuation. Using CFTV, we prove the convergence of tensor voting on a Markov random field (MRF), thus termed as MRFTV, where the structure-aware tensor at each input site reaches a stationary state upon convergence...
Can a significance test be genuinely Bayesian?
Pereira, Carlos A. de B.; Stern, Julio Michael; Wechsler, Sergio
2008-01-01
The Full Bayesian Significance Test, FBST, is extensively reviewed. Its test statistic, a genuine Bayesian measure of evidence, is discussed in detail. Its behavior in some problems of statistical inference like testing for independence in contingency tables is discussed.
Bayesian Inference in Statistical Analysis
Box, George E P
2011-01-01
The Wiley Classics Library consists of selected books that have become recognized classics in their respective fields. With these new unabridged and inexpensive editions, Wiley hopes to extend the life of these important works by making them available to future generations of mathematicians and scientists. Currently available in the Series: T. W. Anderson The Statistical Analysis of Time Series T. S. Arthanari & Yadolah Dodge Mathematical Programming in Statistics Emil Artin Geometric Algebra Norman T. J. Bailey The Elements of Stochastic Processes with Applications to the Natural Sciences Rob
A subsequent closed-form description of propagated signaling phenomena in the membrane of an axon
Melendy, Robert. F.
2016-05-01
I recently introduced a closed-form description of propagated signaling phenomena in the membrane of an axon [R.F. Melendy, Journal of Applied Physics 118, 244701 (2015)]. Those results demonstrate how intracellular conductance, the thermodynamics of magnetization, and current modulation, function together in generating an action potential in a unified, closed-form description. At present, I report on a subsequent closed-form model that unifies intracellular conductance and the thermodynamics of magnetization, with the membrane electric field, Em. It's anticipated this work will compel researchers in biophysics, physical biology, and the computational neurosciences, to probe deeper into the classical and quantum features of membrane magnetization and signaling, informed by the computational features of this subsequent model.
A subsequent closed-form description of propagated signaling phenomena in the membrane of an axon
Melendy, Robert F., E-mail: rfmelendy@liberty.edu [School of Engineering and Computational Science, Liberty University, Lynchburg, Virginia, 24515 (United States)
2016-05-15
I recently introduced a closed-form description of propagated signaling phenomena in the membrane of an axon [R.F. Melendy, Journal of Applied Physics 118, 244701 (2015)]. Those results demonstrate how intracellular conductance, the thermodynamics of magnetization, and current modulation, function together in generating an action potential in a unified, closed-form description. At present, I report on a subsequent closed-form model that unifies intracellular conductance and the thermodynamics of magnetization, with the membrane electric field, E{sub m}. It’s anticipated this work will compel researchers in biophysics, physical biology, and the computational neurosciences, to probe deeper into the classical and quantum features of membrane magnetization and signaling, informed by the computational features of this subsequent model.
Bayesian analysis in plant pathology.
Mila, A L; Carriquiry, A L
2004-09-01
ABSTRACT Bayesian methods are currently much discussed and applied in several disciplines from molecular biology to engineering. Bayesian inference is the process of fitting a probability model to a set of data and summarizing the results via probability distributions on the parameters of the model and unobserved quantities such as predictions for new observations. In this paper, after a short introduction of Bayesian inference, we present the basic features of Bayesian methodology using examples from sequencing genomic fragments and analyzing microarray gene-expressing levels, reconstructing disease maps, and designing experiments.
Closed form for two-photon free-free transition matrix elements
Karule, Erna E-mail: karule@latnet.lv
2000-08-01
Two-photon free-free transitions happen in the multiphoton ionization with more than one excess photon and in Bremsstrahlung. Up to now, the configuration space free-free transition amplitudes have not been written in closed form. We propose a modified Coulomb Green's function (CGF) Sturm ian expansion which allows one to obtain expressions for two-photon radial transition matrix elements in the closed form which are easy to continue analytically to calculate free-free transitions in H.
Xibing Li
2014-02-01
Full Text Available This paper presents an efficient closed-form solution (ECS for acoustic emission(AE source location in three-dimensional structures using time difference of arrival (TDOA measurements from N receivers, N ≥ 6. The nonlinear location equations of TDOA are simplified to linear equations. The unique analytical solution of AE sources for unknown velocity system is obtained by solving the linear equations. The proposed ECS method successfully solved the problems of location errors resulting from measured deviations of velocity as well as the existence and multiplicity of solutions induced by calculations of square roots in existed close-form methods.
Estimation of Ship Long-term Wave-induced Bending Moment using Closed-Form Expressions
Jensen, Jørgen Juncher; Mansour, A. E.
2002-01-01
A semi-analytical approach is used to derive frequency response functions and standard deviations for the wave-induced bending moment amidships for mono-hull ships. The results are given as closed-form expressions and the required input information for the procedure is restricted to the main......-empirical closed-form expression for the skewness. The effect of whipping is included by assuming that whipping and wave-induced responses are conditionally independent given Hs. The procedure is simple and can be used to make quick estimates of the design wave bending moment at the conceptual design phase...
Ransom, Katherine M.; Bell, Andrew M.; Barber, Quinn E.; Kourakos, George; Harter, Thomas
2018-05-01
This study is focused on nitrogen loading from a wide variety of crop and land-use types in the Central Valley, California, USA, an intensively farmed region with high agricultural crop diversity. Nitrogen loading rates for several crop types have been measured based on field-scale experiments, and recent research has calculated nitrogen loading rates for crops throughout the Central Valley based on a mass balance approach. However, research is lacking to infer nitrogen loading rates for the broad diversity of crop and land-use types directly from groundwater nitrate measurements. Relating groundwater nitrate measurements to specific crops must account for the uncertainty about and multiplicity in contributing crops (and other land uses) to individual well measurements, and for the variability of nitrogen loading within farms and from farm to farm for the same crop type. In this study, we developed a Bayesian regression model that allowed us to estimate land-use-specific groundwater nitrogen loading rate probability distributions for 15 crop and land-use groups based on a database of recent nitrate measurements from 2149 private wells in the Central Valley. The water and natural, rice, and alfalfa and pasture groups had the lowest median estimated nitrogen loading rates, each with a median estimate below 5 kg N ha-1 yr-1. Confined animal feeding operations (dairies) and citrus and subtropical crops had the greatest median estimated nitrogen loading rates at approximately 269 and 65 kg N ha-1 yr-1, respectively. In general, our probability-based estimates compare favorably with previous direct measurements and with mass-balance-based estimates of nitrogen loading. Nitrogen mass-balance-based estimates are larger than our groundwater nitrate derived estimates for manured and nonmanured forage, nuts, cotton, tree fruit, and rice crops. These discrepancies are thought to be due to groundwater age mixing, dilution from infiltrating river water, or denitrification
Zabadal, J.; Vilhena, M.T.; Segatto, C.F.; Pazos, R.P.Ruben Panta.
2002-01-01
In this work we construct a closed-form solution for the multidimensional transport equation rewritten in integral form which is expressed in terms of a fractional derivative of the angular flux. We determine the unknown order of the fractional derivative comparing the kernel of the integral equation with the one of the Riemann-Liouville definition of fractional derivative. We report numerical simulations
Zabadal, J. E-mail: jorge.zabadal@ufrgs.br; Vilhena, M.T. E-mail: vilhena@mat.ufrgs.br; Segatto, C.F. E-mail: cynthia@mat.ufrgs.br; Pazos, R.P.Ruben Panta. E-mail: rpp@mat.pucrgs.br
2002-07-01
In this work we construct a closed-form solution for the multidimensional transport equation rewritten in integral form which is expressed in terms of a fractional derivative of the angular flux. We determine the unknown order of the fractional derivative comparing the kernel of the integral equation with the one of the Riemann-Liouville definition of fractional derivative. We report numerical simulations.
Closed-form expressions for integrals of MKdV and sine-Gordon maps
Kamp, Peter H van der; Rojas, O; Quispel, G R W
2007-01-01
We present closed-form expressions for approximately N integrals of 2N-dimensional maps. The maps are obtained by travelling wave reductions of the modified Korteweg-de Vries equation and of the sine-Gordon equation, respectively. We provide the integrating factors corresponding to the integrals. Moreover we show how the integrals and the integrating factors relate to the staircase method
Serge B. Provost
2015-07-01
Full Text Available This paper provides a simplified representation of the exact density function of R, the sample correlation coefficient. The odd and even moments of R are also obtained in closed forms. Being expressed in terms of generalized hypergeometric functions, the resulting representations are readily computable. Some numerical examples corroborate the validity of the results derived herein.
Bouchoucha, Taha
2015-01-01
them hard to use in practice especially for real time radar applications. In this paper, we provide a closed-form solution to design the covariance matrix for a given beampattern in the three dimensional space using planar arrays, which is then used
von der Linden, Wolfgang; Dose, Volker; von Toussaint, Udo
2014-06-01
Preface; Part I. Introduction: 1. The meaning of probability; 2. Basic definitions; 3. Bayesian inference; 4. Combinatrics; 5. Random walks; 6. Limit theorems; 7. Continuous distributions; 8. The central limit theorem; 9. Poisson processes and waiting times; Part II. Assigning Probabilities: 10. Transformation invariance; 11. Maximum entropy; 12. Qualified maximum entropy; 13. Global smoothness; Part III. Parameter Estimation: 14. Bayesian parameter estimation; 15. Frequentist parameter estimation; 16. The Cramer-Rao inequality; Part IV. Testing Hypotheses: 17. The Bayesian way; 18. The frequentist way; 19. Sampling distributions; 20. Bayesian vs frequentist hypothesis tests; Part V. Real World Applications: 21. Regression; 22. Inconsistent data; 23. Unrecognized signal contributions; 24. Change point problems; 25. Function estimation; 26. Integral equations; 27. Model selection; 28. Bayesian experimental design; Part VI. Probabilistic Numerical Techniques: 29. Numerical integration; 30. Monte Carlo methods; 31. Nested sampling; Appendixes; References; Index.
On the closed form mechanistic modeling of milling: Specific cutting energy, torque, and power
Bayoumi, A. E.; Yücesan, G.; Hutton, D. V.
1994-02-01
Specific energy in metal cutting, defined as the energy expended in removing a unit volume of workpiece material, is formulated and determined using a previously developed closed form mechanistic force model for milling operations. Cutting power is computed from the cutting torque, cutting force, kinematics of the cutter, and the volumetric material removal rate. Closed form expressions for specific cutting energy were formulated and found to be functions of the process parameters: pressure and friction for both rake and flank surfaces and chip flow angle at the rake face of the tool. Friction is found to play a very important role in cutting torque and power. Experiments were carried out to determine the effects of feedrate, cutting speed, workpiece material, and flank wear land width on specific cutting energy. It was found that the specific cutting energy increases with a decrease in the chip thickness and with an increase in flank wear land.
Closed-form Solution to Directly Design FACE Waveforms for Beampatterns Using Planar Array
Bouchoucha, Taha; Ahmed, Sajid; Al-Naffouri, Tareq Y.; Alouini, Mohamed-Slim
2015-01-01
In multiple-input multiple-output radar systems, it is usually desirable to steer transmitted power in the region-of-interest. To do this, conventional methods optimize the waveform covariance matrix, R, for the desired beampattern, which is then used to generate actual transmitted waveforms. Both steps require constrained optimization, therefore, use iterative algorithms. The main challenges encountered in the existing approaches are the computational complexity and the design of waveforms to use in practice. In this paper, we provide a closed-form solution to design covariance matrix for the given beampattern using the planar array, which is then used to derive a novel closed-form algorithm to directly design the finite-alphabet constant-envelope (FACE) waveforms. The proposed algorithm exploits the two-dimensional fast-Fourier-transform. The performance of our proposed algorithm is compared with existing methods that are based on semi-definite quadratic programming with the advantage of a considerably reduced complexity.
Closed-form Solution to Directly Design FACE Waveforms for Beampatterns Using Planar Array
Bouchoucha, Taha
2015-04-19
In multiple-input multiple-output radar systems, it is usually desirable to steer transmitted power in the region-of-interest. To do this, conventional methods optimize the waveform covariance matrix, R, for the desired beampattern, which is then used to generate actual transmitted waveforms. Both steps require constrained optimization, therefore, use iterative algorithms. The main challenges encountered in the existing approaches are the computational complexity and the design of waveforms to use in practice. In this paper, we provide a closed-form solution to design covariance matrix for the given beampattern using the planar array, which is then used to derive a novel closed-form algorithm to directly design the finite-alphabet constant-envelope (FACE) waveforms. The proposed algorithm exploits the two-dimensional fast-Fourier-transform. The performance of our proposed algorithm is compared with existing methods that are based on semi-definite quadratic programming with the advantage of a considerably reduced complexity.
Aggelopoulos, Nikolaos C
2015-08-01
Perceptual inference refers to the ability to infer sensory stimuli from predictions that result from internal neural representations built through prior experience. Methods of Bayesian statistical inference and decision theory model cognition adequately by using error sensing either in guiding action or in "generative" models that predict the sensory information. In this framework, perception can be seen as a process qualitatively distinct from sensation, a process of information evaluation using previously acquired and stored representations (memories) that is guided by sensory feedback. The stored representations can be utilised as internal models of sensory stimuli enabling long term associations, for example in operant conditioning. Evidence for perceptual inference is contributed by such phenomena as the cortical co-localisation of object perception with object memory, the response invariance in the responses of some neurons to variations in the stimulus, as well as from situations in which perception can be dissociated from sensation. In the context of perceptual inference, sensory areas of the cerebral cortex that have been facilitated by a priming signal may be regarded as comparators in a closed feedback loop, similar to the better known motor reflexes in the sensorimotor system. The adult cerebral cortex can be regarded as similar to a servomechanism, in using sensory feedback to correct internal models, producing predictions of the outside world on the basis of past experience. Copyright © 2015 Elsevier Ltd. All rights reserved.
Exact closed-form expression for the inverse moments of one-sided correlated Gram matrices
Elkhalil, Khalil
2016-08-15
In this paper, we derive a closed-form expression for the inverse moments of one sided-correlated random Gram matrices. Such a question is mainly motivated by applications in signal processing and wireless communications for which evaluating this quantity is a question of major interest. This is for instance the case of the best linear unbiased estimator, in which the average estimation error corresponds to the first inverse moment of a random Gram matrix.
Exact closed-form expression for the inverse moments of one-sided correlated Gram matrices
Elkhalil, Khalil; Kammoun, Abla; Al-Naffouri, Tareq Y.; Alouini, Mohamed-Slim
2016-01-01
In this paper, we derive a closed-form expression for the inverse moments of one sided-correlated random Gram matrices. Such a question is mainly motivated by applications in signal processing and wireless communications for which evaluating this quantity is a question of major interest. This is for instance the case of the best linear unbiased estimator, in which the average estimation error corresponds to the first inverse moment of a random Gram matrix.
Magnetohydrodynamic viscous flow over a nonlinearly moving surface: Closed-form solutions
Fang, Tiegang
2014-05-01
In this paper, the magnetohydrodynamic (MHD) flow over a nonlinearly (power-law velocity) moving surface is investigated analytically and solutions are presented for a few special conditions. The solutions are obtained in closed forms with hyperbolic functions. The effects of the magnetic, the wall moving, and the mass transpiration parameters are discussed. These solutions are important to show the flow physics as well as to be used as bench mark problems for numerical validation and development of new solution schemes.
Barjaneh, Afshin; Sayyaadi, Hoseyn
2015-01-01
Highlights: • A new closed-form thermal model was developed for SI engines. • Various irreversibilities of real engines were integrated into the model. • The accuracy of the model was examined on two real SI engines. • The superiority of the model to previous closed-form models was shown. • Accuracy and losses were studied over the operating range of engines. - Abstract: A closed form model based on finite speed thermodynamics, FST, modified to consider various losses was developed on Otto cycle. In this regard, the governing equations of the finite speed thermodynamics were developed for expansion/compression processes while heat absorption/rejection of the Otto cycle was determined based on finite time thermodynamics, FTT. In addition, other irreversibility including power loss caused by heat transfer through the cylinder walls and irreversibility due to throttling process was integrated into the model. The developed model was verified by implementing on two different spark ignition internal combustion engines and the results of modeling were compared with experimental results as well as FTT model. It was found that the developed model was not only very simple in use like a closed form thermodynamic model, but also it models a real spark ignition engine with reasonable accuracy. The error in predicting the output power at rated operating range of the engine was 39%, while in the case of the FTT model, this figure was 167.5%. This comparison for predicting thermal efficiency was +7% error (as difference) for the developed model compared to +39.4% error of FTT model.
Szabó, Zsolt, E-mail: szabo@evt.bme.hu [Department of Broadband Infocommunications and Electromagnetic Theory, Budapest University of Technology and Economics, Budapest (Hungary); Füzi, János [Neutron Spectroscopy Department, Wigner Research Centre for Physics, Budapest (Hungary); Faculty of Engineering and Information Technology, University of Pécs (Hungary)
2016-05-15
The Preisach function is considered as a product of two special one dimensional functions, which allows the closed form evaluation of the Everett integral. The deduced closed form expressions are included in Preisach models, in particular in the static model, moving model and a rate dependent hysteresis model, which can simulate the frequency dependence of the magnetization process. The details of the freely available implementations, which are available online are presented. The identification of the model parameters and the accuracy to describe the magnetization process are discussed and demonstrated by fitting measured data. Transient electric circuit simulation with hysteresis demonstrates the applicability of the developed models. - Highlights: • Formulation of the Preisach model with Everett function in closed form. • Identification of the parameters: when the shape of the analytical Preisach function does not matches the ferromagnetic material the moving model can be applied to increase the accuracy. • Novel algorithm with Fixed Point iteration, which utilizes the closed formulation to simulate the frequency dependence of the magnetization process. • The developed hysteresis models are utilized in circuit simulation algorithm to determine the transient behavior of the current, which flows through a toroidal coil with ferromagnetic core.
Borsboom, D.; Haig, B.D.
2013-01-01
Unlike most other statistical frameworks, Bayesian statistical inference is wedded to a particular approach in the philosophy of science (see Howson & Urbach, 2006); this approach is called Bayesianism. Rather than being concerned with model fitting, this position in the philosophy of science
Plug & Play object oriented Bayesian networks
Bangsø, Olav; Flores, J.; Jensen, Finn Verner
2003-01-01
been shown to be quite suitable for dynamic domains as well. However, processing object oriented Bayesian networks in practice does not take advantage of their modular structure. Normally the object oriented Bayesian network is transformed into a Bayesian network and, inference is performed...... dynamic domains. The communication needed between instances is achieved by means of a fill-in propagation scheme....
Ghosh, Sujit K
2010-01-01
Bayesian methods are rapidly becoming popular tools for making statistical inference in various fields of science including biology, engineering, finance, and genetics. One of the key aspects of Bayesian inferential method is its logical foundation that provides a coherent framework to utilize not only empirical but also scientific information available to a researcher. Prior knowledge arising from scientific background, expert judgment, or previously collected data is used to build a prior distribution which is then combined with current data via the likelihood function to characterize the current state of knowledge using the so-called posterior distribution. Bayesian methods allow the use of models of complex physical phenomena that were previously too difficult to estimate (e.g., using asymptotic approximations). Bayesian methods offer a means of more fully understanding issues that are central to many practical problems by allowing researchers to build integrated models based on hierarchical conditional distributions that can be estimated even with limited amounts of data. Furthermore, advances in numerical integration methods, particularly those based on Monte Carlo methods, have made it possible to compute the optimal Bayes estimators. However, there is a reasonably wide gap between the background of the empirically trained scientists and the full weight of Bayesian statistical inference. Hence, one of the goals of this chapter is to bridge the gap by offering elementary to advanced concepts that emphasize linkages between standard approaches and full probability modeling via Bayesian methods.
Bayesian modeling using WinBUGS
Ntzoufras, Ioannis
2009-01-01
A hands-on introduction to the principles of Bayesian modeling using WinBUGS Bayesian Modeling Using WinBUGS provides an easily accessible introduction to the use of WinBUGS programming techniques in a variety of Bayesian modeling settings. The author provides an accessible treatment of the topic, offering readers a smooth introduction to the principles of Bayesian modeling with detailed guidance on the practical implementation of key principles. The book begins with a basic introduction to Bayesian inference and the WinBUGS software and goes on to cover key topics, including: Markov Chain Monte Carlo algorithms in Bayesian inference Generalized linear models Bayesian hierarchical models Predictive distribution and model checking Bayesian model and variable evaluation Computational notes and screen captures illustrate the use of both WinBUGS as well as R software to apply the discussed techniques. Exercises at the end of each chapter allow readers to test their understanding of the presented concepts and all ...
Resolving the biophysics of axon transmembrane polarization in a single closed-form description
Melendy, Robert F., E-mail: rfmelendy@liberty.edu [School of Engineering and Computational Sciences, Liberty University, Lynchburg, Virginia 24515 (United States)
2015-12-28
When a depolarizing event occurs across a cell membrane there is a remarkable change in its electrical properties. A complete depolarization event produces a considerably rapid increase in voltage that propagates longitudinally along the axon and is accompanied by changes in axial conductance. A dynamically changing magnetic field is associated with the passage of the action potential down the axon. Over 75 years of research has gone into the quantification of this phenomenon. To date, no unified model exist that resolves transmembrane polarization in a closed-form description. Here, a simple but formative description of propagated signaling phenomena in the membrane of an axon is presented in closed-form. The focus is on using both biophysics and mathematical methods for elucidating the fundamental mechanisms governing transmembrane polarization. The results presented demonstrate how to resolve electromagnetic and thermodynamic factors that govern transmembrane potential. Computational results are supported by well-established quantitative descriptions of propagated signaling phenomena in the membrane of an axon. The findings demonstrate how intracellular conductance, the thermodynamics of magnetization, and current modulation function together in generating an action potential in a unified closed-form description. The work presented in this paper provides compelling evidence that three basic factors contribute to the propagated signaling in the membrane of an axon. It is anticipated this work will compel those in biophysics, physical biology, and in the computational neurosciences to probe deeper into the classical and quantum features of membrane magnetization and signaling. It is hoped that subsequent investigations of this sort will be advanced by the computational features of this model without having to resort to numerical methods of analysis.
Variational inference & deep learning : A new synthesis
Kingma, D.P.
2017-01-01
In this thesis, Variational Inference and Deep Learning: A New Synthesis, we propose novel solutions to the problems of variational (Bayesian) inference, generative modeling, representation learning, semi-supervised learning, and stochastic optimization.
Variational inference & deep learning: A new synthesis
Kingma, D.P.
2017-01-01
In this thesis, Variational Inference and Deep Learning: A New Synthesis, we propose novel solutions to the problems of variational (Bayesian) inference, generative modeling, representation learning, semi-supervised learning, and stochastic optimization.
Reddy, J N; Chao, W C [Virginia Polytechnic Inst. and State Univ., Blacksburg (USA). Dept. of Engineering Science and Mechanics
1981-04-01
In this study the effects of reduced integration, mesh size, and element type (i.e. linear or quadratic) on the accuracy of a penalty-finite element based on the theory governing thick, laminated, anisotropic composite plates are investigated. In order to assess the accuracy of the present finite element, exact closed-form solutions are developed for cross-ply and antisymmetric angle-ply rectangular plates simply supported and subjected to sinusoidally distributed mechanical and/or thermal loadings, and free vibration.
Closed-form confidence intervals for functions of the normal mean and standard deviation.
Donner, Allan; Zou, G Y
2012-08-01
Confidence interval methods for a normal mean and standard deviation are well known and simple to apply. However, the same cannot be said for important functions of these parameters. These functions include the normal distribution percentiles, the Bland-Altman limits of agreement, the coefficient of variation and Cohen's effect size. We present a simple approach to this problem by using variance estimates recovered from confidence limits computed for the mean and standard deviation separately. All resulting confidence intervals have closed forms. Simulation results demonstrate that this approach performs very well for limits of agreement, coefficients of variation and their differences.
Closed-form pricing formula for exchange option with credit risk
Kim, Geonwoo; Koo, Eunho
2016-01-01
In this paper, we study the valuation of Exchange option with credit risk. Since the over-the-counter (OTC) markets have grown rapidly in size, the counterparty default risk is very important and should be considered for the valuation of options. For modeling of credit risk, we use the structural model of Klein [13]. We derive the closed-form pricing formula for the price of the Exchange option with credit risk via the Mellin transform and provide the experiment results to illustrate the important properties of option with numerical graphs.
R. Bozovic
2017-12-01
Full Text Available Spectrum sensing is the most important process in cognitive radio in order to ensure interference avoidance to primary users. For optimal performance of cognitive radio, it is substantial to monitor and promptly react to dynamic changes in its operating environment. In this paper, energy detector based spectrum sensing is considered. Under the assumption that detected signal can be modelled according to an autoregressive model, noise variance is estimated from that noisy signal, as well as primary user signal power. A closed-form solution for optimal decision threshold in dynamic electromagnetic environment is proposed and analyzed.
A New Closed Form Approximation for BER for Optical Wireless Systems in Weak Atmospheric Turbulence
Kaushik, Rahul; Khandelwal, Vineet; Jain, R. C.
2018-04-01
Weak atmospheric turbulence condition in an optical wireless communication (OWC) is captured by log-normal distribution. The analytical evaluation of average bit error rate (BER) of an OWC system under weak turbulence is intractable as it involves the statistical averaging of Gaussian Q-function over log-normal distribution. In this paper, a simple closed form approximation for BER of OWC system under weak turbulence is given. Computation of BER for various modulation schemes is carried out using proposed expression. The results obtained using proposed expression compare favorably with those obtained using Gauss-Hermite quadrature approximation and Monte Carlo Simulations.
Bayesian methods for proteomic biomarker development
Belinda Hernández
2015-12-01
In this review we provide an introduction to Bayesian inference and demonstrate some of the advantages of using a Bayesian framework. We summarize how Bayesian methods have been used previously in proteomics and other areas of bioinformatics. Finally, we describe some popular and emerging Bayesian models from the statistical literature and provide a worked tutorial including code snippets to show how these methods may be applied for the evaluation of proteomic biomarkers.
Allphin, Devin
Computational fluid dynamics (CFD) solution approximations for complex fluid flow problems have become a common and powerful engineering analysis technique. These tools, though qualitatively useful, remain limited in practice by their underlying inverse relationship between simulation accuracy and overall computational expense. While a great volume of research has focused on remedying these issues inherent to CFD, one traditionally overlooked area of resource reduction for engineering analysis concerns the basic definition and determination of functional relationships for the studied fluid flow variables. This artificial relationship-building technique, called meta-modeling or surrogate/offline approximation, uses design of experiments (DOE) theory to efficiently approximate non-physical coupling between the variables of interest in a fluid flow analysis problem. By mathematically approximating these variables, DOE methods can effectively reduce the required quantity of CFD simulations, freeing computational resources for other analytical focuses. An idealized interpretation of a fluid flow problem can also be employed to create suitably accurate approximations of fluid flow variables for the purposes of engineering analysis. When used in parallel with a meta-modeling approximation, a closed-form approximation can provide useful feedback concerning proper construction, suitability, or even necessity of an offline approximation tool. It also provides a short-circuit pathway for further reducing the overall computational demands of a fluid flow analysis, again freeing resources for otherwise unsuitable resource expenditures. To validate these inferences, a design optimization problem was presented requiring the inexpensive estimation of aerodynamic forces applied to a valve operating on a simulated piston-cylinder heat engine. The determination of these forces was to be found using parallel surrogate and exact approximation methods, thus evidencing the comparative
D. Dimogianopoulos
2017-01-01
Full Text Available This paper presents a novel methodology based on semistatic nondestructive testing of fish for the analytical computation of its textural characteristics via closed-form mathematical expressions. The novelty is that, unlike alternatives, explicit values for both stiffness and viscoelastic textural attributes may be computed, even if fish of different size/weight are tested. Furthermore, the testing procedure may be adapted to the specifications (sampling rate and accuracy of the available equipment. The experimental testing involves a fish placed on the pan of a digital weigh scale, which is subsequently tested with a ramp-like load profile in a custom-made installation. The ramp slope is (to some extent adjustable according to the specification (sampling rate and accuracy of the equipment. The scale’s reaction to fish loading, namely, the reactive force, is collected throughout time and is shown to depend on the fish textural attributes according to a closed-form mathematical formula. The latter is subsequently used along with collected data in order to compute these attributes rapidly and effectively. Four whole raw sea bass (Dicentrarchus labrax of various sizes and textures were tested. Changes in texture, related to different viscoelastic characteristics among the four fish, were correctly detected and quantified using the proposed methodology.
Closed-Form Formula of the Transverse Dynamic Stiffness of a Shallowly Inclined Taut Cable
Dan-hui Dan
2014-01-01
Full Text Available The segmented vibration-governed equations and their general solutions for cables acted upon by intermediate transverse forces are derived by applying Hamilton’s principle. Including the effects of sagging, flexible stiffness, clamped boundary conditions, and inclination angle of the cable, the element-wise dynamic stiffness for each cable segment, split into segments having unique transverse forces, is derived. By using methods from the global stiffness assembly process of FEM, the global level of the cables’ dynamic equilibrium equation is obtained, and, as a result, the final closed-form formula of transverse dynamic stiffness is derived. Additionally, the corresponding analytic form, without considering sagging effects, is also obtained. Case studies are conducted on the aspects of accuracy, rationality of the distribution on the spatial field, and frequency domains of dynamic stiffness calculations. By comparison with the Guyan-based static FEM reduction method, it is shown that the result obtained from the proposed closed-form solution, which includes sagging effects, is exact and rational, thus creating a powerful tool in transverse vibration analysis.
Closed-form kinetic parameter estimation solution to the truncated data problem
Zeng, Gengsheng L; Kadrmas, Dan J; Gullberg, Grant T
2010-01-01
In a dedicated cardiac single photon emission computed tomography (SPECT) system, the detectors are focused on the heart and the background is truncated in the projections. Reconstruction using truncated data results in biased images, leading to inaccurate kinetic parameter estimates. This paper has developed a closed-form kinetic parameter estimation solution to the dynamic emission imaging problem. This solution is insensitive to the bias in the reconstructed images that is caused by the projection data truncation. This paper introduces two new ideas: (1) it includes background bias as an additional parameter to estimate, and (2) it presents a closed-form solution for compartment models. The method is based on the following two assumptions: (i) the amount of the bias is directly proportional to the truncated activities in the projection data, and (ii) the background concentration is directly proportional to the concentration in the myocardium. In other words, the method assumes that the image slice contains only the heart and the background, without other organs, that the heart is not truncated, and that the background radioactivity is directly proportional to the radioactivity in the blood pool. As long as the background activity can be modeled, the proposed method is applicable regardless of the number of compartments in the model. For simplicity, the proposed method is presented and verified using a single compartment model with computer simulations using both noiseless and noisy projections.
Nonlinear Dynamic Analysis and Optimization of Closed-Form Planetary Gear System
Qilin Huang
2013-01-01
Full Text Available A nonlinear purely rotational dynamic model of a multistage closed-form planetary gear set formed by two simple planetary stages is proposed in this study. The model includes time-varying mesh stiffness, excitation fluctuation and gear backlash nonlinearities. The nonlinear differential equations of motion are solved numerically using variable step-size Runge-Kutta. In order to obtain function expression of optimization objective, the nonlinear differential equations of motion are solved analytically using harmonic balance method (HBM. Based on the analytical solution of dynamic equations, the optimization mathematical model which aims at minimizing the vibration displacement of the low-speed carrier and the total mass of the gear transmission system is established. The optimization toolbox in MATLAB program is adopted to obtain the optimal solution. A case is studied to demonstrate the effectiveness of the dynamic model and the optimization method. The results show that the dynamic properties of the closed-form planetary gear transmission system have been improved and the total mass of the gear set has been decreased significantly.
A closed-form solution to tensor voting: theory and applications.
Wu, Tai-Pang; Yeung, Sai-Kit; Jia, Jiaya; Tang, Chi-Keung; Medioni, Gérard
2012-08-01
We prove a closed-form solution to tensor voting (CFTV): Given a point set in any dimensions, our closed-form solution provides an exact, continuous, and efficient algorithm for computing a structure-aware tensor that simultaneously achieves salient structure detection and outlier attenuation. Using CFTV, we prove the convergence of tensor voting on a Markov random field (MRF), thus termed as MRFTV, where the structure-aware tensor at each input site reaches a stationary state upon convergence in structure propagation. We then embed structure-aware tensor into expectation maximization (EM) for optimizing a single linear structure to achieve efficient and robust parameter estimation. Specifically, our EMTV algorithm optimizes both the tensor and fitting parameters and does not require random sampling consensus typically used in existing robust statistical techniques. We performed quantitative evaluation on its accuracy and robustness, showing that EMTV performs better than the original TV and other state-of-the-art techniques in fundamental matrix estimation for multiview stereo matching. The extensions of CFTV and EMTV for extracting multiple and nonlinear structures are underway.
A closed form for the electrostatic interaction between two rod-like charged objects
Askari, M; Abouie, J
2011-01-01
We have calculated the electrostatic interaction between two rod-like charged objects with arbitrary orientations in three dimensions. We obtained a closed-form formula expressing the interaction energy in terms of the separation distance between the centers of the two rod-like objects, r, their lengths (denoted by 2l 1 and 2l 2 ) and their relative orientations (indicated by θ and φ). When the objects have the same length (2l 1 = 2l 2 = l), for particular values of separations, i.e. for r ≤ 0.8l, two types of minimum appear in the interaction energy with respect to θ. By employing the closed-form formula and introducing a scaled temperature t, we have also studied the thermodynamic properties of a 1D system of rod-like charged objects. For different separation distances, the dependence of the specific heat of the system to the scaled temperature has been studied. It is found that, for r < 0.8l, the specific heat has a maximum.
Hanks, Brantley R.; Skelton, Robert E.
1991-01-01
Vibration in modern structural and mechanical systems can be reduced in amplitude by increasing stiffness, redistributing stiffness and mass, and/or adding damping if design techniques are available to do so. Linear Quadratic Regulator (LQR) theory in modern multivariable control design, attacks the general dissipative elastic system design problem in a global formulation. The optimal design, however, allows electronic connections and phase relations which are not physically practical or possible in passive structural-mechanical devices. The restriction of LQR solutions (to the Algebraic Riccati Equation) to design spaces which can be implemented as passive structural members and/or dampers is addressed. A general closed-form solution to the optimal free-decay control problem is presented which is tailored for structural-mechanical system. The solution includes, as subsets, special cases such as the Rayleigh Dissipation Function and total energy. Weighting matrix selection is a constrained choice among several parameters to obtain desired physical relationships. The closed-form solution is also applicable to active control design for systems where perfect, collocated actuator-sensor pairs exist.
A Closed-Form Technique for the Reliability and Risk Assessment of Wind Turbine Systems
Leonardo Dueñas-Osorio
2012-06-01
Full Text Available This paper proposes a closed-form method to evaluate wind turbine system reliability and associated failure consequences. Monte Carlo simulation, a widely used approach for system reliability assessment, usually requires large numbers of computational experiments, while existing analytical methods are limited to simple system event configurations with a focus on average values of reliability metrics. By analyzing a wind turbine system and its components in a combinatorial yet computationally efficient form, the proposed approach provides an entire probability distribution of system failure that contains all possible configurations of component failure and survival events. The approach is also capable of handling unique component attributes such as downtime and repair cost needed for risk estimations, and enables sensitivity analysis for quantifying the criticality of individual components to wind turbine system reliability. Applications of the technique are illustrated by assessing the reliability of a 12-subassembly turbine system. In addition, component downtimes and repair costs of components are embedded in the formulation to compute expected annual wind turbine unavailability and repair cost probabilities, and component importance metrics useful for maintenance planning and research prioritization. Furthermore, this paper introduces a recursive solution to closed-form method and applies this to a 45-component turbine system. The proposed approach proves to be computationally efficient and yields vital reliability information that could be readily used by wind farm stakeholders for decision making and risk management.
Gomes, Guilherme J. C.; Vrugt, Jasper A.; Vargas, Eurípedes A.
2016-04-01
The depth to bedrock controls a myriad of processes by influencing subsurface flow paths, erosion rates, soil moisture, and water uptake by plant roots. As hillslope interiors are very difficult and costly to illuminate and access, the topography of the bedrock surface is largely unknown. This essay is concerned with the prediction of spatial patterns in the depth to bedrock (DTB) using high-resolution topographic data, numerical modeling, and Bayesian analysis. Our DTB model builds on the bottom-up control on fresh-bedrock topography hypothesis of Rempe and Dietrich (2014) and includes a mass movement and bedrock-valley morphology term to extent the usefulness and general applicability of the model. We reconcile the DTB model with field observations using Bayesian analysis with the DREAM algorithm. We investigate explicitly the benefits of using spatially distributed parameter values to account implicitly, and in a relatively simple way, for rock mass heterogeneities that are very difficult, if not impossible, to characterize adequately in the field. We illustrate our method using an artificial data set of bedrock depth observations and then evaluate our DTB model with real-world data collected at the Papagaio river basin in Rio de Janeiro, Brazil. Our results demonstrate that the DTB model predicts accurately the observed bedrock depth data. The posterior mean DTB simulation is shown to be in good agreement with the measured data. The posterior prediction uncertainty of the DTB model can be propagated forward through hydromechanical models to derive probabilistic estimates of factors of safety.
A closed form solution for the response of a long elastic beam to dynamic loading
Mittal, R.K.
1989-01-01
Closed form solutions have been obtained using Fourier transform method for the deflection, curvature and particle velocity of a long elastic beam when it is subjected to a concentrated transverse force which is varying with time. These solutions have been illustrated with the help of two force histories, i.e. a half-sine pulse and a rectangular pulse. Dimensionless parameters representing deflection, curvature and particle velocity have been plotted as functions of dimensionless distance and dimensionless time. Furthermore, the particular case of constant velocity impact which has been studied by other authors using different techniques has also been considered in the present paper and the results compare within numerical errors involved in the evaluation of integrals. (orig.) [de
A closed form solution for vulnerable options with Heston’s stochastic volatility
Lee, Min-Ku; Yang, Sung-Jin; Kim, Jeong-Hoon
2016-01-01
Over-the-counter stock markets in the world have been growing rapidly and vulnerability to default risks of option holders traded in the over-the-counter markets became an important issue, in particular, since the global finance crisis and Eurozone crisis. This paper studies the pricing of European-type vulnerable options when the underlying asset follows the Heston dynamics. In this paper, we obtain a closed form analytic formula of the option price as a stochastic volatility extension of the classical Heston formula and find how the stochastic volatility effect on the Black–Scholes price as well as on the decreasing speed of the option price with credit risk depends on moneyness.
Modelling Stochastic Route Choice Behaviours with a Closed-Form Mixed Logit Model
Xinjun Lai
2015-01-01
Full Text Available A closed-form mixed Logit approach is proposed to model the stochastic route choice behaviours. It combines both the advantages of Probit and Logit to provide a flexible form in alternatives correlation and a tractable form in expression; besides, the heterogeneity in alternative variance can also be addressed. Paths are compared by pairs where the superiority of the binary Probit can be fully used. The Probit-based aggregation is also used for a nested Logit structure. Case studies on both numerical and empirical examples demonstrate that the new method is valid and practical. This paper thus provides an operational solution to incorporate the normal distribution in route choice with an analytical expression.
Closed-form solution to directly design frequency modulated waveforms for beampatterns
Ahmed, Sajid
2018-03-12
The targets image performance depends on the transmit beampattern and power-spectral-density of the probing signal. To design such probing signals for multiple-input multiple output (MIMO) radar, conventional algorithms are iterative in nature, therefore high computational complexity restricts their use in real time applications. In this paper, to achieve the desired beampattern, a novel closed-form algorithm to design frequency-modulated (FM) waveforms for MIMO radar is proposed. The proposed algorithm has negligible computational complexity and yields unity peak-to-average power ratio constant envelope waveforms. Moreover, in contrast to the narrow band algorithms, it has almost flat main and side lobes. In the proposed algorithm, a relationship between the width of symmetric beampattern and the product of initial frequency and duration of the baseband FM waveforms is developed.
Closed-Form Solutions for Gradient Elastic Beams with Geometric Discontinuities by Laplace Transform
Mustafa Özgür Yayli
2013-01-01
Full Text Available The static bending solution of a gradient elastic beam with external discontinuities is presented by Laplace transform. Its utility lies in the ability to switch differential equations to algebraic forms that are more easily solved. A Laplace transformation is applied to the governing equation which is then solved for the static deflection of the microbeam. The exact static response of the gradient elastic beam with external discontinuities is obtained by applying known initial conditions when the others are derived from boundary conditions. The results are given in a series of figures and compared with their classical counterparts. The main contribution of this paper is to provide a closed-form solution for the static deflection of microbeams under geometric discontinuities.
Memristor Multiport Readout: A Closed-Form Solution for Sneak Paths
Zidan, Mohammed A.; Eltawil, Ahmed M.; Fahmy, Hossam A.H.; Kurdahi, Fadi; Salama, Khaled N.
2014-01-01
In this paper, we introduce for the first time, a closed-form solution for the memristor-based memory sneak paths without using any gating elements. The introduced technique fully eliminates the effect of sneak paths by reading the stored data using multiple access points and evaluating a simple addition/subtraction on the different readings. The new method requires fewer reading steps compared to previously reported techniques, and has a very small impact on the memory density. To verify the underlying theory, the proposed system is simulated using Synopsys HSPICE showing the ability to achieve a 100% sneak-path error-free memory. In addition, the effect of quantization bits on the system performance is studied.
Exact closed-form solutions of a fully nonlinear asymptotic two-fluid model
Cheviakov, Alexei F.
2018-05-01
A fully nonlinear model of Choi and Camassa (1999) describing one-dimensional incompressible dynamics of two non-mixing fluids in a horizontal channel, under a shallow water approximation, is considered. An equivalence transformation is presented, leading to a special dimensionless form of the system, involving a single dimensionless constant physical parameter, as opposed to five parameters present in the original model. A first-order dimensionless ordinary differential equation describing traveling wave solutions is analyzed. Several multi-parameter families of physically meaningful exact closed-form solutions of the two-fluid model are derived, corresponding to periodic, solitary, and kink-type bidirectional traveling waves; specific examples are given, and properties of the exact solutions are analyzed.
Unsteady free convection flow of a micropolar fluid with Newtonian heating: Closed form solution
Hussanan Abid
2017-01-01
Full Text Available This article investigates the unsteady free convection flow of a micropolar fluid over a vertical plate oscillating in its own plane with Newtonian heating condition. The problem is modelled in terms of partial differential equations with some physical conditions. Closed form solutions in terms of exponential and complementary error functions of Gauss are obtained by using the Laplace transform technique. They satisfy the governing equations and impose boundary and initial conditions. The present solution in the absence of microrotation reduces to well-known solutions of Newtonian fluid. Graphs are plotted to study the effects of various physical parameters on velocity and microrotation. Numerical results for skin friction and wall couple stress is computed in tables. Apart from the engineering point of view, the present article has strong advantage over the published literature as the exact solutions obtained here can be used as a benchmark for comparison with numerical/ approximate solutions and experimental data.
Memristor Multiport Readout: A Closed-Form Solution for Sneak Paths
Zidan, Mohammed A.
2014-06-18
In this paper, we introduce for the first time, a closed-form solution for the memristor-based memory sneak paths without using any gating elements. The introduced technique fully eliminates the effect of sneak paths by reading the stored data using multiple access points and evaluating a simple addition/subtraction on the different readings. The new method requires fewer reading steps compared to previously reported techniques, and has a very small impact on the memory density. To verify the underlying theory, the proposed system is simulated using Synopsys HSPICE showing the ability to achieve a 100% sneak-path error-free memory. In addition, the effect of quantization bits on the system performance is studied.
Statistical inference an integrated Bayesianlikelihood approach
Aitkin, Murray
2010-01-01
Filling a gap in current Bayesian theory, Statistical Inference: An Integrated Bayesian/Likelihood Approach presents a unified Bayesian treatment of parameter inference and model comparisons that can be used with simple diffuse prior specifications. This novel approach provides new solutions to difficult model comparison problems and offers direct Bayesian counterparts of frequentist t-tests and other standard statistical methods for hypothesis testing.After an overview of the competing theories of statistical inference, the book introduces the Bayes/likelihood approach used throughout. It pre
Bouchoucha, Taha
2015-05-01
Multiple Input Multiple Output (MIMO) radar systems has attracted lately a lot of attention thanks to its advantage over the classical phased array radar systems. We site among these advantages the improvement of parametric identifiability, achievement of higher spatial resolution and design of complex beampatterns. In colocated multiple-input multiple-output radar systems, it is usually desirable to steer transmitted power in the region-of-interest in order to increase the Signal to Noise Ratio (SNR) and reduce any undesired signal and thus improve the detection process. This problem is also known as transmit beampattern design. To achieve this goal, conventional methods optimize the waveform covariance matrix, R, for the desired beampattern, which is then used to generate the actual transmitted waveforms. Both steps require constrained optimization. Most of the existing methods use iterative algorithms to solve these problems, therefore their computational complexity is very high which makes them hard to use in practice especially for real time radar applications. In this paper, we provide a closed-form solution to design the covariance matrix for a given beampattern in the three dimensional space using planar arrays, which is then used to derive a novel closed-form algorithm to directly design the finite-alphabet constant-envelope waveforms. The proposed algorithm exploits the two-dimensional discrete Fourier transform which is implemented using fast Fourier transform algorithm. Consequently, the computational complexity of the proposed beampattern solution is very low allowing it to be used for large arrays to change the beampattern in real time. We also show that the number of required snapshots in each waveform depends on the beampattern and that it is less than the total number of transmit antennas. In addition, we show that the proposed waveform design method can be used with non symmetric beampatterns. The performance of our proposed algorithm compares
L.S. Vismara
2007-12-01
Full Text Available A dinâmica da população de plantas daninhas pode ser representada por um sistema de equações que relaciona as densidades de sementes produzidas e de plântulas em áreas de cultivo. Os valores dos parâmetros dos modelos podem ser inferidos diretamente de experimentação e análise estatística ou extraídos da literatura. O presente trabalho teve por objetivo estimar os parâmetros do modelo de densidade populacional de plantas daninhas, a partir de um experimento conduzido na área experimental da Embrapa Milho e Sorgo, Sete Lagoas, MG, via os procedimentos de inferências clássica e Bayesiana.Dynamics of weed populations can be described as a system of equations relating the produced seed and seedling densities in crop areas. The model parameter values can be either directly inferred from experimentation and statistical analysis or obtained from the literature. The objective of this work was to estimate the weed population density model parameters based on experimental field data at Embrapa Milho e Sorgo, Sete Lagoas, MG, using classic and Bayesian inferences.
José Marques Carneiro Júnior
2010-07-01
Full Text Available Dados simulados foram utilizados para comparar as metodologias Eblup eBayesiana, em dados com homogeneidade de variâncias, heterogeneidade de variância genética e heterogeneidade de variância genética e ambiental. Para obtenção dessas estruturas foram feitos descartes estratégicos dos valores genéticos aditivos e ambientais de acordo com o tipo de heterogeneidade e o nível de variabilidade desejada (alta, média ou baixa, sendo utilizados dois tamanhos de população (grande e pequena. Para a metodologia Bayesiana foram utilizados três níveis de informação a priori: não informativo, pouco informativo e informativo. A presença da heterogeneidade de variâncias causa problemas para a seleção dos melhores indivíduos, principalmente se a heterogeneidade estiver nos componentes de variância genética e ambiental, sendo os animais selecionadosequivocadamente do ambiente mais variável. Os métodos comparados tiveram resultados semelhantes, quando distribuições a priori não informativas foram utilizadas, e as populações de tamanho grande, de modo geral, apresentaram melhores predições de valores genéticos.Foi observado, para a metodologia Bayesiana, que o aumento no nível de informação a priori influencia positivamente as predições dos valores genéticos, principalmente para as populações pequenas. O método Bayesiano é indicado para populações de tamanho pequeno quando há disponibilidade de distribuições a priori informativas.Simulated data were used to compare EBLUP and Bayesian methods in datawith homogeneity of variance, heterogeneity of variance and genetic heterogeneity of genetic and environmental variance. For these structures were strategic disposal of additive genetic and environmental values in accordance with the type of heterogeneity and the desired level of variability: high, medium or low. We used two sizes of population: large and small. For the Bayesian methodology was used three levels of a
Roberts, Stephen A.; Hendry, Jolyon H.
1998-01-01
Purpose: To investigate the role of intertumor heterogeneity in clinical tumor control datasets and the relationship to in vitro measurements of tumor biopsy samples. Specifically, to develop a modified linear-quadratic (LQ) model incorporating such heterogeneity that it is practical to fit to clinical tumor-control datasets. Methods and Materials: We developed a modified version of the linear-quadratic (LQ) model for tumor control, incorporating a (lagged) time factor to allow for tumor cell repopulation. We explicitly took into account the interpatient heterogeneity in clonogen number, radiosensitivity, and repopulation rate. Using this model, we could generate realistic TCP curves using parameter estimates consistent with those reported from in vitro studies, subject to the inclusion of a radiosensitivity (or dose)-modifying factor. We then demonstrated that the model was dominated by the heterogeneity in α (tumor radiosensitivity) and derived an approximate simplified model incorporating this heterogeneity. This simplified model is expressible in a compact closed form, which it is practical to fit to clinical datasets. Using two previously analysed datasets, we fit the model using direct maximum-likelihood techniques and obtained parameter estimates that were, again, consistent with the experimental data on the radiosensitivity of primary human tumor cells. This heterogeneity model includes the same number of adjustable parameters as the standard LQ model. Results: The modified model provides parameter estimates that can easily be reconciled with the in vitro measurements. The simplified (approximate) form of the heterogeneity model is a compact, closed-form probit function that can readily be fitted to clinical series by conventional maximum-likelihood methodology. This heterogeneity model provides a slightly better fit to the datasets than the conventional LQ model, with the same numbers of fitted parameters. The parameter estimates of the clinically
Nam, Sungsik; Hasna, Mazen Omar; Alouini, Mohamed-Slim
2010-01-01
in mind, we capitalize in this paper on some new order statistics results to derive exact closed-form expressions for outage probability of GSC RAKE receivers subject to self-interference over independent and identically distributed Rayleigh fading
Bouchoucha, Taha; Ahmed, Sajid; Al-Naffouri, Tareq Y.; Alouini, Mohamed-Slim
2017-01-01
optimization problems. The computational complexity of these algorithms is very high, which makes them difficult to use in practice. In this paper, to achieve the desired beampattern, a low complexity discrete-Fourier-transform based closed-form covariance
Partner cooperation with decode-and-forward: Closed-form outage analysis and comparison
Benjillali, Mustapha
2013-01-01
In this paper, we investigate the outage performance of "partner cooperation" based on opportunistic Decodeand- Forward with constrained partial selection and reactive relaying strategies in dual-hop cooperative Nakagami-m fading links. The source/destination, which is based on the unique knowledge of local channel state information, selects the best relay to increase the chances of cooperation in both uplink and downlink communications when the direct link is also available. After deriving new expressions for the cumulative distribution functions of the variables of interest, the outage probability of the system is obtained in closed-form. We also derive the ε-outage capacity in different particular cases, and the obtained results - when the channel model is reduced to a Rayleigh fading - either are new or correspond to those previously obtained in other works. Simulation results confirm the accuracy of our analysis for a large selection of system and fading parameters and provide a new insight into the design and optimization of cooperative configurations. © 2012 IEEE.
Closed-form solution for piezoelectric layer with two collinear cracks parallel to the boundaries
B. M. Singh
2006-01-01
Full Text Available We consider the problem of determining the stress distribution in an infinitely long piezoelectric layer of finite width, with two collinear cracks of equal length and parallel to the layer boundaries. Within the framework of reigning piezoelectric theory under mode III, the cracked piezoelectric layer subjected to combined electromechanical loading is analyzed. The faces of the layers are subjected to electromechanical loading. The collinear cracks are located at the middle plane of the layer parallel to its face. By the use of Fourier transforms we reduce the problem to solving a set of triple integral equations with cosine kernel and a weight function. The triple integral equations are solved exactly. Closed form analytical expressions for stress intensity factors, electric displacement intensity factors, and shape of crack and energy release rate are derived. As the limiting case, the solution of the problem with one crack in the layer is derived. Some numerical results for the physical quantities are obtained and displayed graphically.
Lázaro, Mario
2018-01-01
In this paper, nonviscous, nonproportional, vibrating structures are considered. Nonviscously damped systems are characterized by dissipative mechanisms which depend on the history of the response velocities via hereditary kernel functions. Solutions of the free motion equation lead to a nonlinear eigenvalue problem involving mass, stiffness and damping matrices. Viscoelasticity leads to a frequency dependence of this latter. In this work, a novel closed-form expression to estimate complex eigenvalues is derived. The key point is to consider the damping model as perturbed by a continuous fictitious parameter. Assuming then the eigensolutions as function of this parameter, the computation of the eigenvalues sensitivity leads to an ordinary differential equation, from whose solution arises the proposed analytical formula. The resulting expression explicitly depends on the viscoelasticity (frequency derivatives of the damping function), the nonproportionality (influence of the modal damping matrix off-diagonal terms). Eigenvectors are obtained using existing methods requiring only the corresponding eigenvalue. The method is validated using a numerical example which compares proposed with exact ones and with those determined from the linear first order approximation in terms of the damping matrix. Frequency response functions are also plotted showing that the proposed approach is valid even for moderately or highly damped systems.
A Closed-Form Error Model of Straight Lines for Improved Data Association and Sensor Fusing
Volker Sommer
2018-04-01
Full Text Available Linear regression is a basic tool in mobile robotics, since it enables accurate estimation of straight lines from range-bearing scans or in digital images, which is a prerequisite for reliable data association and sensor fusing in the context of feature-based SLAM. This paper discusses, extends and compares existing algorithms for line fitting applicable also in the case of strong covariances between the coordinates at each single data point, which must not be neglected if range-bearing sensors are used. Besides, in particular, the determination of the covariance matrix is considered, which is required for stochastic modeling. The main contribution is a new error model of straight lines in closed form for calculating quickly and reliably the covariance matrix dependent on just a few comprehensible and easily-obtainable parameters. The model can be applied widely in any case when a line is fitted from a number of distinct points also without a priori knowledge of the specific measurement noise. By means of extensive simulations, the performance and robustness of the new model in comparison to existing approaches is shown.
Topics in Bayesian statistics and maximum entropy
Mutihac, R.; Cicuttin, A.; Cerdeira, A.; Stanciulescu, C.
1998-12-01
Notions of Bayesian decision theory and maximum entropy methods are reviewed with particular emphasis on probabilistic inference and Bayesian modeling. The axiomatic approach is considered as the best justification of Bayesian analysis and maximum entropy principle applied in natural sciences. Particular emphasis is put on solving the inverse problem in digital image restoration and Bayesian modeling of neural networks. Further topics addressed briefly include language modeling, neutron scattering, multiuser detection and channel equalization in digital communications, genetic information, and Bayesian court decision-making. (author)
Mørup, Morten; Schmidt, Mikkel N
2012-01-01
Many networks of scientific interest naturally decompose into clusters or communities with comparatively fewer external than internal links; however, current Bayesian models of network communities do not exert this intuitive notion of communities. We formulate a nonparametric Bayesian model...... for community detection consistent with an intuitive definition of communities and present a Markov chain Monte Carlo procedure for inferring the community structure. A Matlab toolbox with the proposed inference procedure is available for download. On synthetic and real networks, our model detects communities...... consistent with ground truth, and on real networks, it outperforms existing approaches in predicting missing links. This suggests that community structure is an important structural property of networks that should be explicitly modeled....
Jafarzadeh, S Reza; Johnson, Wesley O; Gardner, Ian A
2016-03-15
The area under the receiver operating characteristic (ROC) curve (AUC) is used as a performance metric for quantitative tests. Although multiple biomarkers may be available for diagnostic or screening purposes, diagnostic accuracy is often assessed individually rather than in combination. In this paper, we consider the interesting problem of combining multiple biomarkers for use in a single diagnostic criterion with the goal of improving the diagnostic accuracy above that of an individual biomarker. The diagnostic criterion created from multiple biomarkers is based on the predictive probability of disease, conditional on given multiple biomarker outcomes. If the computed predictive probability exceeds a specified cutoff, the corresponding subject is allocated as 'diseased'. This defines a standard diagnostic criterion that has its own ROC curve, namely, the combined ROC (cROC). The AUC metric for cROC, namely, the combined AUC (cAUC), is used to compare the predictive criterion based on multiple biomarkers to one based on fewer biomarkers. A multivariate random-effects model is proposed for modeling multiple normally distributed dependent scores. Bayesian methods for estimating ROC curves and corresponding (marginal) AUCs are developed when a perfect reference standard is not available. In addition, cAUCs are computed to compare the accuracy of different combinations of biomarkers for diagnosis. The methods are evaluated using simulations and are applied to data for Johne's disease (paratuberculosis) in cattle. Copyright © 2015 John Wiley & Sons, Ltd.
Frasso, Gianluca; Lambert, Philippe
2016-10-01
SummaryThe 2014 Ebola outbreak in Sierra Leone is analyzed using a susceptible-exposed-infectious-removed (SEIR) epidemic compartmental model. The discrete time-stochastic model for the epidemic evolution is coupled to a set of ordinary differential equations describing the dynamics of the expected proportions of subjects in each epidemic state. The unknown parameters are estimated in a Bayesian framework by combining data on the number of new (laboratory confirmed) Ebola cases reported by the Ministry of Health and prior distributions for the transition rates elicited using information collected by the WHO during the follow-up of specific Ebola cases. The time-varying disease transmission rate is modeled in a flexible way using penalized B-splines. Our framework represents a valuable stochastic tool for the study of an epidemic dynamic even when only irregularly observed and possibly aggregated data are available. Simulations and the analysis of the 2014 Sierra Leone Ebola data highlight the merits of the proposed methodology. In particular, the flexible modeling of the disease transmission rate makes the estimation of the effective reproduction number robust to the misspecification of the initial epidemic states and to underreporting of the infectious cases. © The Author 2016. Published by Oxford University Press. All rights reserved. For permissions, please e-mail: journals.permissions@oup.com.
Antoniou, Constantinos; Harrison, Glenn W.; Lau, Morten I.
2015-01-01
A large literature suggests that many individuals do not apply Bayes’ Rule when making decisions that depend on them correctly pooling prior information and sample data. We replicate and extend a classic experimental study of Bayesian updating from psychology, employing the methods of experimenta...... economics, with careful controls for the confounding effects of risk aversion. Our results show that risk aversion significantly alters inferences on deviations from Bayes’ Rule....
Analytic Bayesian solution of the two-stage poisson-type problem in probabilistic risk analysis
Frohner, F.H.
1985-01-01
The basic purpose of probabilistic risk analysis is to make inferences about the probabilities of various postulated events, with an account of all relevant information such as prior knowledge and operating experience with the specific system under study, as well as experience with other similar systems. Estimation of the failure rate of a Poisson-type system leads to an especially simple Bayesian solution in closed form if the prior probabilty implied by the invariance properties of the problem is properly taken into account. This basic simplicity persists if a more realistic prior, representing order of magnitude knowledge of the rate parameter, is employed instead. Moreover, the more realistic prior allows direct incorporation of experience gained from other similar systems, without need to postulate a statistical model for an underlying ensemble. The analytic formalism is applied to actual nuclear reactor data
Analytic Closed-Form Solution of a Mixed Layer Model for Stratocumulus Clouds
Akyurek, Bengu Ozge
Stratocumulus clouds play an important role in climate cooling and are hard to predict using global climate and weather forecast models. Thus, previous studies in the literature use observations and numerical simulation tools, such as large-eddy simulation (LES), to solve the governing equations for the evolution of stratocumulus clouds. In contrast to the previous works, this work provides an analytic closed-form solution to the cloud thickness evolution of stratocumulus clouds in a mixed-layer model framework. With a focus on application over coastal lands, the diurnal cycle of cloud thickness and whether or not clouds dissipate are of particular interest. An analytic solution enables the sensitivity analysis of implicitly interdependent variables and extrema analysis of cloud variables that are hard to achieve using numerical solutions. In this work, the sensitivity of inversion height, cloud-base height, and cloud thickness with respect to initial and boundary conditions, such as Bowen ratio, subsidence, surface temperature, and initial inversion height, are studied. A critical initial cloud thickness value that can be dissipated pre- and post-sunrise is provided. Furthermore, an extrema analysis is provided to obtain the minima and maxima of the inversion height and cloud thickness within 24 h. The proposed solution is validated against LES results under the same initial and boundary conditions. Then, the proposed analytic framework is extended to incorporate multiple vertical columns that are coupled by advection through wind flow. This enables a bridge between the micro-scale and the mesoscale relations. The effect of advection on cloud evolution is studied and a sensitivity analysis is provided.
Barraza Bernadas, V.; Grings, F.; Roitberg, E.; Perna, P.; Karszenbaum, H.
2017-12-01
The Dry Chaco region (DCF) has the highest absolute deforestation rates of all Argentinian forests. The most recent report indicates a current deforestation rate of 200,000 Ha year-1. In order to better monitor this process, DCF was chosen to implement an early warning program for illegal deforestation. Although the area is intensively studied using medium resolution imagery (Landsat), the products obtained have a yearly pace and therefore unsuited for an early warning program. In this paper, we evaluated the performance of an online Bayesian change-point detection algorithm for MODIS Enhanced Vegetation Index (EVI) and Land Surface Temperature (LST) datasets. The goal was to to monitor the abrupt changes in vegetation dynamics associated with deforestation events. We tested this model by simulating 16-day EVI and 8-day LST time series with varying amounts of seasonality, noise, length of the time series and by adding abrupt changes with different magnitudes. This model was then tested on real satellite time series available through the Google Earth Engine, over a pilot area in DCF, where deforestation was common in the 2004-2016 period. A comparison with yearly benchmark products based on Landsat images is also presented (REDAF dataset). The results shows the advantages of using an automatic model to detect a changepoint in the time series than using only visual inspection techniques. Simulating time series with varying amounts of seasonality and noise, and by adding abrupt changes at different times and magnitudes, revealed that this model is robust against noise, and is not influenced by changes in amplitude of the seasonal component. Furthermore, the results compared favorably with REDAF dataset (near 65% of agreement). These results show the potential to combine LST and EVI to identify deforestation events. This work is being developed within the frame of the national Forest Law for the protection and sustainable development of Native Forest in Argentina in
Norris, Peter M.; da Silva, Arlindo M.
2018-01-01
Part 1 of this series presented a Monte Carlo Bayesian method for constraining a complex statistical model of global circulation model (GCM) sub-gridcolumn moisture variability using high-resolution Moderate Resolution Imaging Spectroradiometer (MODIS) cloud data, thereby permitting parameter estimation and cloud data assimilation for large-scale models. This article performs some basic testing of this new approach, verifying that it does indeed reduce mean and standard deviation biases significantly with respect to the assimilated MODIS cloud optical depth, brightness temperature and cloud-top pressure and that it also improves the simulated rotational–Raman scattering cloud optical centroid pressure (OCP) against independent (non-assimilated) retrievals from the Ozone Monitoring Instrument (OMI). Of particular interest, the Monte Carlo method does show skill in the especially difficult case where the background state is clear but cloudy observations exist. In traditional linearized data assimilation methods, a subsaturated background cannot produce clouds via any infinitesimal equilibrium perturbation, but the Monte Carlo approach allows non-gradient-based jumps into regions of non-zero cloud probability. In the example provided, the method is able to restore marine stratocumulus near the Californian coast, where the background state has a clear swath. This article also examines a number of algorithmic and physical sensitivities of the new method and provides guidance for its cost-effective implementation. One obvious difficulty for the method, and other cloud data assimilation methods as well, is the lack of information content in passive-radiometer-retrieved cloud observables on cloud vertical structure, beyond cloud-top pressure and optical thickness, thus necessitating strong dependence on the background vertical moisture structure. It is found that a simple flow-dependent correlation modification from Riishojgaard provides some help in this respect, by
da Silva, Arlindo M.; Norris, Peter M.
2013-01-01
Part I presented a Monte Carlo Bayesian method for constraining a complex statistical model of GCM sub-gridcolumn moisture variability using high-resolution MODIS cloud data, thereby permitting large-scale model parameter estimation and cloud data assimilation. This part performs some basic testing of this new approach, verifying that it does indeed significantly reduce mean and standard deviation biases with respect to the assimilated MODIS cloud optical depth, brightness temperature and cloud top pressure, and that it also improves the simulated rotational-Ramman scattering cloud optical centroid pressure (OCP) against independent (non-assimilated) retrievals from the OMI instrument. Of particular interest, the Monte Carlo method does show skill in the especially difficult case where the background state is clear but cloudy observations exist. In traditional linearized data assimilation methods, a subsaturated background cannot produce clouds via any infinitesimal equilibrium perturbation, but the Monte Carlo approach allows finite jumps into regions of non-zero cloud probability. In the example provided, the method is able to restore marine stratocumulus near the Californian coast where the background state has a clear swath. This paper also examines a number of algorithmic and physical sensitivities of the new method and provides guidance for its cost-effective implementation. One obvious difficulty for the method, and other cloud data assimilation methods as well, is the lack of information content in the cloud observables on cloud vertical structure, beyond cloud top pressure and optical thickness, thus necessitating strong dependence on the background vertical moisture structure. It is found that a simple flow-dependent correlation modification due to Riishojgaard (1998) provides some help in this respect, by better honoring inversion structures in the background state.
Norris, Peter M.; da Silva, Arlindo M.
2016-01-01
Part 1 of this series presented a Monte Carlo Bayesian method for constraining a complex statistical model of global circulation model (GCM) sub-gridcolumn moisture variability using high-resolution Moderate Resolution Imaging Spectroradiometer (MODIS) cloud data, thereby permitting parameter estimation and cloud data assimilation for large-scale models. This article performs some basic testing of this new approach, verifying that it does indeed reduce mean and standard deviation biases significantly with respect to the assimilated MODIS cloud optical depth, brightness temperature and cloud-top pressure and that it also improves the simulated rotational-Raman scattering cloud optical centroid pressure (OCP) against independent (non-assimilated) retrievals from the Ozone Monitoring Instrument (OMI). Of particular interest, the Monte Carlo method does show skill in the especially difficult case where the background state is clear but cloudy observations exist. In traditional linearized data assimilation methods, a subsaturated background cannot produce clouds via any infinitesimal equilibrium perturbation, but the Monte Carlo approach allows non-gradient-based jumps into regions of non-zero cloud probability. In the example provided, the method is able to restore marine stratocumulus near the Californian coast, where the background state has a clear swath. This article also examines a number of algorithmic and physical sensitivities of the new method and provides guidance for its cost-effective implementation. One obvious difficulty for the method, and other cloud data assimilation methods as well, is the lack of information content in passive-radiometer-retrieved cloud observables on cloud vertical structure, beyond cloud-top pressure and optical thickness, thus necessitating strong dependence on the background vertical moisture structure. It is found that a simple flow-dependent correlation modification from Riishojgaard provides some help in this respect, by
SU-F-T-144: Analytical Closed Form Approximation for Carbon Ion Bragg Curves in Water
Tuomanen, S; Moskvin, V; Farr, J [St. Jude Children’s Research Hospital, Memphis, TN (United States)
2016-06-15
Purpose: Semi-empirical modeling is a powerful computational method in radiation dosimetry. A set of approximations exist for proton ion depth dose distribution (DDD) in water. However, the modeling is more complicated for carbon ions due to fragmentation. This study addresses this by providing and evaluating a new methodology for DDD modeling of carbon ions in water. Methods: The FLUKA, Monte Carlo (MC) general-purpose transport code was used for simulation of carbon DDDs for energies of 100–400 MeV in water as reference data model benchmarking. Based on Thomas Bortfeld’s closed form equation approximating proton Bragg Curves as a basis, we derived the critical constants for a beam of Carbon ions by applying models of radiation transport by Lee et. al. and Geiger to our simulated Carbon curves. We hypothesized that including a new exponential (κ) residual distance parameter to Bortfeld’s fluence reduction relation would improve DDD modeling for carbon ions. We are introducing an additional term to be added to Bortfeld’s equation to describe fragmentation tail. This term accounts for the pre-peak dose from nuclear fragments (NF). In the post peak region, the NF transport will be treated as new beams utilizing the Glauber model for interaction cross sections and the Abrasion- Ablation fragmentation model. Results: The carbon beam specific constants in the developed model were determined to be : p= 1.75, β=0.008 cm-1, γ=0.6, α=0.0007 cm MeV, σmono=0.08, and the new exponential parameter κ=0.55. This produced a close match for the plateau part of the curve (max deviation 6.37%). Conclusion: The derived semi-empirical model provides an accurate approximation of the MC simulated clinical carbon DDDs. This is the first direct semi-empirical simulation for the dosimetry of therapeutic carbon ions. The accurate modeling of the NF tail in the carbon DDD will provide key insight into distal edge dose deposition formation.
Modeling of Filament Deposition Rapid Prototyping Process with a Closed form Solution
Devlin, Steven Leon
Fused Deposition Modeling (FDM(TM)) or fused filament fabrication (FFF) systems are extrusion-based technologies used to produce functional or near functional parts from a wide variety of plastic materials. First patented by S. Scott Crump and commercialized by Stratasys, Ltd in the early 1990s, this technology, like many additive manufacturing systems, offers significant opportunities for the design and production of complex part structures that are difficult if not impossible to produce using traditional manufacturing methods. Standing on the shoulders of a twenty-five year old invention, a rapidly growing open-source development community has exponentially driven interest in FFF technology. However, part quality often limits use in final product commercial markets. Development of accurate and repeatable methods for determining material strength in FFF produced parts is essential for wide adoption into mainstream manufacturing. This study builds on the empirical, squeeze flow and intermolecular diffusion model research conducted by David Grewell and Avraham Benatar, applying a combined model to predict auto adhesion or healing to FFF part samples. In this research, an experimental study and numerical modeling were performed in order to drive and validate a closed form heat transfer solution for extrusion processes to develop temperature field models. An extrusion-based 3D printing system, with the capacity to vary deposition speeds and temperatures, was used to fabricate the samples. Standardized specimens of Polylactic Acid (PLA) and Acrylonitrile Butadiene Styrene (ABS) filament were used to fabricate the samples with different speeds and temperatures. Micro-scanning of cut and lapped specimens, using an optical microscope, was performed to find the effect of the speed and the temperature on the geometry of the cross-sections. It was found that by increasing the speed of the extrusion printing, the area of the cross-section and the maximum thickness decrease
Advances in Bayesian Modeling in Educational Research
Levy, Roy
2016-01-01
In this article, I provide a conceptually oriented overview of Bayesian approaches to statistical inference and contrast them with frequentist approaches that currently dominate conventional practice in educational research. The features and advantages of Bayesian approaches are illustrated with examples spanning several statistical modeling…
Multiview Bayesian Correlated Component Analysis
Kamronn, Simon Due; Poulsen, Andreas Trier; Hansen, Lars Kai
2015-01-01
are identical. Here we propose a hierarchical probabilistic model that can infer the level of universality in such multiview data, from completely unrelated representations, corresponding to canonical correlation analysis, to identical representations as in correlated component analysis. This new model, which...... we denote Bayesian correlated component analysis, evaluates favorably against three relevant algorithms in simulated data. A well-established benchmark EEG data set is used to further validate the new model and infer the variability of spatial representations across multiple subjects....
A closed form expression for the Drinfeld modular polynomial Φ_{T} (X, Y )
Bassa, Alp; Beelen, Peter
2012-01-01
In this paper we give a closed-form expression for the Drinfeld modular polynomial ΦT (X, Y ) ∈ Fq(T)[X, Y ] for arbitrary q and prove a conjecture of Schweizer. A new identity involving the Catalan numbers plays a central role.......In this paper we give a closed-form expression for the Drinfeld modular polynomial ΦT (X, Y ) ∈ Fq(T)[X, Y ] for arbitrary q and prove a conjecture of Schweizer. A new identity involving the Catalan numbers plays a central role....
Closed-form dynamics of a hexarot parallel manipulator by means of the principle of virtual work
Pedrammehr, Siamak; Nahavandi, Saeid; Abdi, Hamid
2018-04-01
In this research, a systematic approach to solving the inverse dynamics of hexarot manipulators is addressed using the methodology of virtual work. For the first time, a closed form of the mathematical formulation of the standard dynamic model is presented for this class of mechanisms. An efficient algorithm for solving this closed-form dynamic model of the mechanism is developed and it is used to simulate the dynamics of the system for different trajectories. Validation of the proposed model is performed using SimMechanics and it is shown that the results of the proposed mathematical model match with the results obtained by the SimMechanics model.
Panayotounakos D. E.
1996-01-01
Full Text Available We develop a new unique technique in constructing closed-form solutions for several nonlinear partial differential systems appearing in fluid mechanics and gas dynamics. The obtained solutions include fewer arbitrary functions than needed for general solutions, fact that permits us to specify them according to the initial state, or the geometry, of each specific problem under consideration. In order to apply the before mentioned technique we construct closed-form solutions concerning the gas-dynamic equations with constant pressure, the dynamic equations of an ideal gas in isentropic flow, and the two-dimensional incompressible boundary layer flow.
Bayesian Approaches to Imputation, Hypothesis Testing, and Parameter Estimation
Ross, Steven J.; Mackey, Beth
2015-01-01
This chapter introduces three applications of Bayesian inference to common and novel issues in second language research. After a review of the critiques of conventional hypothesis testing, our focus centers on ways Bayesian inference can be used for dealing with missing data, for testing theory-driven substantive hypotheses without a default null…
Bayesian image restoration, using configurations
Thorarinsdottir, Thordis
configurations are expressed in terms of the mean normal measure of the random set. These probabilities are used as prior probabilities in a Bayesian image restoration approach. Estimation of the remaining parameters in the model is outlined for salt and pepper noise. The inference in the model is discussed...
Bayesian image restoration, using configurations
Thorarinsdottir, Thordis Linda
2006-01-01
configurations are expressed in terms of the mean normal measure of the random set. These probabilities are used as prior probabilities in a Bayesian image restoration approach. Estimation of the remaining parameters in the model is outlined for the salt and pepper noise. The inference in the model is discussed...
Kocbach, Ladislav; Liska, Richard
1994-01-01
The three-dimensional exchange integrals in the impact-parameter treatment of heavy particle collisions can be transformed to one-dimensional integrals over finite range. The closed form formula for the integrands of these one-dimensional integrals is derived. (Author)
Lesaffre, Emmanuel
2012-01-01
The growth of biostatistics has been phenomenal in recent years and has been marked by considerable technical innovation in both methodology and computational practicality. One area that has experienced significant growth is Bayesian methods. The growing use of Bayesian methodology has taken place partly due to an increasing number of practitioners valuing the Bayesian paradigm as matching that of scientific discovery. In addition, computational advances have allowed for more complex models to be fitted routinely to realistic data sets. Through examples, exercises and a combination of introd
Probability and Bayesian statistics
1987-01-01
This book contains selected and refereed contributions to the "Inter national Symposium on Probability and Bayesian Statistics" which was orga nized to celebrate the 80th birthday of Professor Bruno de Finetti at his birthplace Innsbruck in Austria. Since Professor de Finetti died in 1985 the symposium was dedicated to the memory of Bruno de Finetti and took place at Igls near Innsbruck from 23 to 26 September 1986. Some of the pa pers are published especially by the relationship to Bruno de Finetti's scientific work. The evolution of stochastics shows growing importance of probability as coherent assessment of numerical values as degrees of believe in certain events. This is the basis for Bayesian inference in the sense of modern statistics. The contributions in this volume cover a broad spectrum ranging from foundations of probability across psychological aspects of formulating sub jective probability statements, abstract measure theoretical considerations, contributions to theoretical statistics an...
ZHOU, Lin
1996-01-01
In this paper I consider social choices under uncertainty. I prove that any social choice rule that satisfies independence of irrelevant alternatives, translation invariance, and weak anonymity is consistent with ex post Bayesian utilitarianism
Hanks, Brantley R.; Skelton, Robert E.
1991-01-01
This paper addresses the restriction of Linear Quadratic Regulator (LQR) solutions to the algebraic Riccati Equation to design spaces which can be implemented as passive structural members and/or dampers. A general closed-form solution to the optimal free-decay control problem is presented which is tailored for structural-mechanical systems. The solution includes, as subsets, special cases such as the Rayleigh Dissipation Function and total energy. Weighting matrix selection is a constrained choice among several parameters to obtain desired physical relationships. The closed-form solution is also applicable to active control design for systems where perfect, collocated actuator-sensor pairs exist. Some examples of simple spring mass systems are shown to illustrate key points.
Zafar, Junaid
2012-01-01
The geometrical relationship between the cut-off and propagating planes of any waveguide system is a prerequisite for any design process. The characterization of cut-off planes and optimisation are challenging for numerical methods, closed-form solutions are always preferred. In this paper Maxwells coupled field equations are used to characterise twin E-plane and H-plane slab loaded boundary value problems. The single mode bandwidths and dispersion characteristics of these structures are pres...
A Bayesian Reflection on Surfaces
David R. Wolf
1999-10-01
Full Text Available Abstract: The topic of this paper is a novel Bayesian continuous-basis field representation and inference framework. Within this paper several problems are solved: The maximally informative inference of continuous-basis fields, that is where the basis for the field is itself a continuous object and not representable in a finite manner; the tradeoff between accuracy of representation in terms of information learned, and memory or storage capacity in bits; the approximation of probability distributions so that a maximal amount of information about the object being inferred is preserved; an information theoretic justification for multigrid methodology. The maximally informative field inference framework is described in full generality and denoted the Generalized Kalman Filter. The Generalized Kalman Filter allows the update of field knowledge from previous knowledge at any scale, and new data, to new knowledge at any other scale. An application example instance, the inference of continuous surfaces from measurements (for example, camera image data, is presented.
Matone, Marco
2016-01-01
Recently it has been introduced an algorithm for the Baker-Campbell-Hausdorff (BCH) formula, which extends the Van-Brunt and Visser recent results, leading to new closed forms of BCH formula. More recently, it has been shown that there are 13 types of such commutator algebras. We show, by providing the explicit solutions, that these include the generators of the semisimple complex Lie algebras. More precisely, for any pair, X, Y of the Cartan-Weyl basis, we find W, linear combination of X, Y, such that exp(X) exp(Y) = exp(W). The derivation of such closed forms follows, in part, by using the above mentioned recent results. The complete derivation is provided by considering the structure of the root system. Furthermore, if X, Y, and Z are three generators of the Cartan-Weyl basis, we find, for a wide class of cases, W, a linear combination of X, Y and Z, such that exp(X) exp(Y) exp(Z) = exp(W). It turns out that the relevant commutator algebras are type 1c-i, type 4 and type 5. A key result concerns an iterative application of the algorithm leading to relevant extensions of the cases admitting closed forms of the BCH formula. Here we provide the main steps of such an iteration that will be developed in a forthcoming paper. (orig.)
Kotaro eKojima
2016-01-01
Full Text Available The double impulse is introduced as a substitute of the fling-step near-fault ground motion. A closed-form solution of the elastic-plastic response of a structure on compliant (flexible ground by the ‘critical double impulse’ is derived for the first time based on the solution for the corresponding structure with fixed base. As in the case of fixed-base model, only the free-vibration appears under such double impulse and the energy approach plays an important role in the derivation of the closed-form solution of a complicated elastic-plastic response on compliant ground. It is remarkable that no iteration is needed in the derivation of the critical elastic-plastic response. It is shown via the closed-form expression that, in the case of a smaller input level of double impulse to the structural strength, as the ground stiffness becomes larger, the maximum plastic deformation becomes larger. On the other hand, in the case of a larger input level of double impulse to the structural strength, as the ground stiffness becomes smaller, the maximum plastic deformation becomes larger. The criticality and validity of the proposed theory are investigated through the comparison with the response analysis to the corresponding one-cycle sinusoidal input as a representative of the fling-step near-fault ground motion. The applicability of the proposed theory to actual recorded pulse-type ground motions is also discussed.
Nam, Sungsik
2010-11-01
Previous work on performance analyses of generalized selection combining (GSC) RAKE receivers based on the signal to noise ratio focused on the development of methodologies to derive exact closed-form expressions for various performance measures. However, some open problems related to the performance evaluation of GSC RAKE receivers still remain to be solved such that an assessment of the impact of self-interference on the performance of GSC RAKE receivers. To have a full and exact understanding of the performance of GSC RAKE receivers, the outage probability of GSC RAKE receivers needs to be analyzed as closed-form expressions. The major difficulty in this problem is to derive some joint statistics of ordered exponential variates. With this motivation in mind, we capitalize in this paper on some new order statistics results to derive exact closed-form expressions for outage probability of GSC RAKE receivers subject to self-interference over independent and identically distributed Rayleigh fading channels. © 2010 IEEE.
Lee, Jaesun; Cho, Younho; Achenbach, Jan D.
2016-01-01
Guided waves can be used for the inspection of long range pipelines. Surface corrosion is often found as a major defect type in pipelines. The reciprocity relation is a well-established theorem by which one can simplify complicated mathematical expressions. The approach has been already applied to plate and half-space structures to obtain the closed-form solutions of scattered amplitude. However, results for the case of cylindrical structures have not been reported yet. In this paper, the scattering of torsional waves, which is widely used in commercial applications, is explored by the reciprocity theorem approach. Obtaining closed-form solutions of the amplitudes of propagating waves is much simplified by using the reciprocal relation. The scattered amplitudes for elliptical and rectangular defect shapes are calculated with respect to defect depth and width, at frequencies between 0 and 500 kHz. The amplitude shows the periodic result as a function of frequency. The derived closed-form solutions can play a significant role in quantitative signal interpretation
Matone, Marco [Universita di Padova, Dipartimento di Fisica e Astronomia ' ' G. Galilei' ' , Padua (Italy); Istituto Nazionale di Fisica Nucleare, Sezione di Padova, Padua (Italy)
2016-11-15
Recently it has been introduced an algorithm for the Baker-Campbell-Hausdorff (BCH) formula, which extends the Van-Brunt and Visser recent results, leading to new closed forms of BCH formula. More recently, it has been shown that there are 13 types of such commutator algebras. We show, by providing the explicit solutions, that these include the generators of the semisimple complex Lie algebras. More precisely, for any pair, X, Y of the Cartan-Weyl basis, we find W, linear combination of X, Y, such that exp(X) exp(Y) = exp(W). The derivation of such closed forms follows, in part, by using the above mentioned recent results. The complete derivation is provided by considering the structure of the root system. Furthermore, if X, Y, and Z are three generators of the Cartan-Weyl basis, we find, for a wide class of cases, W, a linear combination of X, Y and Z, such that exp(X) exp(Y) exp(Z) = exp(W). It turns out that the relevant commutator algebras are type 1c-i, type 4 and type 5. A key result concerns an iterative application of the algorithm leading to relevant extensions of the cases admitting closed forms of the BCH formula. Here we provide the main steps of such an iteration that will be developed in a forthcoming paper. (orig.)
Lee, Jaesun; Cho, Younho [Pusan National Univ., Pusan (Korea, Republic of); Achenbach, Jan D. [Northwestern Univ., Everston (United States)
2016-07-15
Guided waves can be used for the inspection of long range pipelines. Surface corrosion is often found as a major defect type in pipelines. The reciprocity relation is a well-established theorem by which one can simplify complicated mathematical expressions. The approach has been already applied to plate and half-space structures to obtain the closed-form solutions of scattered amplitude. However, results for the case of cylindrical structures have not been reported yet. In this paper, the scattering of torsional waves, which is widely used in commercial applications, is explored by the reciprocity theorem approach. Obtaining closed-form solutions of the amplitudes of propagating waves is much simplified by using the reciprocal relation. The scattered amplitudes for elliptical and rectangular defect shapes are calculated with respect to defect depth and width, at frequencies between 0 and 500 kHz. The amplitude shows the periodic result as a function of frequency. The derived closed-form solutions can play a significant role in quantitative signal interpretation.
Bayesian networks improve causal environmental ...
Rule-based weight of evidence approaches to ecological risk assessment may not account for uncertainties and generally lack probabilistic integration of lines of evidence. Bayesian networks allow causal inferences to be made from evidence by including causal knowledge about the problem, using this knowledge with probabilistic calculus to combine multiple lines of evidence, and minimizing biases in predicting or diagnosing causal relationships. Too often, sources of uncertainty in conventional weight of evidence approaches are ignored that can be accounted for with Bayesian networks. Specifying and propagating uncertainties improve the ability of models to incorporate strength of the evidence in the risk management phase of an assessment. Probabilistic inference from a Bayesian network allows evaluation of changes in uncertainty for variables from the evidence. The network structure and probabilistic framework of a Bayesian approach provide advantages over qualitative approaches in weight of evidence for capturing the impacts of multiple sources of quantifiable uncertainty on predictions of ecological risk. Bayesian networks can facilitate the development of evidence-based policy under conditions of uncertainty by incorporating analytical inaccuracies or the implications of imperfect information, structuring and communicating causal issues through qualitative directed graph formulations, and quantitatively comparing the causal power of multiple stressors on value
Harmonic disturbance location by applying Bayesian inference
Ye, G.; Xiang, Y.; Cuk, V.; Cobben, J.F.G.
2016-01-01
Harmonic pollution is one of the most important power quality issues in electric power systems. Correct location of the main harmonic disturbance source is a key step to solve the problem. This paper presents a method to detect the location of harmonic disturbance source in low voltage network
Polynomial Chaos Surrogates for Bayesian Inference
Le Maitre, Olivier
2016-01-01
, and derive its posterior distribution. In most cases the posterior distribution has no explicit form and has to be sampled, for instance using a Markov-Chain Monte Carlo method. In practice the prior field parameter is decomposed and truncated (e.g. by means
Analysis of KATRIN data using Bayesian inference
Riis, Anna Sejersen; Hannestad, Steen; Weinheimer, Christian
2011-01-01
The KATRIN (KArlsruhe TRItium Neutrino) experiment will be analyzing the tritium beta-spectrum to determine the mass of the neutrino with a sensitivity of 0.2 eV (90% C.L.). This approach to a measurement of the absolute value of the neutrino mass relies only on the principle of energy conservation...
Bayesian inference of the metazoan phylogeny
Glenner, Henrik; Hansen, Anders J; Sørensen, Martin V
2004-01-01
Metazoan phylogeny remains one of evolutionary biology's major unsolved problems. Molecular and morphological data, as well as different analytical approaches, have produced highly conflicting results due to homoplasy resulting from more than 570 million years of evolution. To date, parsimony has...
Image interpolation via graph-based Bayesian label propagation.
Xianming Liu; Debin Zhao; Jiantao Zhou; Wen Gao; Huifang Sun
2014-03-01
In this paper, we propose a novel image interpolation algorithm via graph-based Bayesian label propagation. The basic idea is to first create a graph with known and unknown pixels as vertices and with edge weights encoding the similarity between vertices, then the problem of interpolation converts to how to effectively propagate the label information from known points to unknown ones. This process can be posed as a Bayesian inference, in which we try to combine the principles of local adaptation and global consistency to obtain accurate and robust estimation. Specially, our algorithm first constructs a set of local interpolation models, which predict the intensity labels of all image samples, and a loss term will be minimized to keep the predicted labels of the available low-resolution (LR) samples sufficiently close to the original ones. Then, all of the losses evaluated in local neighborhoods are accumulated together to measure the global consistency on all samples. Moreover, a graph-Laplacian-based manifold regularization term is incorporated to penalize the global smoothness of intensity labels, such smoothing can alleviate the insufficient training of the local models and make them more robust. Finally, we construct a unified objective function to combine together the global loss of the locally linear regression, square error of prediction bias on the available LR samples, and the manifold regularization term. It can be solved with a closed-form solution as a convex optimization problem. Experimental results demonstrate that the proposed method achieves competitive performance with the state-of-the-art image interpolation algorithms.
A Dynamic BI–Orthogonal Field Equation Approach to Efficient Bayesian Inversion
Tagade Piyush M.
2017-06-01
Full Text Available This paper proposes a novel computationally efficient stochastic spectral projection based approach to Bayesian inversion of a computer simulator with high dimensional parametric and model structure uncertainty. The proposed method is based on the decomposition of the solution into its mean and a random field using a generic Karhunen-Loève expansion. The random field is represented as a convolution of separable Hilbert spaces in stochastic and spatial dimensions that are spectrally represented using respective orthogonal bases. In particular, the present paper investigates generalized polynomial chaos bases for the stochastic dimension and eigenfunction bases for the spatial dimension. Dynamic orthogonality is used to derive closed-form equations for the time evolution of mean, spatial and the stochastic fields. The resultant system of equations consists of a partial differential equation (PDE that defines the dynamic evolution of the mean, a set of PDEs to define the time evolution of eigenfunction bases, while a set of ordinary differential equations (ODEs define dynamics of the stochastic field. This system of dynamic evolution equations efficiently propagates the prior parametric uncertainty to the system response. The resulting bi-orthogonal expansion of the system response is used to reformulate the Bayesian inference for efficient exploration of the posterior distribution. The efficacy of the proposed method is investigated for calibration of a 2D transient diffusion simulator with an uncertain source location and diffusivity. The computational efficiency of the method is demonstrated against a Monte Carlo method and a generalized polynomial chaos approach.
Bayesian ARTMAP for regression.
Sasu, L M; Andonie, R
2013-10-01
Bayesian ARTMAP (BA) is a recently introduced neural architecture which uses a combination of Fuzzy ARTMAP competitive learning and Bayesian learning. Training is generally performed online, in a single-epoch. During training, BA creates input data clusters as Gaussian categories, and also infers the conditional probabilities between input patterns and categories, and between categories and classes. During prediction, BA uses Bayesian posterior probability estimation. So far, BA was used only for classification. The goal of this paper is to analyze the efficiency of BA for regression problems. Our contributions are: (i) we generalize the BA algorithm using the clustering functionality of both ART modules, and name it BA for Regression (BAR); (ii) we prove that BAR is a universal approximator with the best approximation property. In other words, BAR approximates arbitrarily well any continuous function (universal approximation) and, for every given continuous function, there is one in the set of BAR approximators situated at minimum distance (best approximation); (iii) we experimentally compare the online trained BAR with several neural models, on the following standard regression benchmarks: CPU Computer Hardware, Boston Housing, Wisconsin Breast Cancer, and Communities and Crime. Our results show that BAR is an appropriate tool for regression tasks, both for theoretical and practical reasons. Copyright © 2013 Elsevier Ltd. All rights reserved.
Approximate Bayesian computation.
Mikael Sunnåker
Full Text Available Approximate Bayesian computation (ABC constitutes a class of computational methods rooted in Bayesian statistics. In all model-based statistical inference, the likelihood function is of central importance, since it expresses the probability of the observed data under a particular statistical model, and thus quantifies the support data lend to particular values of parameters and to choices among different models. For simple models, an analytical formula for the likelihood function can typically be derived. However, for more complex models, an analytical formula might be elusive or the likelihood function might be computationally very costly to evaluate. ABC methods bypass the evaluation of the likelihood function. In this way, ABC methods widen the realm of models for which statistical inference can be considered. ABC methods are mathematically well-founded, but they inevitably make assumptions and approximations whose impact needs to be carefully assessed. Furthermore, the wider application domain of ABC exacerbates the challenges of parameter estimation and model selection. ABC has rapidly gained popularity over the last years and in particular for the analysis of complex problems arising in biological sciences (e.g., in population genetics, ecology, epidemiology, and systems biology.
Al-Shawba, Altaf Abdulkarem; Gepreel, K. A.; Abdullah, F. A.; Azmi, A.
2018-06-01
In current study, we use the (G‧ / G) -expansion method to construct the closed form solutions of the seventh order time fractional Sawada-Kotera-Ito (TFSKI) equation based on conformable fractional derivative. As a result, trigonometric, hyperbolic and rational functions solutions with arbitrary constants are obtained. When the arbitrary constants are taken some special values, the periodic and soliton solutions are obtained from the travelling wave solutions. The obtained solutions are new and not found elsewhere. The effect of the fractional order on some of these solutions are represented graphically to illustrate the behavior of the exact solutions when the parameter take some special choose.
Closed-form estimates of the domain of attraction for nonlinear systems via fuzzy-polynomial models.
Pitarch, José Luis; Sala, Antonio; Ariño, Carlos Vicente
2014-04-01
In this paper, the domain of attraction of the origin of a nonlinear system is estimated in closed form via level sets with polynomial boundaries, iteratively computed. In particular, the domain of attraction is expanded from a previous estimate, such as a classical Lyapunov level set. With the use of fuzzy-polynomial models, the domain of attraction analysis can be carried out via sum of squares optimization and an iterative algorithm. The result is a function that bounds the domain of attraction, free from the usual restriction of being positive and decrescent in all the interior of its level sets.
Pan Zhao
2018-01-01
Full Text Available In this paper we consider pricing problems of the geometric average Asian options under a non-Gaussian model, in which the underlying stock price is driven by a process based on non-extensive statistical mechanics. The model can describe the peak and fat tail characteristics of returns. Thus, the description of underlying asset price and the pricing of options are more accurate. Moreover, using the martingale method, we obtain closed form solutions for geometric average Asian options. Furthermore, the numerical analysis shows that the model can avoid underestimating risks relative to the Black-Scholes model.
Gonis, Antonios; Daene, Markus W.; Nicholson, Don M.; Stocks, George Malcolm
2012-01-01
We have developed and tested in terms of atomic calculations an exact, analytic and computationally simple procedure for determining the functional derivative of the exchange energy with respect to the density in the implementation of the Kohn Sham formulation of density functional theory (KS-DFT), providing an analytic, closed-form solution of the self-interaction problem in KS-DFT. We demonstrate the efficacy of our method through ground-state calculations of the exchange potential and energy for atomic He and Be atoms, and comparisons with experiment and the results obtained within the optimized effective potential (OEP) method.
MCMC for parameters estimation by bayesian approach
Ait Saadi, H.; Ykhlef, F.; Guessoum, A.
2011-01-01
This article discusses the parameter estimation for dynamic system by a Bayesian approach associated with Markov Chain Monte Carlo methods (MCMC). The MCMC methods are powerful for approximating complex integrals, simulating joint distributions, and the estimation of marginal posterior distributions, or posterior means. The MetropolisHastings algorithm has been widely used in Bayesian inference to approximate posterior densities. Calibrating the proposal distribution is one of the main issues of MCMC simulation in order to accelerate the convergence.
A Bayesian Method for Weighted Sampling
Lo, Albert Y.
1993-01-01
Bayesian statistical inference for sampling from weighted distribution models is studied. Small-sample Bayesian bootstrap clone (BBC) approximations to the posterior distribution are discussed. A second-order property for the BBC in unweighted i.i.d. sampling is given. A consequence is that BBC approximations to a posterior distribution of the mean and to the sampling distribution of the sample average, can be made asymptotically accurate by a proper choice of the random variables that genera...
Jamison, J. W.
1994-01-01
CFORM was developed by the Kennedy Space Center Robotics Lab to assist in linear control system design and analysis using closed form and transient response mechanisms. The program computes the closed form solution and transient response of a linear (constant coefficient) differential equation. CFORM allows a choice of three input functions: the Unit Step (a unit change in displacement); the Ramp function (step velocity); and the Parabolic function (step acceleration). It is only accurate in cases where the differential equation has distinct roots, and does not handle the case for roots at the origin (s=0). Initial conditions must be zero. Differential equations may be input to CFORM in two forms - polynomial and product of factors. In some linear control analyses, it may be more appropriate to use a related program, Linear Control System Design and Analysis (KSC-11376), which uses root locus and frequency response methods. CFORM was written in VAX FORTRAN for a VAX 11/780 under VAX VMS 4.7. It has a central memory requirement of 30K. CFORM was developed in 1987.
Closed-form solution of a two-dimensional fuel temperature model for TRIGA-type reactors
Rivard, J B [Sandia Laboratories (United States)
1974-07-01
If azimuthal power density variations are ignored, the steady-state temperature distribution within a TRIGA-type fuel element is given by the solution of the Poisson equation in two dimensions (r and z) . This paper presents a closed-form solution of this equation as a function of the axial and radial power density profiles, the conductivity of the U-ZrH, the inlet temperature, specific heat and flow rate of the coolant, and the overall heat transfer coefficient. The method begins with the development of a system of linear ordinary differential equations describing mass and energy balances in the fuel and coolant. From the solution of this system, an expression for the second derivative of the fuel temperature distribution in the axial (z) direction is found. Substitution of this expression into the Poisson equation for T(r,z) reduces it from a partial differential equation to an ordinary differential equation in r, which is subsequently solved in closed-form. The results of typical calculations using the model are presented. (author)
Milani, Gabriele, E-mail: milani@stru.polimi.it, E-mail: gabriele.milani@polimi.it [Politecnico di Milano, Piazza Leonardo da Vinci 32, 20133 Milan (Italy); Hanel, Thomas; Donetti, Raffaella [Pirelli Tyre, Via Alberto e Piero Pirelli 25, 20126 Milan (Italy); Milani, Federico [CHEMCO Consultant, Via J.F. Kennedy 2, 45030 Occhiobello (Italy)
2015-03-10
The basic reaction scheme due to Han and co-workers for NR vulcanized with sulphur is adopted and modified taking into account the single contributions of the different accelerators, focusing in particular on some experimental data ad hoc obtained at Pirelli’s laboratories, where NR was vulcanized at different temperatures (from 150 to 180 °C) and concentrations of sulphur, using TBBS and DPG in the mixture as co-agents. Typically, the chain reactions are initiated by the formation of macro-compounds that are responsible of the formation of the unmatured crosslinked polymer. This first reaction depends on the reciprocal concentrations of all components and their chemical nature. In presence of two accelerators, it was considered that the reactions between each single accelerator and the NR raw material occur in parallel, making the reasonable assumption that there are no mutual reactions between the two accelerators. From the kinetic scheme adopted, a closed form solution was found for the crosslink density, with the only limitation that the induction period is excluded from computations. Even kinetic constants are evaluated in closed form, avoiding a numerically demanding least-squares best fitting on rheometer experimental data. Two series of experiments available, relying into rheometer curves at different temperatures and different concentrations of sulphur and accelerator, are utilized to evaluate the fitting capabilities of the mathematical model. Very good agreement between numerical output and experimental data is experienced in all cases analysed.
A closed-form solution for steady-state coupled phloem/xylem flow using the Lambert-W function.
Hall, A J; Minchin, P E H
2013-12-01
A closed-form solution for steady-state coupled phloem/xylem flow is presented. This incorporates the basic Münch flow model of phloem transport, the cohesion model of xylem flow, and local variation in the xylem water potential and lateral water flow along the transport pathway. Use of the Lambert-W function allows this solution to be obtained under much more general and realistic conditions than has previously been possible. Variation in phloem resistance (i.e. viscosity) with solute concentration, and deviations from the Van't Hoff expression for osmotic potential are included. It is shown that the model predictions match those of the equilibrium solution of a numerical time-dependent model based upon the same mechanistic assumptions. The effect of xylem flow upon phloem flow can readily be calculated, which has not been possible in any previous analytical model. It is also shown how this new analytical solution can handle multiple sources and sinks within a complex architecture, and can describe competition between sinks. The model provides new insights into Münch flow by explicitly including interactions with xylem flow and water potential in the closed-form solution, and is expected to be useful as a component part of larger numerical models of entire plants. © 2013 John Wiley & Sons Ltd.
Bouchoucha, Taha
2017-01-23
In multiple-input multiple-out (MIMO) radar, for desired transmit beampatterns, appropriate correlated waveforms are designed. To design such waveforms, conventional MIMO radar methods use two steps. In the first step, the waveforms covariance matrix, R, is synthesized to achieve the desired beampattern. While in the second step, to realize the synthesized covariance matrix, actual waveforms are designed. Most of the existing methods use iterative algorithms to solve these constrained optimization problems. The computational complexity of these algorithms is very high, which makes them difficult to use in practice. In this paper, to achieve the desired beampattern, a low complexity discrete-Fourier-transform based closed-form covariance matrix design technique is introduced for a MIMO radar. The designed covariance matrix is then exploited to derive a novel closed-form algorithm to directly design the finite-alphabet constant-envelope waveforms for the desired beampattern. The proposed technique can be used to design waveforms for large antenna array to change the beampattern in real time. It is also shown that the number of transmitted symbols from each antenna depends on the beampattern and is less than the total number of transmit antenna elements.
David Heimann
2007-08-01
Full Text Available In supply chains, domestic and global, a producer must decide on an optimal quantity of items to order from suppliers and at what inventory level to place this order (the EOQ problem. We discuss how to modify the EOQ in the face of failures and recoveries by the supplier. This is the EOQ with disruption problem (EOQD. The supplier makes transitions between being capable and not being capable of filling an order in a Markov failure and recovery process. The producer adjusts the reorder point and the inventories to provide a margin of safety. Numerical solutions to the EOQD problem have been developed. In addition, a closed-form approximate solution has been developed for the zero inventory option (ZIO, where the inventory level on reordering is set to be zero. This paper develops a closed-form approximate solution for the EOQD problem when the reorder point can be non-zero, obtaining for that situation an optimal reorder quantity and optimal reorder point that represents an improvement on the optimal ZIO solution. The paper also supplies numerical examples demonstrating the cost savings against the ZIO situation, as well as the accuracy of the approximation technique.
Drobnitzky, Matthias; Klose, Uwe
2017-03-01
Magnetization-prepared rapid gradient-echo (MPRAGE) sequences are commonly employed for T1-weighted structural brain imaging. Following a contrast preparation radiofrequency (RF) pulse, the data acquisition proceeds under nonequilibrium conditions of the relaxing longitudinal magnetization. Variation of the flip angle can be used to maximize total available signal. Simulated annealing or greedy algorithms have so far been published to numerically solve this problem, with signal-to-noise ratios optimized for clinical imaging scenarios by adhering to a predefined shape of the signal evolution. We propose an unconstrained optimization of the MPRAGE experiment that employs techniques from resource allocation theory. A new dynamic programming solution is introduced that yields closed-form expressions for optimal flip angle variation. Flip angle series are proposed that maximize total transverse magnetization (Mxy) for a range of physiologic T1 values. A 3D MPRAGE sequence is modified to allow for a controlled variation of the excitation angle. Experiments employing a T1 contrast phantom are performed at 3T. 1D acquisitions without phase encoding permit measurement of the temporal development of Mxy. Image mean signal and standard deviation for reference flip angle trains are compared in 2D measurements. Signal profiles at sharp phantom edges are acquired to access image blurring related to nonuniform Mxy development. A novel closed-form expression for flip angle variation is found that constitutes the optimal policy to reach maximum total signal. It numerically equals previously published results of other authors when evaluated under their simplifying assumptions. Longitudinal magnetization (Mz) is exhaustively used without causing abrupt changes in the measured MR signal, which is a prerequisite for artifact free images. Phantom experiments at 3T verify the expected benefit for total accumulated k-space signal when compared with published flip angle series. Describing
Nonparametric Bayesian Modeling of Complex Networks
Schmidt, Mikkel Nørgaard; Mørup, Morten
2013-01-01
an infinite mixture model as running example, we go through the steps of deriving the model as an infinite limit of a finite parametric model, inferring the model parameters by Markov chain Monte Carlo, and checking the model?s fit and predictive performance. We explain how advanced nonparametric models......Modeling structure in complex networks using Bayesian nonparametrics makes it possible to specify flexible model structures and infer the adequate model complexity from the observed data. This article provides a gentle introduction to nonparametric Bayesian modeling of complex networks: Using...
Ahmed, Sajid
2016-11-24
Various examples of methods and systems are provided for direct closed-form finite alphabet constant-envelope waveforms for planar array beampatterns. In one example, a method includes defining a waveform covariance matrix based at least in part upon a two-dimensional fast Fourier transform (2D-FFT) analysis of a frequency domain matrix Hf associated with a planar array of antennas. Symbols can be encoded based upon the waveform covariance matrix and the encoded symbols can be transmitted via the planar array of antennas. In another embodiment, a system comprises an N x M planar array of antennas and transmission circuitry configured to transmit symbols via a two-dimensional waveform beampattern defined based at least in part upon a 2D-FFT analysis of a frequency domain matrix Hf associated with the planar array of antennas.
Pedersen, Preben Terndrup; Jensen, Jørgen Juncher
2009-01-01
A simple but rational procedure for prediction of extreme wave-induced hull girder bending moment is presented. The procedure takes into account main ship hull characteristics such as: length, breadth, draught, block coefficient, bow flare coefficient, forward speed and hull flexibility. The wave......-linear strip theory calculations and supplemented with new closed form results for the hogging bending moment. Focus is on the extreme hull girder hogging bending moment. Due to the few input parameters this procedure can be used to estimate the wave-induced bending moments at the conceptual design phase....... Another application area is for novel single hull ship types not presently covered by the rules of the classification societies. As one application example the container ship M/S Napoli is considered....
Li, M. P.; Sun, Q. P.
2018-01-01
We investigate the roles of grain size (lg) and grain boundary thickness (lb) on the stress-induced phase transition (PT) behaviors of nanocrystalline shape memory alloys (SMAs) by using a Core-shell type "crystallite-amorphous composite" model. A non-dimensionalized length scale lbarg(=lg /lb) is identified as the governing parameter which is indicative of the energy competition between the crystallite and the grain boundary. Closed form analytical solutions of a reduced effective 1D model with embedded microstructure length scales of lg and lb are presented in this paper. It is shown that, with lbarg reduction, the energy of the elastic non-transformable grain boundary will gradually become dominant in the phase transition process, and eventually bring fundamental changes of the deformation behaviors: breakdown of two-phase coexistence and vanishing of superelastic hysteresis. The predictions are supported by experimental data of nanocrystalline NiTi SMAs.
Mohamed, Refaat; Ismail, Mahmoud H.; Newagy, Fatma; Mourad, Heba M.
2013-03-01
Stemming from the fact that the α-μ fading distribution is one of the very general fading models used in the literature to describe the small scale fading phenomenon, in this paper, closed-form expressions for the Shannon capacity of the α-μ fading channel operating under four main adaptive transmission strategies are derived assuming integer values for μ. These expressions are derived for the case of no diversity as well as for selection combining diversity with independent and identically distributed branches. The obtained expressions reduce to those previously derived in the literature for the Weibull as well as the Rayleigh fading cases, which are both special cases of the α-μ channel. Numerical results are presented for the capacity under the four adaptive transmission strategies and the effect of the fading parameter as well as the number of diversity branches is studied.
Closed-form plastic collapse loads of pipe bends under combined pressure and in-plane bending
Oh, Chang Sik; Kim, Yun Jae
2006-01-01
Based on three-dimensional (3-D) FE limit analyses, this paper provides plastic limit, collapse and instability load solutions for pipe bends under combined pressure and in-plane bending. The plastic limit loads are determined from FE limit analyses based on elastic-perfectly plastic materials using the small geometry change option, and the FE limit analyses using the large geometry change option provide plastic collapse loads (using the twice-elastic-slope method) and instability loads. For the bending mode, both closing bending and opening bending are considered, and a wide range of parameters related to the bend geometry is considered. Based on the FE results, closed-form approximations of plastic limit and collapse load solutions for pipe bends under combined pressure and bending are proposed