Bayesian models a statistical primer for ecologists
Hobbs, N Thompson
2015-01-01
Bayesian modeling has become an indispensable tool for ecological research because it is uniquely suited to deal with complexity in a statistically coherent way. This textbook provides a comprehensive and accessible introduction to the latest Bayesian methods-in language ecologists can understand. Unlike other books on the subject, this one emphasizes the principles behind the computations, giving ecologists a big-picture understanding of how to implement this powerful statistical approach. Bayesian Models is an essential primer for non-statisticians. It begins with a definition of probabili
Draper, D.
2001-01-01
© 2012 Springer Science+Business Media, LLC. All rights reserved. Article Outline: Glossary Definition of the Subject and Introduction The Bayesian Statistical Paradigm Three Examples Comparison with the Frequentist Statistical Paradigm Future Directions Bibliography
Bayesian statistic methods and theri application in probabilistic simulation models
Directory of Open Access Journals (Sweden)
Sergio Iannazzo
2007-03-01
Full Text Available Bayesian statistic methods are facing a rapidly growing level of interest and acceptance in the field of health economics. The reasons of this success are probably to be found on the theoretical fundaments of the discipline that make these techniques more appealing to decision analysis. To this point should be added the modern IT progress that has developed different flexible and powerful statistical software framework. Among them probably one of the most noticeably is the BUGS language project and its standalone application for MS Windows WinBUGS. Scope of this paper is to introduce the subject and to show some interesting applications of WinBUGS in developing complex economical models based on Markov chains. The advantages of this approach reside on the elegance of the code produced and in its capability to easily develop probabilistic simulations. Moreover an example of the integration of bayesian inference models in a Markov model is shown. This last feature let the analyst conduce statistical analyses on the available sources of evidence and exploit them directly as inputs in the economic model.
Statistical modelling of railway track geometry degradation using hierarchical Bayesian models
Andrade, António Ramos; Teixeira, P. Fonseca
2015-01-01
Railway maintenance planners require a predictive model that can assess the railway track geometry degradation. The present paper uses a hierarchical Bayesian model as a tool to model the main two quality indicators related to railway track geometry degradation: the standard deviation of longitudinal level defects and the standard deviation of horizontal alignment defects. Hierarchical Bayesian Models (HBM) are flexible statistical models that allow specifying different spatially correlated c...
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
Bayesian statistics an introduction
Lee, Peter M
2012-01-01
Bayesian Statistics is the school of thought that combines prior beliefs with the likelihood of a hypothesis to arrive at posterior beliefs. The first edition of Peter Lee’s book appeared in 1989, but the subject has moved ever onwards, with increasing emphasis on Monte Carlo based techniques. This new fourth edition looks at recent techniques such as variational methods, Bayesian importance sampling, approximate Bayesian computation and Reversible Jump Markov Chain Monte Carlo (RJMCMC), providing a concise account of the way in which the Bayesian approach to statistics develops as wel
Statistical performance analysis by loopy belief propagation in Bayesian image modeling
International Nuclear Information System (INIS)
The mathematical structures of loopy belief propagation are reviewed for Bayesian image modeling from the standpoint of statistical mechanical informatics. We propose some schemes for evaluating the statistical performance of probabilistic binary image restoration. The schemes are constructed by means of the LBP, which is known as the Bethe approximation in statistical mechanics. We show some results of numerical experiments obtained by using the LBP algorithm as well as the statistical performance analysis for the probabilistic image restorations.
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...
Statistical modelling of railway track geometry degradation using Hierarchical Bayesian models
International Nuclear Information System (INIS)
Railway maintenance planners require a predictive model that can assess the railway track geometry degradation. The present paper uses a Hierarchical Bayesian model as a tool to model the main two quality indicators related to railway track geometry degradation: the standard deviation of longitudinal level defects and the standard deviation of horizontal alignment defects. Hierarchical Bayesian Models (HBM) are flexible statistical models that allow specifying different spatially correlated components between consecutive track sections, namely for the deterioration rates and the initial qualities parameters. HBM are developed for both quality indicators, conducting an extensive comparison between candidate models and a sensitivity analysis on prior distributions. HBM is applied to provide an overall assessment of the degradation of railway track geometry, for the main Portuguese railway line Lisbon–Oporto. - Highlights: • Rail track geometry degradation is analysed using Hierarchical Bayesian models. • A Gibbs sampling strategy is put forward to estimate the HBM. • Model comparison and sensitivity analysis find the most suitable model. • We applied the most suitable model to all the segments of the main Portuguese line. • Tackling spatial correlations using CAR structures lead to a better model fit
Use of SAMC for Bayesian analysis of statistical models with intractable normalizing constants
Jin, Ick Hoon
2014-03-01
Statistical inference for the models with intractable normalizing constants has attracted much attention. During the past two decades, various approximation- or simulation-based methods have been proposed for the problem, such as the Monte Carlo maximum likelihood method and the auxiliary variable Markov chain Monte Carlo methods. The Bayesian stochastic approximation Monte Carlo algorithm specifically addresses this problem: It works by sampling from a sequence of approximate distributions with their average converging to the target posterior distribution, where the approximate distributions can be achieved using the stochastic approximation Monte Carlo algorithm. A strong law of large numbers is established for the Bayesian stochastic approximation Monte Carlo estimator under mild conditions. Compared to the Monte Carlo maximum likelihood method, the Bayesian stochastic approximation Monte Carlo algorithm is more robust to the initial guess of model parameters. Compared to the auxiliary variable MCMC methods, the Bayesian stochastic approximation Monte Carlo algorithm avoids the requirement for perfect samples, and thus can be applied to many models for which perfect sampling is not available or very expensive. The Bayesian stochastic approximation Monte Carlo algorithm also provides a general framework for approximate Bayesian analysis. © 2012 Elsevier B.V. All rights reserved.
A new model test in high energy physics in frequentist and Bayesian statistical formalisms
Kamenshchikov, Andrey
2016-01-01
A problem of a new physical model test given observed experimental data is a typical one for modern experiments of high energy physics (HEP). A solution of the problem may be provided with two alternative statistical formalisms, namely frequentist and Bayesian, which are widely spread in contemporary HEP searches. A characteristic experimental situation is modeled from general considerations and both the approaches are utilized in order to test a new model. The results are juxtaposed, what de...
A new model test in high energy physics in frequentist and Bayesian statistical formalisms
Kamenshchikov, Andrey
2016-01-01
A problem of a new physical model test given observed experimental data is a typical one for modern experiments of high energy physics (HEP). A solution of the problem may be provided with two alternative statistical formalisms, namely frequentist and Bayesian, which are widely spread in contemporary HEP searches. A characteristic experimental situation is modeled from general considerations and both the approaches are utilized in order to test a new model. The results are juxtaposed, what demonstrates their consistency in this work. An effect of a systematic uncertainty treatment in the statistical analysis is also considered.
GNU MCSim : bayesian statistical inference for SBML-coded systems biology models
Bois, Frédéric Y.
2009-01-01
International audience Statistical inference about the parameter values of complex models, such as the ones routinely developed in systems biology, is efficiently performed through Bayesian numerical techniques. In that framework, prior information and multiple levels of uncertainty can be seamlessly integrated. GNU MCSim was precisely developed to achieve those aims, in a general non-linear differential context. Starting with version 5.3.0, GNU MCSim reads in and simulates Systems Biology...
Directory of Open Access Journals (Sweden)
C. Mukherjee
2011-01-01
Full Text Available Inverse modeling applications in atmospheric chemistry are increasingly addressing the challenging statistical issues of data synthesis by adopting refined statistical analysis methods. This paper advances this line of research by addressing several central questions in inverse modeling, focusing specifically on Bayesian statistical computation. Motivated by problems of refining bottom-up estimates of source/sink fluxes of trace gas and aerosols based on increasingly high-resolution satellite retrievals of atmospheric chemical concentrations, we address head-on the need for integrating formal spatial statistical methods of residual error structure in global scale inversion models. We do this using analytically and computationally tractable spatial statistical models, know as conditional autoregressive spatial models, as components of a global inversion framework. We develop Markov chain Monte Carlo methods to explore and fit these spatial structures in an overall statistical framework that simultaneously estimates source fluxes. Additional aspects of the study extend the statistical framework to utilize priors in a more physically realistic manner, and to formally address and deal with missing data in satellite retrievals. We demonstrate the analysis in the context of inferring carbon monoxide (CO sources constrained by satellite retrievals of column CO from the Measurement of Pollution in the Troposphere (MOPITT instrument on the TERRA satellite, paying special attention to evaluating performance of the inverse approach using various statistical diagnostic metrics. This is developed using synthetic data generated to resemble MOPITT data to define a~proof-of-concept and model assessment, and then in analysis of real MOPITT data.
Bayesian default probability models
Andrlíková, Petra
2014-01-01
This paper proposes a methodology for default probability estimation for low default portfolios, where the statistical inference may become troublesome. The author suggests using logistic regression models with the Bayesian estimation of parameters. The piecewise logistic regression model and Box-Cox transformation of credit risk score is used to derive the estimates of probability of default, which extends the work by Neagu et al. (2009). The paper shows that the Bayesian models are more acc...
Zhang, Xianliang; Yan, Xiaodong
2015-11-01
A new statistical downscaling method was developed and applied to downscale monthly total precipitation from 583 stations in China. Generally, there are two steps involved in statistical downscaling: first, the predictors are selected (large-scale variables) and transformed; and second, a model between the predictors and the predictand (in this case, precipitation) is established. In the first step, a selection process of the predictor domain, called the optimum correlation method (OCM), was developed to transform the predictors. The transformed series obtained by the OCM showed much better correlation with the predictand than those obtained by the traditional transform method for the same predictor. Moreover, the method combining OCM and linear regression obtained better downscaling results than the traditional linear regression method, suggesting that the OCM could be used to improve the results of statistical downscaling. In the second step, Bayesian model averaging (BMA) was adopted as an alternative to linear regression. The method combining the OCM and BMA showed much better performance than the method combining the OCM and linear regression. Thus, BMA could be used as an alternative to linear regression in the second step of statistical downscaling. In conclusion, the downscaling method combining OCM and BMA produces more accurate results than the multiple linear regression method when used to statistically downscale large-scale variables.
Schöniger, Anneli; Wöhling, Thomas; Nowak, Wolfgang
2015-09-01
Bayesian model averaging (BMA) ranks the plausibility of alternative conceptual models according to Bayes' theorem. A prior belief about each model's adequacy is updated to a posterior model probability based on the skill to reproduce observed data and on the principle of parsimony. The posterior model probabilities are then used as model weights for model ranking, selection, or averaging. Despite the statistically rigorous BMA procedure, model weights can become uncertain quantities due to measurement noise in the calibration data set or due to uncertainty in model input. Uncertain weights may in turn compromise the reliability of BMA results. We present a new statistical concept to investigate this weighting uncertainty, and thus, to assess the significance of model weights and the confidence in model ranking. Our concept is to resample the uncertain input or output data and then to analyze the induced variability in model weights. In the special case of weighting uncertainty due to measurement noise in the calibration data set, we interpret statistics of Bayesian model evidence to assess the distance of a model's performance from the theoretical upper limit. To illustrate our suggested approach, we investigate the reliability of soil-plant model selection following up on a study by Wöhling et al. (2015). Results show that the BMA routine should be equipped with our suggested upgrade to (1) reveal the significant but otherwise undetected impact of measurement noise on model ranking results and (2) to decide whether the considered set of models should be extended with better performing alternatives.
Directory of Open Access Journals (Sweden)
C. Mukherjee
2011-06-01
Full Text Available We present and discuss the use of Bayesian modeling and computational methods for atmospheric chemistry inverse analyses that incorporate evaluation of spatial structure in model-data residuals. Motivated by problems of refining bottom-up estimates of source/sink fluxes of trace gas and aerosols based on satellite retrievals of atmospheric chemical concentrations, we address the need for formal modeling of spatial residual error structure in global scale inversion models. We do this using analytically and computationally tractable conditional autoregressive (CAR spatial models as components of a global inversion framework. We develop Markov chain Monte Carlo methods to explore and fit these spatial structures in an overall statistical framework that simultaneously estimates source fluxes. Additional aspects of the study extend the statistical framework to utilize priors on source fluxes in a physically realistic manner, and to formally address and deal with missing data in satellite retrievals. We demonstrate the analysis in the context of inferring carbon monoxide (CO sources constrained by satellite retrievals of column CO from the Measurement of Pollution in the Troposphere (MOPITT instrument on the TERRA satellite, paying special attention to evaluating performance of the inverse approach using various statistical diagnostic metrics. This is developed using synthetic data generated to resemble MOPITT data to define a proof-of-concept and model assessment, and then in analysis of real MOPITT data. These studies demonstrate the ability of these simple spatial models to substantially improve over standard non-spatial models in terms of statistical fit, ability to recover sources in synthetic examples, and predictive match with real data.
Herschtal, A.; Foroudi, F.; Greer, P. B.; Eade, T. N.; Hindson, B. R.; Kron, T.
2012-05-01
Early approaches to characterizing errors in target displacement during a fractionated course of radiotherapy assumed that the underlying fraction-to-fraction variability in target displacement, known as the ‘treatment error’ or ‘random error’, could be regarded as constant across patients. More recent approaches have modelled target displacement allowing for differences in random error between patients. However, until recently it has not been feasible to compare the goodness of fit of alternate models of random error rigorously. This is because the large volumes of real patient data necessary to distinguish between alternative models have only very recently become available. This work uses real-world displacement data collected from 365 patients undergoing radical radiotherapy for prostate cancer to compare five candidate models for target displacement. The simplest model assumes constant random errors across patients, while other models allow for random errors that vary according to one of several candidate distributions. Bayesian statistics and Markov Chain Monte Carlo simulation of the model parameters are used to compare model goodness of fit. We conclude that modelling the random error as inverse gamma distributed provides a clearly superior fit over all alternatives considered. This finding can facilitate more accurate margin recipes and correction strategies.
Directory of Open Access Journals (Sweden)
Sarah Depaoli
2015-03-01
Full Text Available Background: After traumatic events, such as disaster, war trauma, and injuries including burns (which is the focus here, the risk to develop posttraumatic stress disorder (PTSD is approximately 10% (Breslau & Davis, 1992. Latent Growth Mixture Modeling can be used to classify individuals into distinct groups exhibiting different patterns of PTSD (Galatzer-Levy, 2015. Currently, empirical evidence points to four distinct trajectories of PTSD patterns in those who have experienced burn trauma. These trajectories are labeled as: resilient, recovery, chronic, and delayed onset trajectories (e.g., Bonanno, 2004; Bonanno, Brewin, Kaniasty, & Greca, 2010; Maercker, Gäbler, O'Neil, Schützwohl, & Müller, 2013; Pietrzak et al., 2013. The delayed onset trajectory affects only a small group of individuals, that is, about 4–5% (O'Donnell, Elliott, Lau, & Creamer, 2007. In addition to its low frequency, the later onset of this trajectory may contribute to the fact that these individuals can be easily overlooked by professionals. In this special symposium on Estimating PTSD trajectories (Van de Schoot, 2015a, we illustrate how to properly identify this small group of individuals through the Bayesian estimation framework using previous knowledge through priors (see, e.g., Depaoli & Boyajian, 2014; Van de Schoot, Broere, Perryck, Zondervan-Zwijnenburg, & Van Loey, 2015. Method: We used latent growth mixture modeling (LGMM (Van de Schoot, 2015b to estimate PTSD trajectories across 4 years that followed a traumatic burn. We demonstrate and compare results from traditional (maximum likelihood and Bayesian estimation using priors (see, Depaoli, 2012, 2013. Further, we discuss where priors come from and how to define them in the estimation process. Results: We demonstrate that only the Bayesian approach results in the desired theory-driven solution of PTSD trajectories. Since the priors are chosen subjectively, we also present a sensitivity analysis of the
Francis, Royce A; Vanbriesen, Jeanne M; Small, Mitchell J
2010-02-15
Statistical models are developed for bromine incorporation in the trihalomethane (THM), trihaloacetic acids (THAA), dihaloacetic acid (DHAA), and dihaloacetonitrile (DHAN) subclasses of disinfection byproducts (DBPs) using distribution system samples from plants applying only free chlorine as a primary or residual disinfectant in the Information Collection Rule (ICR) database. The objective of this study is to characterize the effect of water quality conditions before, during, and post-treatment on distribution system bromine incorporation into DBP mixtures. Bayesian Markov Chain Monte Carlo (MCMC) methods are used to model individual DBP concentrations and estimate the coefficients of the linear models used to predict the bromine incorporation fraction for distribution system DBP mixtures in each of the four priority DBP classes. The bromine incorporation models achieve good agreement with the data. The most important predictors of bromine incorporation fraction across DBP classes are alkalinity, specific UV absorption (SUVA), and the bromide to total organic carbon ratio (Br:TOC) at the first point of chlorine addition. Free chlorine residual in the distribution system, distribution system residence time, distribution system pH, turbidity, and temperature only slightly influence bromine incorporation. The bromide to applied chlorine (Br:Cl) ratio is not a significant predictor of the bromine incorporation fraction (BIF) in any of the four classes studied. These results indicate that removal of natural organic matter and the location of chlorine addition are important treatment decisions that have substantial implications for bromine incorporation into disinfection byproduct in drinking waters. PMID:20095529
Topics in Nonparametric Bayesian Statistics
2003-01-01
The intersection set of Bayesian and nonparametric statistics was almost empty until about 1973, but now seems to be growing at a healthy rate. This chapter gives an overview of various theoretical and applied research themes inside this field, partly complementing and extending recent reviews of Dey, Müller and Sinha (1998) and Walker, Damien, Laud and Smith (1999). The intention is not to be complete or exhaustive, but rather to touch on research areas of interest, partly by example.
Automated parameter estimation for biological models using Bayesian statistical model checking
Hussain, Faraz; Langmead, Christopher J.; Mi, Qi; Dutta-Moscato, Joyeeta; Vodovotz, Yoram; Jha, Sumit K.
2015-01-01
Background Probabilistic models have gained widespread acceptance in the systems biology community as a useful way to represent complex biological systems. Such models are developed using existing knowledge of the structure and dynamics of the system, experimental observations, and inferences drawn from statistical analysis of empirical data. A key bottleneck in building such models is that some system variables cannot be measured experimentally. These variables are incorporated into the mode...
DEFF Research Database (Denmark)
Jensen, Finn Verner; Nielsen, Thomas Dyhre
2016-01-01
Mathematically, a Bayesian graphical model is a compact representation of the joint probability distribution for a set of variables. The most frequently used type of Bayesian graphical models are Bayesian networks. The structural part of a Bayesian graphical model is a graph consisting of nodes and...... largely due to the availability of efficient inference algorithms for answering probabilistic queries about the states of the variables in the network. Furthermore, to support the construction of Bayesian network models, learning algorithms are also available. We give an overview of the Bayesian network...
12th Brazilian Meeting on Bayesian Statistics
Louzada, Francisco; Rifo, Laura; Stern, Julio; Lauretto, Marcelo
2015-01-01
Through refereed papers, this volume focuses on the foundations of the Bayesian paradigm; their comparison to objectivistic or frequentist Statistics counterparts; and the appropriate application of Bayesian foundations. This research in Bayesian Statistics is applicable to data analysis in biostatistics, clinical trials, law, engineering, and the social sciences. EBEB, the Brazilian Meeting on Bayesian Statistics, is held every two years by the ISBrA, the International Society for Bayesian Analysis, one of the most active chapters of the ISBA. The 12th meeting took place March 10-14, 2014 in Atibaia. Interest in foundations of inductive Statistics has grown recently in accordance with the increasing availability of Bayesian methodological alternatives. Scientists need to deal with the ever more difficult choice of the optimal method to apply to their problem. This volume shows how Bayes can be the answer. The examination and discussion on the foundations work towards the goal of proper application of Bayesia...
Congdon, Peter
2014-01-01
This book provides an accessible approach to Bayesian computing and data analysis, with an emphasis on the interpretation of real data sets. Following in the tradition of the successful first edition, this book aims to make a wide range of statistical modeling applications accessible using tested code that can be readily adapted to the reader's own applications. The second edition has been thoroughly reworked and updated to take account of advances in the field. A new set of worked examples is included. The novel aspect of the first edition was the coverage of statistical modeling using WinBU
Topics in Bayesian statistics and maximum entropy
International Nuclear Information System (INIS)
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)
Bayesian Statistics for Biological Data: Pedigree Analysis
Stanfield, William D.; Carlton, Matthew A.
2004-01-01
The use of Bayes' formula is applied to the biological problem of pedigree analysis to show that the Bayes' formula and non-Bayesian or "classical" methods of probability calculation give different answers. First year college students of biology can be introduced to the Bayesian statistics.
Baltic sea algae analysis using Bayesian spatial statistics methods
Directory of Open Access Journals (Sweden)
Eglė Baltmiškytė
2013-03-01
Full Text Available Spatial statistics is one of the fields in statistics dealing with spatialy spread data analysis. Recently, Bayes methods are often applied for data statistical analysis. A spatial data model for predicting algae quantity in the Baltic Sea is made and described in this article. Black Carrageen is a dependent variable and depth, sand, pebble, boulders are independent variables in the described model. Two models with different covariation functions (Gaussian and exponential are built to estimate the best model fitting for algae quantity prediction. Unknown model parameters are estimated and Bayesian kriging prediction posterior distribution is computed in OpenBUGS modeling environment by using Bayesian spatial statistics methods.
Cubillos, Patricio; Harrington, Joseph; Blecic, Jasmina; Stemm, Madison M.; Lust, Nate B.; Foster, Andrew S.; Rojo, Patricio M.; Loredo, Thomas J.
2014-11-01
Multi-wavelength secondary-eclipse and transit depths probe the thermo-chemical properties of exoplanets. In recent years, several research groups have developed retrieval codes to analyze the existing data and study the prospects of future facilities. However, the scientific community has limited access to these packages. Here we premiere the open-source Bayesian Atmospheric Radiative Transfer (BART) code. We discuss the key aspects of the radiative-transfer algorithm and the statistical package. The radiation code includes line databases for all HITRAN molecules, high-temperature H2O, TiO, and VO, and includes a preprocessor for adding additional line databases without recompiling the radiation code. Collision-induced absorption lines are available for H2-H2 and H2-He. The parameterized thermal and molecular abundance profiles can be modified arbitrarily without recompilation. The generated spectra are integrated over arbitrary bandpasses for comparison to data. BART's statistical package, Multi-core Markov-chain Monte Carlo (MC3), is a general-purpose MCMC module. MC3 implements the Differental-evolution Markov-chain Monte Carlo algorithm (ter Braak 2006, 2009). MC3 converges 20-400 times faster than the usual Metropolis-Hastings MCMC algorithm, and in addition uses the Message Passing Interface (MPI) to parallelize the MCMC chains. We apply the BART retrieval code to the HD 209458b data set to estimate the planet's temperature profile and molecular abundances. This work was supported by NASA Planetary Atmospheres grant NNX12AI69G and NASA Astrophysics Data Analysis Program grant NNX13AF38G. JB holds a NASA Earth and Space Science Fellowship.
Introduction to applied Bayesian statistics and estimation for social scientists
Lynch, Scott M
2007-01-01
""Introduction to Applied Bayesian Statistics and Estimation for Social Scientists"" covers the complete process of Bayesian statistical analysis in great detail from the development of a model through the process of making statistical inference. The key feature of this book is that it covers models that are most commonly used in social science research - including the linear regression model, generalized linear models, hierarchical models, and multivariate regression models - and it thoroughly develops each real-data example in painstaking detail.The first part of the book provides a detailed
Bayesian Stable Isotope Mixing Models
Parnell, Andrew C.; Phillips, Donald L.; Bearhop, Stuart; Semmens, Brice X.; Ward, Eric J.; Moore, Jonathan W.; Andrew L Jackson; Inger, Richard
2012-01-01
In this paper we review recent advances in Stable Isotope Mixing Models (SIMMs) and place them into an over-arching Bayesian statistical framework which allows for several useful extensions. SIMMs are used to quantify the proportional contributions of various sources to a mixture. The most widely used application is quantifying the diet of organisms based on the food sources they have been observed to consume. At the centre of the multivariate statistical model we propose is a compositional m...
Comparison of the Bayesian and Frequentist Approach to the Statistics
Hakala, Michal
2015-01-01
The Thesis deals with introduction to Bayesian statistics and comparing Bayesian approach with frequentist approach to statistics. Bayesian statistics is modern branch of statistics which provides an alternative comprehensive theory to the frequentist approach. Bayesian concepts provides solution for problems not being solvable by frequentist theory. In the thesis are compared definitions, concepts and quality of statistical inference. The main interest is focused on a point estimation, an in...
Wahl, E. R.
2008-12-01
A strict process model for pollen as a climate proxy is currently not approachable beyond localized spatial scales; more generally, the canonical model for vegetation-pollen registration itself requires assimilation of empirically-derived information. In this paper, a taxonomically "reduced-space" climate-pollen forward model is developed, based on the performance of a parallel inverse model. The goal is inclusion of the forward model in a Bayesian climate reconstruction framework, following a 4-step process. (1) Ratios of pollen types calibrated to temperature are examined to determine if they can equal or surpass the skill of multi-taxonomic calibrations using the modern analog technique (MAT) optimized with receiver operating characteristic (ROC) analysis. The first phase of this examination, using modern pollen data from SW N America, demonstrates that the ratio method can give calibrations as skillful as the MAT when vegetation representation (and associated climate gradients) are characterized by two dominant pollen taxa, in this case pine and oak. Paleotemperature reconstructions using the ratio method also compare well to MAT reconstructions, showing very minor differences. [Ratio values are defined as pine/(pine + oak), so they vary between 0 and 1.] (2) Uncertainty analysis is carried out in independent steps, which are combined to give overall probabilistic confidence ranges. Monte Carlo (MC) analysis utilizing Poisson distributions to model the inherent variability of pollen representation in relation to climate (assuming defined temperature normals at the modern calibration sites) allows independent statistical estimation of this component of uncertainty, for both the modern calibration and fossil pollen data sets. In turn, MC analysis utilizing normal distributions allows independent estimation of the addition to overall uncertainty from climate variation itself. (3) Because the quality tests in (1) indicate the ratio method has the capacity to carry
Application of a Bayesian algorithm for the Statistical Energy model updating of a railway coach
DEFF Research Database (Denmark)
Sadri, Mehran; Brunskog, Jonas; Younesian, Davood
2016-01-01
presence of possible strong coupling between subsystems and the lack of diffuseness result in a significant uncertainty. This is the main motivation for the present study, where a procedure to update SEA models is proposed. The proposed procedure is the combination of the classical SEA method and a...... the performance of the proposed strategy, the SEA model updating of a railway passenger coach is carried out. First, a sensitivity analysis is carried out to select the most sensitive parameters of the SEA model. For the selected parameters of the model, prior probability density functions are then...... efficiently used to update the SEA models with a high number of unknown parameters....
Summary Statistics in Approximate Bayesian Computation
Prangle, Dennis
2015-01-01
This document is due to appear as a chapter of the forthcoming Handbook of Approximate Bayesian Computation (ABC) edited by S. Sisson, Y. Fan, and M. Beaumont. Since the earliest work on ABC, it has been recognised that using summary statistics is essential to produce useful inference results. This is because ABC suffers from a curse of dimensionality effect, whereby using high dimensional inputs causes large approximation errors in the output. It is therefore crucial to find low dimensional ...
Bayesian Tracking of Emerging Epidemics Using Ensemble Optimal Statistical Interpolation
Cobb, Loren; Krishnamurthy, Ashok; Mandel, Jan; Beezley, Jonathan D.
2014-01-01
We present a preliminary test of the Ensemble Optimal Statistical Interpolation (EnOSI) method for the statistical tracking of an emerging epidemic, with a comparison to its popular relative for Bayesian data assimilation, the Ensemble Kalman Filter (EnKF). The spatial data for this test was generated by a spatial susceptible-infectious-removed (S-I-R) epidemic model of an airborne infectious disease. Both tracking methods in this test employed Poisson rather than Gaussian noise, so as to han...
A Quasirandom Approach to Integration in Bayesian Statistics
Shaw, J. E. H.
1988-01-01
Practical Bayesian statistics with realistic models usually gives posterior distributions that are analytically intractable, and inferences must be made via numerical integration. In many cases, the integrands can be transformed into periodic functions on the unit $d$-dimensional cube, for which quasirandom sequences are known to give efficient numerical integration rules. This paper reviews some relevant theory, defines new criteria for identifying suitable quasirandom sequences and suggests...
Bayesian credible interval construction for Poisson statistics
Institute of Scientific and Technical Information of China (English)
ZHU Yong-Sheng
2008-01-01
The construction of the Bayesian credible (confidence) interval for a Poisson observable including both the signal and background with and without systematic uncertainties is presented.Introducing the conditional probability satisfying the requirement of the background not larger than the observed events to construct the Bayesian credible interval is also discussed.A Fortran routine,BPOCI,has been developed to implement the calculation.
Statistical assignment of DNA sequences using Bayesian phylogenetics
DEFF Research Database (Denmark)
Terkelsen, Kasper Munch; Boomsma, Wouter Krogh; Huelsenbeck, John P;
2008-01-01
We provide a new automated statistical method for DNA barcoding based on a Bayesian phylogenetic analysis. The method is based on automated database sequence retrieval, alignment, and phylogenetic analysis using a custom-built program for Bayesian phylogenetic analysis. We show on real data that...
Complex Bayesian models: construction, and sampling strategies
Huston, Carolyn Marie
2011-01-01
Bayesian models are useful tools for realistically modeling processes occurring in the real world. In particular, we consider models for spatio-temporal data where the response vector is compositional, ie. has components that sum-to-one. A unique multivariate conditional hierarchical model (MVCAR) is proposed. Statistical methods for MVCAR models are well developed and we extend these tools for use with a discrete compositional response. We harness the advantages of an MVCAR model when the re...
Bayesian Analysis of Multiple Populations I: Statistical and Computational Methods
Stenning, D C; Robinson, E; van Dyk, D A; von Hippel, T; Sarajedini, A; Stein, N
2016-01-01
We develop a Bayesian model for globular clusters composed of multiple stellar populations, extending earlier statistical models for open clusters composed of simple (single) stellar populations (vanDyk et al. 2009, Stein et al. 2013). Specifically, we model globular clusters with two populations that differ in helium abundance. Our model assumes a hierarchical structuring of the parameters in which physical properties---age, metallicity, helium abundance, distance, absorption, and initial mass---are common to (i) the cluster as a whole or to (ii) individual populations within a cluster, or are unique to (iii) individual stars. An adaptive Markov chain Monte Carlo (MCMC) algorithm is devised for model fitting that greatly improves convergence relative to its precursor non-adaptive MCMC algorithm. Our model and computational tools are incorporated into an open-source software suite known as BASE-9. We use numerical studies to demonstrate that our method can recover parameters of two-population clusters, and al...
Fully Bayesian tests of neutrality using genealogical summary statistics
Directory of Open Access Journals (Sweden)
Drummond Alexei J
2008-10-01
Full Text Available Abstract Background Many data summary statistics have been developed to detect departures from neutral expectations of evolutionary models. However questions about the neutrality of the evolution of genetic loci within natural populations remain difficult to assess. One critical cause of this difficulty is that most methods for testing neutrality make simplifying assumptions simultaneously about the mutational model and the population size model. Consequentially, rejecting the null hypothesis of neutrality under these methods could result from violations of either or both assumptions, making interpretation troublesome. Results Here we harness posterior predictive simulation to exploit summary statistics of both the data and model parameters to test the goodness-of-fit of standard models of evolution. We apply the method to test the selective neutrality of molecular evolution in non-recombining gene genealogies and we demonstrate the utility of our method on four real data sets, identifying significant departures of neutrality in human influenza A virus, even after controlling for variation in population size. Conclusion Importantly, by employing a full model-based Bayesian analysis, our method separates the effects of demography from the effects of selection. The method also allows multiple summary statistics to be used in concert, thus potentially increasing sensitivity. Furthermore, our method remains useful in situations where analytical expectations and variances of summary statistics are not available. This aspect has great potential for the analysis of temporally spaced data, an expanding area previously ignored for limited availability of theory and methods.
Bayesian inference on the sphere beyond statistical isotropy
Das, Santanu; Souradeep, Tarun
2015-01-01
We present a general method for Bayesian inference of the underlying covariance structure of random fields on a sphere. We employ the Bipolar Spherical Harmonic (BipoSH) representation of general covariance structure on the sphere. We illustrate the efficacy of the method as a principled approach to assess violation of statistical isotropy (SI) in the sky maps of Cosmic Microwave Background (CMB) fluctuations. SI violation in observed CMB maps arise due to known physical effects such as Doppler boost and weak lensing; yet unknown theoretical possibilities like cosmic topology and subtle violations of the cosmological principle, as well as, expected observational artefacts of scanning the sky with a non-circular beam, masking, foreground residuals, anisotropic noise, etc. We explicitly demonstrate the recovery of the input SI violation signals with their full statistics in simulated CMB maps. Our formalism easily adapts to exploring parametric physical models with non-SI covariance, as we illustrate for the in...
Algebraic methods for evaluating integrals In Bayesian statistics
Lin, Shaowei
2011-01-01
The accurate evaluation of marginal likelihood integrals is a difficult fundamental problem in Bayesian inference that has important applications in machine learning and computational biology. Following the recent success of algebraic statistics in frequentist inference and inspired by Watanabe's foundational approach to singular learning theory, the goal of this dissertation is to study algebraic, geometric and combinatorial methods for computing Bayesian integrals effectively, and to explor...
Defining statistical perceptions with an empirical Bayesian approach
Tajima, Satohiro
2013-04-01
Extracting statistical structures (including textures or contrasts) from a natural stimulus is a central challenge in both biological and engineering contexts. This study interprets the process of statistical recognition in terms of hyperparameter estimations and free-energy minimization procedures with an empirical Bayesian approach. This mathematical interpretation resulted in a framework for relating physiological insights in animal sensory systems to the functional properties of recognizing stimulus statistics. We applied the present theoretical framework to two typical models of natural images that are encoded by a population of simulated retinal neurons, and demonstrated that the resulting cognitive performances could be quantified with the Fisher information measure. The current enterprise yielded predictions about the properties of human texture perception, suggesting that the perceptual resolution of image statistics depends on visual field angles, internal noise, and neuronal information processing pathways, such as the magnocellular, parvocellular, and koniocellular systems. Furthermore, the two conceptually similar natural-image models were found to yield qualitatively different predictions, striking a note of warning against confusing the two models when describing a natural image.
Bayesian Model Averaging for Propensity Score Analysis
Kaplan, David; Chen, Jianshen
2013-01-01
The purpose of this study is to explore Bayesian model averaging in the propensity score context. Previous research on Bayesian propensity score analysis does not take into account model uncertainty. In this regard, an internally consistent Bayesian framework for model building and estimation must also account for model uncertainty. The…
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 ...
Bayesian mixture models for Poisson astronomical images
Guglielmetti, Fabrizia; Fischer, Rainer; Dose, Volker
2012-01-01
Astronomical images in the Poisson regime are typically characterized by a spatially varying cosmic background, large variety of source morphologies and intensities, data incompleteness, steep gradients in the data, and few photon counts per pixel. The Background-Source separation technique is developed with the aim to detect faint and extended sources in astronomical images characterized by Poisson statistics. The technique employs Bayesian mixture models to reliably detect the background as...
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 estimation of parameters in a regional hydrological model
Engeland, K.; Gottschalk, L.
2002-01-01
This study evaluates the applicability of the distributed, process-oriented Ecomag model for prediction of daily streamflow in ungauged basins. The Ecomag model is applied as a regional model to nine catchments in the NOPEX area, using Bayesian statistics to estimate the posterior distribution of the model parameters conditioned on the observed streamflow. The distribution is calculated by Markov Chain Monte Carlo (MCMC) analysis. The Bayesian method requires formulation of a likelihood funct...
Bayesian estimation of parameters in a regional hydrological model
Engeland, K.; Gottschalk, L.
2002-01-01
This study evaluates the applicability of the distributed, process-oriented Ecomag model for prediction of daily streamflow in ungauged basins. The Ecomag model is applied as a regional model to nine catchments in the NOPEX area, using Bayesian statistics to estimate the posterior distribution of the model parameters conditioned on the observed streamflow. The distribution is calculated by Markov Chain Monte Carlo (MCMC) analysis. The Bayesian method requires formulation of ...
Bayesian Analysis of Dynamic Multivariate Models with Multiple Structural Breaks
Sugita, Katsuhiro
2006-01-01
This paper considers a vector autoregressive model or a vector error correction model with multiple structural breaks in any subset of parameters, using a Bayesian approach with Markov chain Monte Carlo simulation technique. The number of structural breaks is determined as a sort of model selection by the posterior odds. For a cointegrated model, cointegrating rank is also allowed to change with breaks. Bayesian approach by Strachan (Journal of Business and Economic Statistics 21 (2003) 185) ...
Bayesian kinematic earthquake source models
Minson, S. E.; Simons, M.; Beck, J. L.; Genrich, J. F.; Galetzka, J. E.; Chowdhury, F.; Owen, S. E.; Webb, F.; Comte, D.; Glass, B.; Leiva, C.; Ortega, F. H.
2009-12-01
Most coseismic, postseismic, and interseismic slip models are based on highly regularized optimizations which yield one solution which satisfies the data given a particular set of regularizing constraints. This regularization hampers our ability to answer basic questions such as whether seismic and aseismic slip overlap or instead rupture separate portions of the fault zone. We present a Bayesian methodology for generating kinematic earthquake source models with a focus on large subduction zone earthquakes. Unlike classical optimization approaches, Bayesian techniques sample the ensemble of all acceptable models presented as an a posteriori probability density function (PDF), and thus we can explore the entire solution space to determine, for example, which model parameters are well determined and which are not, or what is the likelihood that two slip distributions overlap in space. Bayesian sampling also has the advantage that all a priori knowledge of the source process can be used to mold the a posteriori ensemble of models. Although very powerful, Bayesian methods have up to now been of limited use in geophysical modeling because they are only computationally feasible for problems with a small number of free parameters due to what is called the "curse of dimensionality." However, our methodology can successfully sample solution spaces of many hundreds of parameters, which is sufficient to produce finite fault kinematic earthquake models. Our algorithm is a modification of the tempered Markov chain Monte Carlo (tempered MCMC or TMCMC) method. In our algorithm, we sample a "tempered" a posteriori PDF using many MCMC simulations running in parallel and evolutionary computation in which models which fit the data poorly are preferentially eliminated in favor of models which better predict the data. We present results for both synthetic test problems as well as for the 2007 Mw 7.8 Tocopilla, Chile earthquake, the latter of which is constrained by InSAR, local high
A Bayesian Nonparametric IRT Model
Karabatsos, George
2015-01-01
This paper introduces a flexible Bayesian nonparametric Item Response Theory (IRT) model, which applies to dichotomous or polytomous item responses, and which can apply to either unidimensional or multidimensional scaling. This is an infinite-mixture IRT model, with person ability and item difficulty parameters, and with a random intercept parameter that is assigned a mixing distribution, with mixing weights a probit function of other person and item parameters. As a result of its flexibility...
Bayesian Model Averaging in the Instrumental Variable Regression Model
Gary Koop; Robert Leon Gonzalez; Rodney Strachan
2011-01-01
This paper considers the instrumental variable regression model when there is uncertainly about the set of instruments, exogeneity restrictions, the validity of identifying restrictions and the set of exogenous regressors. This uncertainly can result in a huge number of models. To avoid statistical problems associated with standard model selection procedures, we develop a reversible jump Markov chain Monte Carlo algorithm that allows us to do Bayesian model averaging. The algorithm is very fl...
EVENT MODEL: A ROBUST BAYESIAN TOOL FOR CHRONOLOGICAL MODELING
Lanos, Philippe; Philippe, Anne
2015-01-01
We propose a new modeling approach for combining dates through the Event model by using hierarchical Bayesian statistics. The Event model aims to estimate the date of a context (unit of stratification) from individual dates assumed to be contemporaneous and which are affected by errors of different types: laboratory and calibration curve errors and also irreducible errors related to contaminations, taphonomic disturbances, etc, hence the possible presence of outliers. The Event model has a hi...
Bayesian variable order Markov models: Towards Bayesian predictive state representations
C. Dimitrakakis
2009-01-01
We present a Bayesian variable order Markov model that shares many similarities with predictive state representations. The resulting models are compact and much easier to specify and learn than classical predictive state representations. Moreover, we show that they significantly outperform a more st
Bayesian statistical ionospheric tomography improved by incorporating ionosonde measurements
Norberg, Johannes; Virtanen, Ilkka I.; Roininen, Lassi; Vierinen, Juha; Orispää, Mikko; Kauristie, Kirsti; Lehtinen, Markku S.
2016-04-01
We validate two-dimensional ionospheric tomography reconstructions against EISCAT incoherent scatter radar measurements. Our tomography method is based on Bayesian statistical inversion with prior distribution given by its mean and covariance. We employ ionosonde measurements for the choice of the prior mean and covariance parameters and use the Gaussian Markov random fields as a sparse matrix approximation for the numerical computations. This results in a computationally efficient tomographic inversion algorithm with clear probabilistic interpretation. We demonstrate how this method works with simultaneous beacon satellite and ionosonde measurements obtained in northern Scandinavia. The performance is compared with results obtained with a zero-mean prior and with the prior mean taken from the International Reference Ionosphere 2007 model. In validating the results, we use EISCAT ultra-high-frequency incoherent scatter radar measurements as the ground truth for the ionization profile shape. We find that in comparison to the alternative prior information sources, ionosonde measurements improve the reconstruction by adding accurate information about the absolute value and the altitude distribution of electron density. With an ionosonde at continuous disposal, the presented method enhances stand-alone near-real-time ionospheric tomography for the given conditions significantly.
Nonparametric Bayesian Modeling of Complex Networks
DEFF Research Database (Denmark)
Schmidt, Mikkel Nørgaard; Mørup, Morten
2013-01-01
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...... for complex networks can be derived and point out relevant literature....
Bayesian Inference and Optimal Design in the Sparse Linear Model
Seeger, Matthias; Steinke, Florian; Tsuda, Koji
2007-01-01
The sparse linear model has seen many successful applications in Statistics, Machine Learning, and Computational Biology, such as identification of gene regulatory networks from micro-array expression data. Prior work has either approximated Bayesian inference by expensive Markov chain Monte Carlo, or replaced it by point estimation. We show how to obtain a good approximation to Bayesian analysis efficiently, using the Expectation Propagation method. We also address the problems of optimal de...
Bayesians versus frequentists a philosophical debate on statistical reasoning
Vallverdú, Jordi
2016-01-01
This book analyzes the origins of statistical thinking as well as its related philosophical questions, such as causality, determinism or chance. Bayesian and frequentist approaches are subjected to a historical, cognitive and epistemological analysis, making it possible to not only compare the two competing theories, but to also find a potential solution. The work pursues a naturalistic approach, proceeding from the existence of numerosity in natural environments to the existence of contemporary formulas and methodologies to heuristic pragmatism, a concept introduced in the book’s final section. This monograph will be of interest to philosophers and historians of science and students in related fields. Despite the mathematical nature of the topic, no statistical background is required, making the book a valuable read for anyone interested in the history of statistics and human cognition.
The subjectivity of scientists and the Bayesian statistical approach
Press, James S
2001-01-01
Comparing and contrasting the reality of subjectivity in the work of history's great scientists and the modern Bayesian approach to statistical analysisScientists and researchers are taught to analyze their data from an objective point of view, allowing the data to speak for themselves rather than assigning them meaning based on expectations or opinions. But scientists have never behaved fully objectively. Throughout history, some of our greatest scientific minds have relied on intuition, hunches, and personal beliefs to make sense of empirical data-and these subjective influences have often a
A Bayesian approach to model uncertainty
International Nuclear Information System (INIS)
A Bayesian approach to model uncertainty is taken. For the case of a finite number of alternative models, the model uncertainty is equivalent to parameter uncertainty. A derivation based on Savage's partition problem is given
Bayesian estimation of parameters in a regional hydrological model
Directory of Open Access Journals (Sweden)
K. Engeland
2002-01-01
Full Text Available This study evaluates the applicability of the distributed, process-oriented Ecomag model for prediction of daily streamflow in ungauged basins. The Ecomag model is applied as a regional model to nine catchments in the NOPEX area, using Bayesian statistics to estimate the posterior distribution of the model parameters conditioned on the observed streamflow. The distribution is calculated by Markov Chain Monte Carlo (MCMC analysis. The Bayesian method requires formulation of a likelihood function for the parameters and three alternative formulations are used. The first is a subjectively chosen objective function that describes the goodness of fit between the simulated and observed streamflow, as defined in the GLUE framework. The second and third formulations are more statistically correct likelihood models that describe the simulation errors. The full statistical likelihood model describes the simulation errors as an AR(1 process, whereas the simple model excludes the auto-regressive part. The statistical parameters depend on the catchments and the hydrological processes and the statistical and the hydrological parameters are estimated simultaneously. The results show that the simple likelihood model gives the most robust parameter estimates. The simulation error may be explained to a large extent by the catchment characteristics and climatic conditions, so it is possible to transfer knowledge about them to ungauged catchments. The statistical models for the simulation errors indicate that structural errors in the model are more important than parameter uncertainties. Keywords: regional hydrological model, model uncertainty, Bayesian analysis, Markov Chain Monte Carlo analysis
Bayesian Estimation of a Mixture Model
Directory of Open Access Journals (Sweden)
Ilhem Merah
2015-05-01
Full Text Available We present the properties of a bathtub curve reliability model having both a sufficient adaptability and a minimal number of parameters introduced by Idée and Pierrat (2010. This one is a mixture of a Gamma distribution G(2, (1/θ and a new distribution L(θ. We are interesting by Bayesian estimation of the parameters and survival function of this model with a squared-error loss function and non-informative prior using the approximations of Lindley (1980 and Tierney and Kadane (1986. Using a statistical sample of 60 failure data relative to a technical device, we illustrate the results derived. Based on a simulation study, comparisons are made between these two methods and the maximum likelihood method of this two parameters model.
Computational methods for Bayesian model choice
Robert, Christian P.; Wraith, Darren
2009-01-01
In this note, we shortly survey some recent approaches on the approximation of the Bayes factor used in Bayesian hypothesis testing and in Bayesian model choice. In particular, we reassess importance sampling, harmonic mean sampling, and nested sampling from a unified perspective.
Bayesian Variable Selection in Spatial Autoregressive Models
Jesus Crespo Cuaresma; Philipp Piribauer
2015-01-01
This paper compares the performance of Bayesian variable selection approaches for spatial autoregressive models. We present two alternative approaches which can be implemented using Gibbs sampling methods in a straightforward way and allow us to deal with the problem of model uncertainty in spatial autoregressive models in a flexible and computationally efficient way. In a simulation study we show that the variable selection approaches tend to outperform existing Bayesian model averaging tech...
Bayesian Models of Brain and Behaviour
Penny, William
2012-01-01
This paper presents a review of Bayesian models of brain and behaviour. We first review the basic principles of Bayesian inference. This is followed by descriptions of sampling and variational methods for approximate inference, and forward and backward recursions in time for inference in dynamical models. The review of behavioural models covers work in visual processing, sensory integration, sensorimotor integration, and collective decision making. The review of brain models covers a range of...
Analysis of Gumbel Model for Software Reliability Using Bayesian Paradigm
Directory of Open Access Journals (Sweden)
Raj Kumar
2012-12-01
Full Text Available In this paper, we have illustrated the suitability of Gumbel Model for software reliability data. The model parameters are estimated using likelihood based inferential procedure: classical as well as Bayesian. The quasi Newton-Raphson algorithm is applied to obtain the maximum likelihood estimates and associated probability intervals. The Bayesian estimates of the parameters of Gumbel model are obtained using Markov Chain Monte Carlo(MCMC simulation method in OpenBUGS(established software for Bayesian analysis using Markov Chain Monte Carlo methods. The R functions are developed to study the statistical properties, model validation and comparison tools of the model and the output analysis of MCMC samples generated from OpenBUGS. Details of applying MCMC to parameter estimation for the Gumbel model are elaborated and a real software reliability data set is considered to illustrate the methods of inference discussed in this paper.
Bayesian Statistical Analysis Applied to NAA Data for Neutron Flux Spectrum Determination
Chiesa, D.; Previtali, E.; Sisti, M.
2014-04-01
In this paper, we present a statistical method, based on Bayesian statistics, to evaluate the neutron flux spectrum from the activation data of different isotopes. The experimental data were acquired during a neutron activation analysis (NAA) experiment [A. Borio di Tigliole et al., Absolute flux measurement by NAA at the Pavia University TRIGA Mark II reactor facilities, ENC 2012 - Transactions Research Reactors, ISBN 978-92-95064-14-0, 22 (2012)] performed at the TRIGA Mark II reactor of Pavia University (Italy). In order to evaluate the neutron flux spectrum, subdivided in energy groups, we must solve a system of linear equations containing the grouped cross sections and the activation rate data. We solve this problem with Bayesian statistical analysis, including the uncertainties of the coefficients and the a priori information about the neutron flux. A program for the analysis of Bayesian hierarchical models, based on Markov Chain Monte Carlo (MCMC) simulations, is used to define the problem statistical model and solve it. The energy group fluxes and their uncertainties are then determined with great accuracy and the correlations between the groups are analyzed. Finally, the dependence of the results on the prior distribution choice and on the group cross section data is investigated to confirm the reliability of the analysis.
Bayesian nonparametric estimation of hazard rate in monotone Aalen model
Czech Academy of Sciences Publication Activity Database
Timková, Jana
2014-01-01
Roč. 50, č. 6 (2014), s. 849-868. ISSN 0023-5954 Institutional support: RVO:67985556 Keywords : Aalen model * Bayesian estimation * MCMC Subject RIV: BB - Applied Statistics, Operational Research Impact factor: 0.541, year: 2014 http://library.utia.cas.cz/separaty/2014/SI/timkova-0438210.pdf
An Inhomogeneous Bayesian Texture Model for Spatially Varying Parameter Estimation
Dharmagunawardhana, Chathurika; Mahmoodi, Sasan; Bennett, Michael; Niranjan, Mahesan
2014-01-01
In statistical model based texture feature extraction, features based on spatially varying parameters achieve higher discriminative performances compared to spatially constant parameters. In this paper we formulate a novel Bayesian framework which achieves texture characterization by spatially varying parameters based on Gaussian Markov random fields. The parameter estimation is carried out by Metropolis-Hastings algorithm. The distributions of estimated spatially varying paramete...
A study of finite mixture model: Bayesian approach on financial time series data
Phoong, Seuk-Yen; Ismail, Mohd Tahir
2014-07-01
Recently, statistician have emphasized on the fitting finite mixture model by using Bayesian method. Finite mixture model is a mixture of distributions in modeling a statistical distribution meanwhile Bayesian method is a statistical method that use to fit the mixture model. Bayesian method is being used widely because it has asymptotic properties which provide remarkable result. In addition, Bayesian method also shows consistency characteristic which means the parameter estimates are close to the predictive distributions. In the present paper, the number of components for mixture model is studied by using Bayesian Information Criterion. Identify the number of component is important because it may lead to an invalid result. Later, the Bayesian method is utilized to fit the k-component mixture model in order to explore the relationship between rubber price and stock market price for Malaysia, Thailand, Philippines and Indonesia. Lastly, the results showed that there is a negative effect among rubber price and stock market price for all selected countries.
Bayesian mixture models for Poisson astronomical images
Guglielmetti, Fabrizia; Dose, Volker
2012-01-01
Astronomical images in the Poisson regime are typically characterized by a spatially varying cosmic background, large variety of source morphologies and intensities, data incompleteness, steep gradients in the data, and few photon counts per pixel. The Background-Source separation technique is developed with the aim to detect faint and extended sources in astronomical images characterized by Poisson statistics. The technique employs Bayesian mixture models to reliably detect the background as well as the sources with their respective uncertainties. Background estimation and source detection is achieved in a single algorithm. A large variety of source morphologies is revealed. The technique is applied in the X-ray part of the electromagnetic spectrum on ROSAT and Chandra data sets and it is under a feasibility study for the forthcoming eROSITA mission.
Merging Digital Surface Models Implementing Bayesian Approaches
Sadeq, H.; Drummond, J.; Li, Z.
2016-06-01
In this research different DSMs from different sources have been merged. The merging is based on a probabilistic model using a Bayesian Approach. The implemented data have been sourced from very high resolution satellite imagery sensors (e.g. WorldView-1 and Pleiades). It is deemed preferable to use a Bayesian Approach when the data obtained from the sensors are limited and it is difficult to obtain many measurements or it would be very costly, thus the problem of the lack of data can be solved by introducing a priori estimations of data. To infer the prior data, it is assumed that the roofs of the buildings are specified as smooth, and for that purpose local entropy has been implemented. In addition to the a priori estimations, GNSS RTK measurements have been collected in the field which are used as check points to assess the quality of the DSMs and to validate the merging result. The model has been applied in the West-End of Glasgow containing different kinds of buildings, such as flat roofed and hipped roofed buildings. Both quantitative and qualitative methods have been employed to validate the merged DSM. The validation results have shown that the model was successfully able to improve the quality of the DSMs and improving some characteristics such as the roof surfaces, which consequently led to better representations. In addition to that, the developed model has been compared with the well established Maximum Likelihood model and showed similar quantitative statistical results and better qualitative results. Although the proposed model has been applied on DSMs that were derived from satellite imagery, it can be applied to any other sourced DSMs.
Baltic sea algae analysis using Bayesian spatial statistics methods
Eglė Baltmiškytė; Kęstutis Dučinskas
2013-01-01
Spatial statistics is one of the fields in statistics dealing with spatialy spread data analysis. Recently, Bayes methods are often applied for data statistical analysis. A spatial data model for predicting algae quantity in the Baltic Sea is made and described in this article. Black Carrageen is a dependent variable and depth, sand, pebble, boulders are independent variables in the described model. Two models with different covariation functions (Gaussian and exponential) are built to estima...
Spatial and spatio-temporal bayesian models with R - INLA
Blangiardo, Marta
2015-01-01
Dedication iiiPreface ix1 Introduction 11.1 Why spatial and spatio-temporal statistics? 11.2 Why do we use Bayesian methods for modelling spatial and spatio-temporal structures? 21.3 Why INLA? 31.4 Datasets 32 Introduction to 212.1 The language 212.2 objects 222.3 Data and session management 342.4 Packages 352.5 Programming in 362.6 Basic statistical analysis with 393 Introduction to Bayesian Methods 533.1 Bayesian Philosophy 533.2 Basic Probability Elements 573.3 Bayes Theorem 623.4 Prior and Posterior Distributions 643.5 Working with the Posterior Distribution 663.6 Choosing the Prior Distr
Bayesian model mixing for cold rolling mills: Test results
Czech Academy of Sciences Publication Activity Database
Ettler, P.; Puchr, I.; Dedecius, Kamil
Slovensko: Slovak University of Technology, 2013, s. 359-364. ISBN 978-1-4799-0926-1. [19th International Conference on Process Control . Štrbské Pleso (SK), 18.06.2013-21.06.2013] R&D Projects: GA MŠk(CZ) 7D09008; GA MŠk 7D12004 Keywords : Bayesian statistics * model mixing * process control Subject RIV: BC - Control Systems Theory http://library.utia.cas.cz/separaty/2013/AS/dedecius-bayesian model mixing for cold rolling mills test results.pdf
Bayesian Analysis of Multivariate Probit Models
Siddhartha Chib; Edward Greenberg
1996-01-01
This paper provides a unified simulation-based Bayesian and non-Bayesian analysis of correlated binary data using the multivariate probit model. The posterior distribution is simulated by Markov chain Monte Carlo methods, and maximum likelihood estimates are obtained by a Markov chain Monte Carlo version of the E-M algorithm. Computation of Bayes factors from the simulation output is also considered. The methods are applied to a bivariate data set, to a 534-subject, four-year longitudinal dat...
Bayesian Network Models for Adaptive Testing
Czech Academy of Sciences Publication Activity Database
Plajner, Martin; Vomlel, Jiří
Achen: Sun SITE Central Europe, 2016 - (Agosta, J.; Carvalho, R.), s. 24-33. (CEUR Workshop Proceedings. Vol 1565). ISSN 1613-0073. [The Twelfth UAI Bayesian Modeling Applications Workshop (BMAW 2015). Amsterdam (NL), 16.07.2015] R&D Projects: GA ČR GA13-20012S Institutional support: RVO:67985556 Keywords : Bayesian networks * Computerized adaptive testing Subject RIV: JD - Computer Applications, Robotics http://library.utia.cas.cz/separaty/2016/MTR/plajner-0458062.pdf
A Bayesian Markov geostatistical model for estimation of hydrogeological properties
International Nuclear Information System (INIS)
A geostatistical methodology based on Markov-chain analysis and Bayesian statistics was developed for probability estimations of hydrogeological and geological properties in the siting process of a nuclear waste repository. The probability estimates have practical use in decision-making on issues such as siting, investigation programs, and construction design. The methodology is nonparametric which makes it possible to handle information that does not exhibit standard statistical distributions, as is often the case for classified information. Data do not need to meet the requirements on additivity and normality as with the geostatistical methods based on regionalized variable theory, e.g., kriging. The methodology also has a formal way for incorporating professional judgments through the use of Bayesian statistics, which allows for updating of prior estimates to posterior probabilities each time new information becomes available. A Bayesian Markov Geostatistical Model (BayMar) software was developed for implementation of the methodology in two and three dimensions. This paper gives (1) a theoretical description of the Bayesian Markov Geostatistical Model; (2) a short description of the BayMar software; and (3) an example of application of the model for estimating the suitability for repository establishment with respect to the three parameters of lithology, hydraulic conductivity, and rock quality designation index (RQD) at 400--500 meters below ground surface in an area around the Aespoe Hard Rock Laboratory in southeastern Sweden
A new approach for Bayesian model averaging
Institute of Scientific and Technical Information of China (English)
TIAN XiangJun; XIE ZhengHui; WANG AiHui; YANG XiaoChun
2012-01-01
Bayesian model averaging (BMA) is a recently proposed statistical method for calibrating forecast ensembles from numerical weather models.However,successful implementation of BMA requires accurate estimates of the weights and variances of the individual competing models in the ensemble.Two methods,namely the Expectation-Maximization (EM) and the Markov Chain Monte Carlo (MCMC) algorithms,are widely used for BMA model training.Both methods have their own respective strengths and weaknesses.In this paper,we first modify the BMA log-likelihood function with the aim of removing the additional limitation that requires that the BMA weights add to one,and then use a limited memory quasi-Newtonian algorithm for solving the nonlinear optimization problem,thereby formulating a new approach for BMA (referred to as BMA-BFGS).Several groups of multi-model soil moisture simulation experiments from three land surface models show that the performance of BMA-BFGS is similar to the MCMC method in terms of simulation accuracy,and that both are superior to the EM algorithm.On the other hand,the computational cost of the BMA-BFGS algorithm is substantially less than for MCMC and is almost equivalent to that for EM.
On Bayesian Nonparametric Continuous Time Series Models
Karabatsos, George; Walker, Stephen G.
2013-01-01
This paper is a note on the use of Bayesian nonparametric mixture models for continuous time series. We identify a key requirement for such models, and then establish that there is a single type of model which meets this requirement. As it turns out, the model is well known in multiple change-point problems.
Bayesian statistics for the calibration of the LISA Pathfinder experiment
Armano, M.; Audley, H.; Auger, G.; Binetruy, P.; Born, M.; Bortoluzzi, D.; Brandt, N.; Bursi, A.; Caleno, M.; Cavalleri, A.; Cesarini, A.; Cruise, M.; Danzmann, K.; Diepholz, I.; Dolesi, R.; Dunbar, N.; Ferraioli, L.; Ferroni, V.; Fitzsimons, E.; Freschi, M.; García Marirrodriga, C.; Gerndt, R.; Gesa, L.; Gibert, F.; Giardini, D.; Giusteri, R.; Grimani, C.; Harrison, I.; Heinzel, G.; Hewitson, M.; Hollington, D.; Hueller, M.; Huesler, J.; Inchauspé, H.; Jennrich, O.; Jetzer, P.; Johlander, B.; Karnesis, N.; Kaune, B.; Korsakova, N.; Killow, C.; Lloro, I.; Maarschalkerweerd, R.; Madden, S.; Mance, D.; Martin, V.; Martin-Porqueras, F.; Mateos, I.; McNamara, P.; Mendes, J.; Mitchell, E.; Moroni, A.; Nofrarias, M.; Paczkowski, S.; Perreur-Lloyd, M.; Pivato, P.; Plagnol, E.; Prat, P.; Ragnit, U.; Ramos-Castro, J.; Reiche, J.; Romera Perez, J. A.; Robertson, D.; Rozemeijer, H.; Russano, G.; Sarra, P.; Schleicher, A.; Slutsky, J.; Sopuerta, C. F.; Sumner, T.; Texier, D.; Thorpe, J.; Trenkel, C.; Tu, H. B.; Vitale, S.; Wanner, G.; Ward, H.; Waschke, S.; Wass, P.; Wealthy, D.; Wen, S.; Weber, W.; Wittchen, A.; Zanoni, C.; Ziegler, T.; Zweifel, P.
2015-05-01
The main goal of LISA Pathfinder (LPF) mission is to estimate the acceleration noise models of the overall LISA Technology Package (LTP) experiment on-board. This will be of crucial importance for the future space-based Gravitational-Wave (GW) detectors, like eLISA. Here, we present the Bayesian analysis framework to process the planned system identification experiments designed for that purpose. In particular, we focus on the analysis strategies to predict the accuracy of the parameters that describe the system in all degrees of freedom. The data sets were generated during the latest operational simulations organised by the data analysis team and this work is part of the LTPDA Matlab toolbox.
Introduction to Hierarchical Bayesian Modeling for Ecological Data
Parent, Eric
2012-01-01
Making statistical modeling and inference more accessible to ecologists and related scientists, Introduction to Hierarchical Bayesian Modeling for Ecological Data gives readers a flexible and effective framework to learn about complex ecological processes from various sources of data. It also helps readers get started on building their own statistical models. The text begins with simple models that progressively become more complex and realistic through explanatory covariates and intermediate hidden states variables. When fitting the models to data, the authors gradually present the concepts a
Bayesian Statistical Approach To Binary Asteroid Orbit Determination
Dmitrievna Kovalenko, Irina; Stoica, Radu S.
2015-08-01
Orbit determination from observations is one of the classical problems in celestial mechanics. Deriving the trajectory of binary asteroid with high precision is much more complicate than the trajectory of simple asteroid. Here we present a method of orbit determination based on the algorithm of Monte Carlo Markov Chain (MCMC). This method can be used for the preliminary orbit determination with relatively small number of observations, or for adjustment of orbit previously determined.The problem consists on determination of a conditional a posteriori probability density with given observations. Applying the Bayesian statistics, the a posteriori probability density of the binary asteroid orbital parameters is proportional to the a priori and likelihood probability densities. The likelihood function is related to the noise probability density and can be calculated from O-C deviations (Observed minus Calculated positions). The optionally used a priori probability density takes into account information about the population of discovered asteroids. The a priori probability density is used to constrain the phase space of possible orbits.As a MCMC method the Metropolis-Hastings algorithm has been applied, adding a globally convergent coefficient. The sequence of possible orbits derives through the sampling of each orbital parameter and acceptance criteria.The method allows to determine the phase space of every possible orbit considering each parameter. It also can be used to derive one orbit with the biggest probability density of orbital elements.
Bayesian semiparametric dynamic Nelson-Siegel model
C. Cakmakli
2011-01-01
This paper proposes the Bayesian semiparametric dynamic Nelson-Siegel model where the density of the yield curve factors and thereby the density of the yields are estimated along with other model parameters. This is accomplished by modeling the error distributions of the factors according to a Diric
Bayesian calibration of car-following models
Van Hinsbergen, C.P.IJ.; Van Lint, H.W.C.; Hoogendoorn, S.P.; Van Zuylen, H.J.
2010-01-01
Recent research has revealed that there exist large inter-driver differences in car-following behavior such that different car-following models may apply to different drivers. This study applies Bayesian techniques to the calibration of car-following models, where prior distributions on each model p
Non-stationarity in GARCH models: A Bayesian analysis
Kleibergen, Frank; Dijk, Herman
1993-01-01
textabstractFirst, the non-stationarity properties of the conditional variances in the GARCH(1,1) model are analysed using the concept of infinite persistence of shocks. Given a time sequence of probabilities for increasing/decreasing conditional variances, a theoretical formula for quasi-strict non-stationarity is defined. The resulting conditions for the GARCH(1,1) model are shown to differ from the weak stationarity conditions mainly used in the literature. Bayesian statistical analysis us...
A New Bayesian Unit Root Test in Stochastic Volatility Models
Yong Li; Jun Yu
2010-01-01
A new posterior odds analysis is proposed to test for a unit root in volatility dynamics in the context of stochastic volatility models. This analysis extends the Bayesian unit root test of So and Li (1999, Journal of Business Economic Statistics) in two important ways. First, a numerically more stable algorithm is introduced to compute the Bayes factor, taking into account the special structure of the competing models. Owing to its numerical stability, the algorithm overcomes the problem of ...
Bayesian modeling and prediction of solar particles flux
Czech Academy of Sciences Publication Activity Database
Dedecius, Kamil; Kalová, J.
18/56/, 7/8 (2010), s. 228-230. ISSN 1210-7085 R&D Projects: GA MŠk 1M0572 Institutional research plan: CEZ:AV0Z10750506 Keywords : mathematical models * solar activity * solar flares * solar flux * solar particles Subject RIV: BB - Applied Statistics, Operational Research http://library.utia.cas.cz/separaty/2010/AS/dedecius-bayesian modeling and prediction of solar particles flux.pdf
Hierarchical Bayesian Modeling of Hitting Performance in Baseball
Jensen, Shane T.; McShane, Blake; Wyner, Abraham J.
2009-01-01
We have developed a sophisticated statistical model for predicting the hitting performance of Major League baseball players. The Bayesian paradigm provides a principled method for balancing past performance with crucial covariates, such as player age and position. We share information across time and across players by using mixture distributions to control shrinkage for improved accuracy. We compare the performance of our model to current sabermetric methods on a held-out seaso...
Ockham's razor and Bayesian analysis. [statistical theory for systems evaluation
Jefferys, William H.; Berger, James O.
1992-01-01
'Ockham's razor', the ad hoc principle enjoining the greatest possible simplicity in theoretical explanations, is presently shown to be justifiable as a consequence of Bayesian inference; Bayesian analysis can, moreover, clarify the nature of the 'simplest' hypothesis consistent with the given data. By choosing the prior probabilities of hypotheses, it becomes possible to quantify the scientific judgment that simpler hypotheses are more likely to be correct. Bayesian analysis also shows that a hypothesis with fewer adjustable parameters intrinsically possesses an enhanced posterior probability, due to the clarity of its predictions.
Bayesian Semiparametric Modeling of Realized Covariance Matrices
Jin, Xin; John M Maheu
2014-01-01
This paper introduces several new Bayesian nonparametric models suitable for capturing the unknown conditional distribution of realized covariance (RCOV) matrices. Existing dynamic Wishart models are extended to countably infinite mixture models of Wishart and inverse-Wishart distributions. In addition to mixture models with constant weights we propose models with time-varying weights to capture time dependence in the unknown distribution. Each of our models can be combined with returns...
Bayesian Approach to Neuro-Rough Models for Modelling HIV
Marwala, Tshilidzi
2007-01-01
This paper proposes a new neuro-rough model for modelling the risk of HIV from demographic data. The model is formulated using Bayesian framework and trained using Markov Chain Monte Carlo method and Metropolis criterion. When the model was tested to estimate the risk of HIV infection given the demographic data it was found to give the accuracy of 62% as opposed to 58% obtained from a Bayesian formulated rough set model trained using Markov chain Monte Carlo method and 62% obtained from a Bayesian formulated multi-layered perceptron (MLP) model trained using hybrid Monte. The proposed model is able to combine the accuracy of the Bayesian MLP model and the transparency of Bayesian rough set model.
Survey of Bayesian Models for Modelling of Stochastic Temporal Processes
Energy Technology Data Exchange (ETDEWEB)
Ng, B
2006-10-12
This survey gives an overview of popular generative models used in the modeling of stochastic temporal systems. In particular, this survey is organized into two parts. The first part discusses the discrete-time representations of dynamic Bayesian networks and dynamic relational probabilistic models, while the second part discusses the continuous-time representation of continuous-time Bayesian networks.
Errata: A survey of Bayesian predictive methods for model assessment, selection and comparison
Directory of Open Access Journals (Sweden)
Aki Vehtari
2014-03-01
Full Text Available Errata for “A survey of Bayesian predictive methods for model assessment, selection and comparison” by A. Vehtari and J. Ojanen, Statistics Surveys, 6 (2012, 142–228. doi:10.1214/12-SS102.
Differential gene co-expression networks via Bayesian biclustering models
Gao, Chuan; Zhao, Shiwen; McDowell, Ian C.; Brown, Christopher D.; Barbara E Engelhardt
2014-01-01
Identifying latent structure in large data matrices is essential for exploring biological processes. Here, we consider recovering gene co-expression networks from gene expression data, where each network encodes relationships between genes that are locally co-regulated by shared biological mechanisms. To do this, we develop a Bayesian statistical model for biclustering to infer subsets of co-regulated genes whose covariation may be observed in only a subset of the samples. Our biclustering me...
Diffusion Estimation Of State-Space Models: Bayesian Formulation
Czech Academy of Sciences Publication Activity Database
Dedecius, Kamil
Reims: IEEE, 2014. ISBN 978-1-4799-3693-9. [The 24th IEEE International Workshop on Machine Learning for Signal Processing (MLSP2014). Reims (FR), 21.09.2014-24.09.2014] R&D Projects: GA ČR(CZ) GP14-06678P Keywords : distributed estimation * state-space models * Bayesian estimation Subject RIV: BB - Applied Statistics, Operational Research http://library.utia.cas.cz/separaty/2014/AS/dedecius-0431804.pdf
Bayesian Statistics at Work: the Troublesome Extraction of the CKM Phase α
International Nuclear Information System (INIS)
In Bayesian statistics, one's prior beliefs about underlying model parameters are revised with the information content of observed data from which, using Bayes' rule, a posterior belief is obtained. A non-trivial example taken from the isospin analysis of B → PP (P = π or ρ) decays in heavy-flavor physics is chosen to illustrate the effect of the naive 'objective' choice of flat priors in a multi- dimensional parameter space in presence of mirror solutions. It is demonstrated that the posterior distribution for the parameter of interest, the phase α, strongly depends on the choice of the parameterization in which the priors are uniform, and on the validity range in which the (un-normalizable) priors are truncated. We prove that the most probable values found by the Bayesian treatment do not coincide with the explicit analytical solutions, in contrast to the frequentist approach. It is also shown in the appendix that the α → 0 limit cannot be consistently treated in the Bayesian paradigm, because the latter violates the physical symmetries of the problem. (authors)
Bayesian Statistics at Work: the Troublesome Extraction of the CKM Phase {alpha}
Energy Technology Data Exchange (ETDEWEB)
Charles, J. [CPT, Luminy Case 907, F-13288 Marseille Cedex 9 (France); Hoecker, A. [CERN, CH-1211 Geneva 23 (Switzerland); Lacker, H. [TU Dresden, IKTP, D-01062 Dresden (Germany); Le Diberder, F.R. [LAL, CNRS/IN2P3, Universite Paris-Sud 11, Bat. 200, BP 34, F-91898 Orsay Cedex (France); T' Jampens, S. [LAPP, CNRS/IN2P3, Universite de Savoie, 9 Chemin de Bellevue, BP 110, F-74941 Annecy-le-Vieux Cedex (France)
2007-04-15
In Bayesian statistics, one's prior beliefs about underlying model parameters are revised with the information content of observed data from which, using Bayes' rule, a posterior belief is obtained. A non-trivial example taken from the isospin analysis of B {yields} PP (P = {pi} or {rho}) decays in heavy-flavor physics is chosen to illustrate the effect of the naive 'objective' choice of flat priors in a multi- dimensional parameter space in presence of mirror solutions. It is demonstrated that the posterior distribution for the parameter of interest, the phase {alpha}, strongly depends on the choice of the parameterization in which the priors are uniform, and on the validity range in which the (un-normalizable) priors are truncated. We prove that the most probable values found by the Bayesian treatment do not coincide with the explicit analytical solutions, in contrast to the frequentist approach. It is also shown in the appendix that the {alpha} {yields} 0 limit cannot be consistently treated in the Bayesian paradigm, because the latter violates the physical symmetries of the problem. (authors)
Bayesian Spatial Modelling with R-INLA
Finn Lindgren; Håvard Rue
2015-01-01
The principles behind the interface to continuous domain spatial models in the R- INLA software package for R are described. The integrated nested Laplace approximation (INLA) approach proposed by Rue, Martino, and Chopin (2009) is a computationally effective alternative to MCMC for Bayesian inference. INLA is designed for latent Gaussian models, a very wide and flexible class of models ranging from (generalized) linear mixed to spatial and spatio-temporal models. Combined with the stochastic...
Hierarchical Bayesian spatial models for multispecies conservation planning and monitoring.
Carroll, Carlos; Johnson, Devin S; Dunk, Jeffrey R; Zielinski, William J
2010-12-01
Biologists who develop and apply habitat models are often familiar with the statistical challenges posed by their data's spatial structure but are unsure of whether the use of complex spatial models will increase the utility of model results in planning. We compared the relative performance of nonspatial and hierarchical Bayesian spatial models for three vertebrate and invertebrate taxa of conservation concern (Church's sideband snails [Monadenia churchi], red tree voles [Arborimus longicaudus], and Pacific fishers [Martes pennanti pacifica]) that provide examples of a range of distributional extents and dispersal abilities. We used presence-absence data derived from regional monitoring programs to develop models with both landscape and site-level environmental covariates. We used Markov chain Monte Carlo algorithms and a conditional autoregressive or intrinsic conditional autoregressive model framework to fit spatial models. The fit of Bayesian spatial models was between 35 and 55% better than the fit of nonspatial analogue models. Bayesian spatial models outperformed analogous models developed with maximum entropy (Maxent) methods. Although the best spatial and nonspatial models included similar environmental variables, spatial models provided estimates of residual spatial effects that suggested how ecological processes might structure distribution patterns. Spatial models built from presence-absence data improved fit most for localized endemic species with ranges constrained by poorly known biogeographic factors and for widely distributed species suspected to be strongly affected by unmeasured environmental variables or population processes. By treating spatial effects as a variable of interest rather than a nuisance, hierarchical Bayesian spatial models, especially when they are based on a common broad-scale spatial lattice (here the national Forest Inventory and Analysis grid of 24 km(2) hexagons), can increase the relevance of habitat models to multispecies
Statistical Modeling Efforts for Headspace Gas
International Nuclear Information System (INIS)
The purpose of this document is to describe the statistical modeling effort for gas concentrations in WIPP storage containers. The concentration (in ppm) of CO2 in the headspace volume of standard waste box (SWB) 68685 is shown. A Bayesian approach and an adaptive Metropolis-Hastings algorithm were used.
Statistical Modeling Efforts for Headspace Gas
Energy Technology Data Exchange (ETDEWEB)
Weaver, Brian Phillip [Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
2016-03-17
The purpose of this document is to describe the statistical modeling effort for gas concentrations in WIPP storage containers. The concentration (in ppm) of CO_{2} in the headspace volume of standard waste box (SWB) 68685 is shown. A Bayesian approach and an adaptive Metropolis-Hastings algorithm were used.
Bayesian Subset Modeling for High-Dimensional Generalized Linear Models
Liang, Faming
2013-06-01
This article presents a new prior setting for high-dimensional generalized linear models, which leads to a Bayesian subset regression (BSR) with the maximum a posteriori model approximately equivalent to the minimum extended Bayesian information criterion model. The consistency of the resulting posterior is established under mild conditions. Further, a variable screening procedure is proposed based on the marginal inclusion probability, which shares the same properties of sure screening and consistency with the existing sure independence screening (SIS) and iterative sure independence screening (ISIS) procedures. However, since the proposed procedure makes use of joint information from all predictors, it generally outperforms SIS and ISIS in real applications. This article also makes extensive comparisons of BSR with the popular penalized likelihood methods, including Lasso, elastic net, SIS, and ISIS. The numerical results indicate that BSR can generally outperform the penalized likelihood methods. The models selected by BSR tend to be sparser and, more importantly, of higher prediction ability. In addition, the performance of the penalized likelihood methods tends to deteriorate as the number of predictors increases, while this is not significant for BSR. Supplementary materials for this article are available online. © 2013 American Statistical Association.
Bayesian modeling and classification of neural signals
Lewicki, Michael S.
1994-01-01
Signal processing and classification algorithms often have limited applicability resulting from an inaccurate model of the signal's underlying structure. We present here an efficient, Bayesian algorithm for modeling a signal composed of the superposition of brief, Poisson-distributed functions. This methodology is applied to the specific problem of modeling and classifying extracellular neural waveforms which are composed of a superposition of an unknown number of action potentials CAPs). ...
Modeling error distributions of growth curve models through Bayesian methods.
Zhang, Zhiyong
2016-06-01
Growth curve models are widely used in social and behavioral sciences. However, typical growth curve models often assume that the errors are normally distributed although non-normal data may be even more common than normal data. In order to avoid possible statistical inference problems in blindly assuming normality, a general Bayesian framework is proposed to flexibly model normal and non-normal data through the explicit specification of the error distributions. A simulation study shows when the distribution of the error is correctly specified, one can avoid the loss in the efficiency of standard error estimates. A real example on the analysis of mathematical ability growth data from the Early Childhood Longitudinal Study, Kindergarten Class of 1998-99 is used to show the application of the proposed methods. Instructions and code on how to conduct growth curve analysis with both normal and non-normal error distributions using the the MCMC procedure of SAS are provided. PMID:26019004
Distributed Bayesian Networks for User Modeling
DEFF Research Database (Denmark)
Tedesco, Roberto; Dolog, Peter; Nejdl, Wolfgang;
2006-01-01
The World Wide Web is a popular platform for providing eLearning applications to a wide spectrum of users. However – as users differ in their preferences, background, requirements, and goals – applications should provide personalization mechanisms. In the Web context, user models used by such...... adaptive applications are often partial fragments of an overall user model. The fragments have then to be collected and merged into a global user profile. In this paper we investigate and present algorithms able to cope with distributed, fragmented user models – based on Bayesian Networks – in the context...... mechanism efficiently combines distributed learner models without the need to exchange internal structure of local Bayesian networks, nor local evidence between the involved platforms....
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 ...
Bayesian hierarchical modelling of weak lensing - the golden goal
Heavens, Alan; Jaffe, Andrew; Hoffmann, Till; Kiessling, Alina; Wandelt, Benjamin
2016-01-01
To accomplish correct Bayesian inference from weak lensing shear data requires a complete statistical description of the data. The natural framework to do this is a Bayesian Hierarchical Model, which divides the chain of reasoning into component steps. Starting with a catalogue of shear estimates in tomographic bins, we build a model that allows us to sample simultaneously from the the underlying tomographic shear fields and the relevant power spectra (E-mode, B-mode, and E-B, for auto- and cross-power spectra). The procedure deals easily with masked data and intrinsic alignments. Using Gibbs sampling and messenger fields, we show with simulated data that the large (over 67000-)dimensional parameter space can be efficiently sampled and the full joint posterior probability density function for the parameters can feasibly be obtained. The method correctly recovers the underlying shear fields and all of the power spectra, including at levels well below the shot noise.
Bayesian Network Based XP Process Modelling
Directory of Open Access Journals (Sweden)
Mohamed Abouelela
2010-07-01
Full Text Available A Bayesian Network based mathematical model has been used for modelling Extreme Programmingsoftware development process. The model is capable of predicting the expected finish time and theexpected defect rate for each XP release. Therefore, it can be used to determine the success/failure of anyXP Project. The model takes into account the effect of three XP practices, namely: Pair Programming,Test Driven Development and Onsite Customer practices. The model’s predictions were validated againsttwo case studies. Results show the precision of our model especially in predicting the project finish time.
Embracing Uncertainty: The Interface of Bayesian Statistics and Cognitive Psychology
Directory of Open Access Journals (Sweden)
Judith L. Anderson
1998-06-01
Full Text Available Ecologists working in conservation and resource management are discovering the importance of using Bayesian analytic methods to deal explicitly with uncertainty in data analyses and decision making. However, Bayesian procedures require, as inputs and outputs, an idea that is problematic for the human brain: the probability of a hypothesis ("single-event probability". I describe several cognitive concepts closely related to single-event probabilities, and discuss how their interchangeability in the human mind results in "cognitive illusions," apparent deficits in reasoning about uncertainty. Each cognitive illusion implies specific possible pitfalls for the use of single-event probabilities in ecology and resource management. I then discuss recent research in cognitive psychology showing that simple tactics of communication, suggested by an evolutionary perspective on human cognition, help people to process uncertain information more effectively as they read and talk about probabilities. In addition, I suggest that carefully considered standards for methodology and conventions for presentation may also make Bayesian analyses easier to understand.
A Bayesian Modelling of Wildfires in Portugal
Silva, Giovani L.; Soares, Paulo; Marques, Susete; Dias, Inês M.; Oliveira, Manuela M.; Borges, Guilherme J.
2015-01-01
In the last decade wildfires became a serious problem in Portugal due to different issues such as climatic characteristics and nature of Portuguese forest. In order to analyse wildfire data, we employ beta regression for modelling the proportion of burned forest area, under a Bayesian perspective. Our main goal is to find out fire risk factors that influence the proportion of area burned and what may make a forest type susceptible or resistant to fire. Then, we analyse wildfire...
Market Segmentation Using Bayesian Model Based Clustering
Van Hattum, P.
2009-01-01
This dissertation deals with two basic problems in marketing, that are market segmentation, which is the grouping of persons who share common aspects, and market targeting, which is focusing your marketing efforts on one or more attractive market segments. For the grouping of persons who share common aspects a Bayesian model based clustering approach is proposed such that it can be applied to data sets that are specifically used for market segmentation. The cluster algorithm can handle very l...
Centralized Bayesian reliability modelling with sensor networks
Czech Academy of Sciences Publication Activity Database
Dedecius, Kamil; Sečkárová, Vladimíra
2013-01-01
Roč. 19, č. 5 (2013), s. 471-482. ISSN 1387-3954 R&D Projects: GA MŠk 7D12004 Grant ostatní: GA MŠk(CZ) SVV-265315 Keywords : Bayesian modelling * Sensor network * Reliability Subject RIV: BD - Theory of Information Impact factor: 0.984, year: 2013 http://library.utia.cas.cz/separaty/2013/AS/dedecius-0392551.pdf
Targeted search for continuous gravitational waves: Bayesian versus maximum-likelihood statistics
Prix, R.; Krishnan, B.
2009-01-01
We investigate the Bayesian framework for detection of continuous gravitational waves (GWs) in the context of targeted searches, where the phase evolution of the GW signal is assumed to be known, while the four amplitude parameters are unknown. We show that the orthodox maximum-likelihood statistic (known as {\\cal F} -statistic) can be rediscovered as a Bayes factor with an unphysical prior in amplitude parameter space. We introduce an alternative detection statistic ('{\\cal B} -statistic') u...
Modelling of Traffic Flow with Bayesian Autoregressive Model with Variable Partial Forgetting
Czech Academy of Sciences Publication Activity Database
Dedecius, Kamil; Nagy, Ivan; Hofman, Radek
Praha : ČVUT v Praze, 2011, s. 1-11. [CTU Workshop 2011. Praha (CZ), 01.02.2011-01.02.2011] Grant ostatní: ČVUT v Praze(CZ) SGS 10/099/OHK3/1T/16 Institutional research plan: CEZ:AV0Z10750506 Keywords : Bayesian modelling * traffic modelling Subject RIV: BB - Applied Statistics, Operational Research http://library.utia.cas.cz/separaty/2011/AS/dedecius-modelling of traffic flow with bayesian autoregressive model with variable partial forgetting.pdf
Directory of Open Access Journals (Sweden)
D. Das
2014-04-01
Full Text Available Climate projections simulated by Global Climate Models (GCM are often used for assessing the impacts of climate change. However, the relatively coarse resolutions of GCM outputs often precludes their application towards accurately assessing the effects of climate change on finer regional scale phenomena. Downscaling of climate variables from coarser to finer regional scales using statistical methods are often performed for regional climate projections. Statistical downscaling (SD is based on the understanding that the regional climate is influenced by two factors – the large scale climatic state and the regional or local features. A transfer function approach of SD involves learning a regression model which relates these features (predictors to a climatic variable of interest (predictand based on the past observations. However, often a single regression model is not sufficient to describe complex dynamic relationships between the predictors and predictand. We focus on the covariate selection part of the transfer function approach and propose a nonparametric Bayesian mixture of sparse regression models based on Dirichlet Process (DP, for simultaneous clustering and discovery of covariates within the clusters while automatically finding the number of clusters. Sparse linear models are parsimonious and hence relatively more generalizable than non-sparse alternatives, and lends to domain relevant interpretation. Applications to synthetic data demonstrate the value of the new approach and preliminary results related to feature selection for statistical downscaling shows our method can lead to new insights.
Bayesian Inference of a Multivariate Regression Model
Directory of Open Access Journals (Sweden)
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.
Bayesian meta-analysis models for microarray data: a comparative study
Song Joon J; Conlon Erin M; Liu Anna
2007-01-01
Abstract Background With the growing abundance of microarray data, statistical methods are increasingly needed to integrate results across studies. Two common approaches for meta-analysis of microarrays include either combining gene expression measures across studies or combining summaries such as p-values, probabilities or ranks. Here, we compare two Bayesian meta-analysis models that are analogous to these methods. Results Two Bayesian meta-analysis models for microarray data have recently ...
Targeted search for continuous gravitational waves: Bayesian versus maximum-likelihood statistics
International Nuclear Information System (INIS)
We investigate the Bayesian framework for detection of continuous gravitational waves (GWs) in the context of targeted searches, where the phase evolution of the GW signal is assumed to be known, while the four amplitude parameters are unknown. We show that the orthodox maximum-likelihood statistic (known as F-statistic) can be rediscovered as a Bayes factor with an unphysical prior in amplitude parameter space. We introduce an alternative detection statistic ('B-statistic') using the Bayes factor with a more natural amplitude prior, namely an isotropic probability distribution for the orientation of GW sources. Monte Carlo simulations of targeted searches show that the resulting Bayesian B-statistic is more powerful in the Neyman-Pearson sense (i.e., has a higher expected detection probability at equal false-alarm probability) than the frequentist F-statistic.
Bayesian Kinematic Finite Fault Source Models (Invited)
Minson, S. E.; Simons, M.; Beck, J. L.
2010-12-01
Finite fault earthquake source models are inherently under-determined: there is no unique solution to the inverse problem of determining the rupture history at depth as a function of time and space when our data are only limited observations at the Earth's surface. Traditional inverse techniques rely on model constraints and regularization to generate one model from the possibly broad space of all possible solutions. However, Bayesian methods allow us to determine the ensemble of all possible source models which are consistent with the data and our a priori assumptions about the physics of the earthquake source. Until now, Bayesian techniques have been of limited utility because they are computationally intractable for problems with as many free parameters as kinematic finite fault models. We have developed a methodology called Cascading Adaptive Tempered Metropolis In Parallel (CATMIP) which allows us to sample very high-dimensional problems in a parallel computing framework. The CATMIP algorithm combines elements of simulated annealing and genetic algorithms with the Metropolis algorithm to dynamically optimize the algorithm's efficiency as it runs. We will present synthetic performance tests of finite fault models made with this methodology as well as a kinematic source model for the 2007 Mw 7.7 Tocopilla, Chile earthquake. This earthquake was well recorded by multiple ascending and descending interferograms and a network of high-rate GPS stations whose records can be used as near-field seismograms.
Bayesian Estimation of a Mixture Model
Ilhem Merah; Assia Chadli
2015-01-01
We present the properties of a bathtub curve reliability model having both a sufficient adaptability and a minimal number of parameters introduced by Idée and Pierrat (2010). This one is a mixture of a Gamma distribution G(2, (1/θ)) and a new distribution L(θ). We are interesting by Bayesian estimation of the parameters and survival function of this model with a squared-error loss function and non-informative prior using the approximations of Lindley (1980) and Tierney and Kadane (1986). Usin...
Bayesian mixture models for partially verified data
DEFF Research Database (Denmark)
Kostoulas, Polychronis; Browne, William J.; Nielsen, Søren Saxmose;
2013-01-01
, where a perfect reference test does not exist. However, their discriminatory ability diminishes with increasing overlap of the distributions and with increasing number of latent infection stages to be discriminated. We provide a method that uses partially verified data, with known infection status for......Bayesian mixture models can be used to discriminate between the distributions of continuous test responses for different infection stages. These models are particularly useful in case of chronic infections with a long latent period, like Mycobacterium avium subsp. paratuberculosis (MAP) infection...
Quantum-Like Bayesian Networks for Modeling Decision Making.
Moreira, Catarina; Wichert, Andreas
2016-01-01
In this work, we explore an alternative quantum structure to perform quantum probabilistic inferences to accommodate the paradoxical findings of the Sure Thing Principle. We propose a Quantum-Like Bayesian Network, which consists in replacing classical probabilities by quantum probability amplitudes. However, since this approach suffers from the problem of exponential growth of quantum parameters, we also propose a similarity heuristic that automatically fits quantum parameters through vector similarities. This makes the proposed model general and predictive in contrast to the current state of the art models, which cannot be generalized for more complex decision scenarios and that only provide an explanatory nature for the observed paradoxes. In the end, the model that we propose consists in a nonparametric method for estimating inference effects from a statistical point of view. It is a statistical model that is simpler than the previous quantum dynamic and quantum-like models proposed in the literature. We tested the proposed network with several empirical data from the literature, mainly from the Prisoner's Dilemma game and the Two Stage Gambling game. The results obtained show that the proposed quantum Bayesian Network is a general method that can accommodate violations of the laws of classical probability theory and make accurate predictions regarding human decision-making in these scenarios. PMID:26858669
Non-parametric Bayesian modeling of cervical mucus symptom
Bin, Riccardo De; Scarpa, Bruno
2014-01-01
The analysis of the cervical mucus symptom is useful to identify the period of maximum fertility of a woman. In this paper we analyze the daily evolution of the cervical mucus symptom during the menstrual cycle, based on the data collected in two retrospective studies, in which the mucus symptom is treated as an ordinal variable. To produce our statistical model, we follow a non-parametric Bayesian approach. In particular, we use the idea of non-parametric mixtures of rounded continuous kerne...
Dynamic model based on Bayesian method for energy security assessment
International Nuclear Information System (INIS)
Highlights: • Methodology for dynamic indicator model construction and forecasting of indicators. • Application of dynamic indicator model for energy system development scenarios. • Expert judgement involvement using Bayesian method. - Abstract: The methodology for the dynamic indicator model construction and forecasting of indicators for the assessment of energy security level is presented in this article. An indicator is a special index, which provides numerical values to important factors for the investigated area. In real life, models of different processes take into account various factors that are time-dependent and dependent on each other. Thus, it is advisable to construct a dynamic model in order to describe these dependences. The energy security indicators are used as factors in the dynamic model. Usually, the values of indicators are obtained from statistical data. The developed dynamic model enables to forecast indicators’ variation taking into account changes in system configuration. The energy system development is usually based on a new object construction. Since the parameters of changes of the new system are not exactly known, information about their influences on indicators could not be involved in the model by deterministic methods. Thus, dynamic indicators’ model based on historical data is adjusted by probabilistic model with the influence of new factors on indicators using the Bayesian method
A Nonparametric Bayesian Model for Nested Clustering.
Lee, Juhee; Müller, Peter; Zhu, Yitan; Ji, Yuan
2016-01-01
We propose a nonparametric Bayesian model for clustering where clusters of experimental units are determined by a shared pattern of clustering another set of experimental units. The proposed model is motivated by the analysis of protein activation data, where we cluster proteins such that all proteins in one cluster give rise to the same clustering of patients. That is, we define clusters of proteins by the way that patients group with respect to the corresponding protein activations. This is in contrast to (almost) all currently available models that use shared parameters in the sampling model to define clusters. This includes in particular model based clustering, Dirichlet process mixtures, product partition models, and more. We show results for two typical biostatistical inference problems that give rise to clustering. PMID:26519174
Bayesian Spatial Modelling with R-INLA
Directory of Open Access Journals (Sweden)
Finn Lindgren
2015-02-01
Full Text Available The principles behind the interface to continuous domain spatial models in the R- INLA software package for R are described. The integrated nested Laplace approximation (INLA approach proposed by Rue, Martino, and Chopin (2009 is a computationally effective alternative to MCMC for Bayesian inference. INLA is designed for latent Gaussian models, a very wide and flexible class of models ranging from (generalized linear mixed to spatial and spatio-temporal models. Combined with the stochastic partial differential equation approach (SPDE, Lindgren, Rue, and Lindstrm 2011, one can accommodate all kinds of geographically referenced data, including areal and geostatistical ones, as well as spatial point process data. The implementation interface covers stationary spatial mod- els, non-stationary spatial models, and also spatio-temporal models, and is applicable in epidemiology, ecology, environmental risk assessment, as well as general geostatistics.
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; Scavino, Marco; Szabó, Barna; Tempone, Raúl
2016-06-01
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.
Statistical Modeling for Radiation Hardness Assurance
Ladbury, Raymond L.
2014-01-01
We cover the models and statistics associated with single event effects (and total ionizing dose), why we need them, and how to use them: What models are used, what errors exist in real test data, and what the model allows us to say about the DUT will be discussed. In addition, how to use other sources of data such as historical, heritage, and similar part and how to apply experience, physics, and expert opinion to the analysis will be covered. Also included will be concepts of Bayesian statistics, data fitting, and bounding rates.
Bayesian Discovery of Linear Acyclic Causal Models
Hoyer, Patrik O
2012-01-01
Methods for automated discovery of causal relationships from non-interventional data have received much attention recently. A widely used and well understood model family is given by linear acyclic causal models (recursive structural equation models). For Gaussian data both constraint-based methods (Spirtes et al., 1993; Pearl, 2000) (which output a single equivalence class) and Bayesian score-based methods (Geiger and Heckerman, 1994) (which assign relative scores to the equivalence classes) are available. On the contrary, all current methods able to utilize non-Gaussianity in the data (Shimizu et al., 2006; Hoyer et al., 2008) always return only a single graph or a single equivalence class, and so are fundamentally unable to express the degree of certainty attached to that output. In this paper we develop a Bayesian score-based approach able to take advantage of non-Gaussianity when estimating linear acyclic causal models, and we empirically demonstrate that, at least on very modest size networks, its accur...
Adversarial life testing: A Bayesian negotiation model
International Nuclear Information System (INIS)
Life testing is a procedure intended for facilitating the process of making decisions in the context of industrial reliability. On the other hand, negotiation is a process of making joint decisions that has one of its main foundations in decision theory. A Bayesian sequential model of negotiation in the context of adversarial life testing is proposed. This model considers a general setting for which a manufacturer offers a product batch to a consumer. It is assumed that the reliability of the product is measured in terms of its lifetime. Furthermore, both the manufacturer and the consumer have to use their own information with respect to the quality of the product. Under these assumptions, two situations can be analyzed. For both of them, the main aim is to accept or reject the product batch based on the product reliability. This topic is related to a reliability demonstration problem. The procedure is applied to a class of distributions that belong to the exponential family. Thus, a unified framework addressing the main topics in the considered Bayesian model is presented. An illustrative example shows that the proposed technique can be easily applied in practice
Stenning, D. C.; Wagner-Kaiser, R.; Robinson, E.; van Dyk, D. A.; von Hippel, T.; Sarajedini, A.; Stein, N.
2016-07-01
We develop a Bayesian model for globular clusters composed of multiple stellar populations, extending earlier statistical models for open clusters composed of simple (single) stellar populations. Specifically, we model globular clusters with two populations that differ in helium abundance. Our model assumes a hierarchical structuring of the parameters in which physical properties—age, metallicity, helium abundance, distance, absorption, and initial mass—are common to (i) the cluster as a whole or to (ii) individual populations within a cluster, or are unique to (iii) individual stars. An adaptive Markov chain Monte Carlo (MCMC) algorithm is devised for model fitting that greatly improves convergence relative to its precursor non-adaptive MCMC algorithm. Our model and computational tools are incorporated into an open-source software suite known as BASE-9. We use numerical studies to demonstrate that our method can recover parameters of two-population clusters, and also show how model misspecification can potentially be identified. As a proof of concept, we analyze the two stellar populations of globular cluster NGC 5272 using our model and methods. (BASE-9 is available from GitHub: https://github.com/argiopetech/base/releases).
Polyhedral approach to statistical learning graphical models
Czech Academy of Sciences Publication Activity Database
Studený, Milan; Hemmecke, R.; Vomlel, Jiří; Lindner, S.
Osaka : JST CREST, 2010. s. 1-4. [The 2nd CREST-SBM International Conference "Harmony of Groebner Bases and the Moderm Industrial Socienty". 28.06.2010-02.07.2010, Hotel Hankyu Expo Park, Osaka] Institutional research plan: CEZ:AV0Z10750506 Keywords : Bayesian network * polyhedral approach * imset Subject RIV: BA - General Mathematics http://library.utia.cas.cz/separaty/2010/MTR/studeny-polyhedral approach to statistical learning graphical models.pdf
Jones, Matt; Love, Bradley C
2011-08-01
The prominence of Bayesian modeling of cognition has increased recently largely because of mathematical advances in specifying and deriving predictions from complex probabilistic models. Much of this research aims to demonstrate that cognitive behavior can be explained from rational principles alone, without recourse to psychological or neurological processes and representations. We note commonalities between this rational approach and other movements in psychology - namely, Behaviorism and evolutionary psychology - that set aside mechanistic explanations or make use of optimality assumptions. Through these comparisons, we identify a number of challenges that limit the rational program's potential contribution to psychological theory. Specifically, rational Bayesian models are significantly unconstrained, both because they are uninformed by a wide range of process-level data and because their assumptions about the environment are generally not grounded in empirical measurement. The psychological implications of most Bayesian models are also unclear. Bayesian inference itself is conceptually trivial, but strong assumptions are often embedded in the hypothesis sets and the approximation algorithms used to derive model predictions, without a clear delineation between psychological commitments and implementational details. Comparing multiple Bayesian models of the same task is rare, as is the realization that many Bayesian models recapitulate existing (mechanistic level) theories. Despite the expressive power of current Bayesian models, we argue they must be developed in conjunction with mechanistic considerations to offer substantive explanations of cognition. We lay out several means for such an integration, which take into account the representations on which Bayesian inference operates, as well as the algorithms and heuristics that carry it out. We argue this unification will better facilitate lasting contributions to psychological theory, avoiding the pitfalls
Lack of confidence in approximate Bayesian computation model choice.
Robert, Christian P; Cornuet, Jean-Marie; Marin, Jean-Michel; Pillai, Natesh S
2011-09-13
Approximate Bayesian computation (ABC) have become an essential tool for the analysis of complex stochastic models. Grelaud et al. [(2009) Bayesian Anal 3:427-442] advocated the use of ABC for model choice in the specific case of Gibbs random fields, relying on an intermodel sufficiency property to show that the approximation was legitimate. We implemented ABC model choice in a wide range of phylogenetic models in the Do It Yourself-ABC (DIY-ABC) software [Cornuet et al. (2008) Bioinformatics 24:2713-2719]. We now present arguments as to why the theoretical arguments for ABC model choice are missing, because the algorithm involves an unknown loss of information induced by the use of insufficient summary statistics. The approximation error of the posterior probabilities of the models under comparison may thus be unrelated with the computational effort spent in running an ABC algorithm. We then conclude that additional empirical verifications of the performances of the ABC procedure as those available in DIY-ABC are necessary to conduct model choice. PMID:21876135
B2Z: R Package for Bayesian Two-Zone Models
Directory of Open Access Journals (Sweden)
João Vitor Dias Monteiro
2011-08-01
Full Text Available A primary issue in industrial hygiene is the estimation of a worker's exposure to chemical, physical and biological agents. Mathematical modeling is increasingly being used as a method for assessing occupational exposures. However, predicting exposure in real settings is constrained by lack of quantitative knowledge of exposure determinants. Recently, Zhang, Banerjee, Yang, Lungu, and Ramachandran (2009 proposed Bayesian hierarchical models for estimating parameters and exposure concentrations for the two-zone differential equation models and for predicting concentrations in a zone near and far away from the source of contamination.Bayesian estimation, however, can often require substantial amounts of user-defined code and tuning. In this paper, we introduce a statistical software package, B2Z, built upon the R statistical computing platform that implements a Bayesian model for estimating model parameters and exposure concentrations in two-zone models. We discuss the algorithms behind our package and illustrate its use with simulated and real data examples.
Bayesian predictive modeling for genomic based personalized treatment selection.
Ma, Junsheng; Stingo, Francesco C; Hobbs, Brian P
2016-06-01
Efforts to personalize medicine in oncology have been limited by reductive characterizations of the intrinsically complex underlying biological phenomena. Future advances in personalized medicine will rely on molecular signatures that derive from synthesis of multifarious interdependent molecular quantities requiring robust quantitative methods. However, highly parameterized statistical models when applied in these settings often require a prohibitively large database and are sensitive to proper characterizations of the treatment-by-covariate interactions, which in practice are difficult to specify and may be limited by generalized linear models. In this article, we present a Bayesian predictive framework that enables the integration of a high-dimensional set of genomic features with clinical responses and treatment histories of historical patients, providing a probabilistic basis for using the clinical and molecular information to personalize therapy for future patients. Our work represents one of the first attempts to define personalized treatment assignment rules based on large-scale genomic data. We use actual gene expression data acquired from The Cancer Genome Atlas in the settings of leukemia and glioma to explore the statistical properties of our proposed Bayesian approach for personalizing treatment selection. The method is shown to yield considerable improvements in predictive accuracy when compared to penalized regression approaches. PMID:26575856
The Bayesian Modelling Of Inflation Rate In Romania
Mihaela Simionescu
2014-01-01
Bayesian econometrics knew a considerable increase in popularity in the last years, joining the interests of various groups of researchers in economic sciences and additional ones as specialists in econometrics, commerce, industry, marketing, finance, micro-economy, macro-economy and other domains. The purpose of this research is to achieve an introduction in Bayesian approach applied in economics, starting with Bayes theorem. For the Bayesian linear regression models the methodology of estim...
A tutorial introduction to Bayesian models of cognitive development
Perfors, Amy; Tenenbaum, Joshua B.; Griffiths, Thomas L.; Xu, Fei
2010-01-01
We present an introduction to Bayesian inference as it is used in probabilistic models of cognitive development. Our goal is to provide an intuitive and accessible guide to the what, the how, and the why of the Bayesian approach: what sorts of problems and data the framework is most relevant for, and how and why it may be useful for developmentalists. We emphasize a qualitative understanding of Bayesian inference, but also include information about additional resources for those interested in...
Bayesian Models of Graphs, Arrays and Other Exchangeable Random Structures.
Orbanz, Peter; Roy, Daniel M
2015-02-01
The natural habitat of most Bayesian methods is data represented by exchangeable sequences of observations, for which de Finetti's theorem provides the theoretical foundation. Dirichlet process clustering, Gaussian process regression, and many other parametric and nonparametric Bayesian models fall within the remit of this framework; many problems arising in modern data analysis do not. This article provides an introduction to Bayesian models of graphs, matrices, and other data that can be modeled by random structures. We describe results in probability theory that generalize de Finetti's theorem to such data and discuss their relevance to nonparametric Bayesian modeling. With the basic ideas in place, we survey example models available in the literature; applications of such models include collaborative filtering, link prediction, and graph and network analysis. We also highlight connections to recent developments in graph theory and probability, and sketch the more general mathematical foundation of Bayesian methods for other types of data beyond sequences and arrays. PMID:26353253
Modeling Social Annotation: a Bayesian Approach
Plangprasopchok, Anon
2008-01-01
Collaborative tagging systems, such as del.icio.us, CiteULike, and others, allow users to annotate objects, e.g., Web pages or scientific papers, with descriptive labels called tags. The social annotations, contributed by thousands of users, can potentially be used to infer categorical knowledge, classify documents or recommend new relevant information. Traditional text inference methods do not make best use of socially-generated data, since they do not take into account variations in individual users' perspectives and vocabulary. In a previous work, we introduced a simple probabilistic model that takes interests of individual annotators into account in order to find hidden topics of annotated objects. Unfortunately, our proposed approach had a number of shortcomings, including overfitting, local maxima and the requirement to specify values for some parameters. In this paper we address these shortcomings in two ways. First, we extend the model to a fully Bayesian framework. Second, we describe an infinite ver...
Improving randomness characterization through Bayesian model selection
R., Rafael Díaz-H; Martínez, Alí M Angulo; U'Ren, Alfred B; Hirsch, Jorge G; Marsili, Matteo; Castillo, Isaac Pérez
2016-01-01
Nowadays random number generation plays an essential role in technology with important applications in areas ranging from cryptography, which lies at the core of current communication protocols, to Monte Carlo methods, and other probabilistic algorithms. In this context, a crucial scientific endeavour is to develop effective methods that allow the characterization of random number generators. However, commonly employed methods either lack formality (e.g. the NIST test suite), or are inapplicable in principle (e.g. the characterization derived from the Algorithmic Theory of Information (ATI)). In this letter we present a novel method based on Bayesian model selection, which is both rigorous and effective, for characterizing randomness in a bit sequence. We derive analytic expressions for a model's likelihood which is then used to compute its posterior probability distribution. Our method proves to be more rigorous than NIST's suite and the Borel-Normality criterion and its implementation is straightforward. We...
Applied Bayesian statistical studies in biology and medicine
D’Amore, G; Scalfari, F
2004-01-01
It was written on another occasion· that "It is apparent that the scientific culture, if one means production of scientific papers, is growing exponentially, and chaotically, in almost every field of investigation". The biomedical sciences sensu lato and mathematical statistics are no exceptions. One might say then, and with good reason, that another collection of bio statistical papers would only add to the overflow and cause even more confusion. Nevertheless, this book may be greeted with some interest if we state that most of the papers in it are the result of a collaboration between biologists and statisticians, and partly the product of the Summer School th "Statistical Inference in Human Biology" which reaches its 10 edition in 2003 (information about the School can be obtained at the Web site http://www2. stat. unibo. itleventilSito%20scuolalindex. htm). is common experience - and not only This is rather important. Indeed, it in Italy - that encounters between statisticians and researchers are spora...
Bayesian modeling and significant features exploration in wavelet power spectra
Directory of Open Access Journals (Sweden)
D. V. Divine
2007-01-01
Full Text Available This study proposes and justifies a Bayesian approach to modeling wavelet coefficients and finding statistically significant features in wavelet power spectra. The approach utilizes ideas elaborated in scale-space smoothing methods and wavelet data analysis. We treat each scale of the discrete wavelet decomposition as a sequence of independent random variables and then apply Bayes' rule for constructing the posterior distribution of the smoothed wavelet coefficients. Samples drawn from the posterior are subsequently used for finding the estimate of the true wavelet spectrum at each scale. The method offers two different significance testing procedures for wavelet spectra. A traditional approach assesses the statistical significance against a red noise background. The second procedure tests for homoscedasticity of the wavelet power assessing whether the spectrum derivative significantly differs from zero at each particular point of the spectrum. Case studies with simulated data and climatic time-series prove the method to be a potentially useful tool in data analysis.
Bayesian Dose-Response Modeling in Sparse Data
Kim, Steven B.
This book discusses Bayesian dose-response modeling in small samples applied to two different settings. The first setting is early phase clinical trials, and the second setting is toxicology studies in cancer risk assessment. In early phase clinical trials, experimental units are humans who are actual patients. Prior to a clinical trial, opinions from multiple subject area experts are generally more informative than the opinion of a single expert, but we may face a dilemma when they have disagreeing prior opinions. In this regard, we consider compromising the disagreement and compare two different approaches for making a decision. In addition to combining multiple opinions, we also address balancing two levels of ethics in early phase clinical trials. The first level is individual-level ethics which reflects the perspective of trial participants. The second level is population-level ethics which reflects the perspective of future patients. We extensively compare two existing statistical methods which focus on each perspective and propose a new method which balances the two conflicting perspectives. In toxicology studies, experimental units are living animals. Here we focus on a potential non-monotonic dose-response relationship which is known as hormesis. Briefly, hormesis is a phenomenon which can be characterized by a beneficial effect at low doses and a harmful effect at high doses. In cancer risk assessments, the estimation of a parameter, which is known as a benchmark dose, can be highly sensitive to a class of assumptions, monotonicity or hormesis. In this regard, we propose a robust approach which considers both monotonicity and hormesis as a possibility. In addition, We discuss statistical hypothesis testing for hormesis and consider various experimental designs for detecting hormesis based on Bayesian decision theory. Past experiments have not been optimally designed for testing for hormesis, and some Bayesian optimal designs may not be optimal under a
Bayesian statistical analysis of censored data in geotechnical engineering
DEFF Research Database (Denmark)
Ditlevsen, Ove Dalager; Tarp-Johansen, Niels Jacob; Denver, Hans
2000-01-01
The geotechnical engineer is often faced with the problem ofhow to assess the statistical properties of a soil parameter on the basis ofa sample measured in-situ or in the laboratory with the defect that somevalues have been replaced by interval bounds because the corresponding soilparameter values...... a small censored sample is given. To estimate the char-acteristic value de¯ned as a lower fractile value corresponding to a codi¯edprobability value, the geotechnical engineer is thus urged to supplement theinformation from the measurements at the actual location by consideringwhatever prior knowledge...
Directory of Open Access Journals (Sweden)
J. Norberg
2015-09-01
Full Text Available We validate two-dimensional ionospheric tomography reconstructions against EISCAT incoherent scatter radar measurements. Our tomography method is based on Bayesian statistical inversion with prior distribution given by its mean and covariance. We employ ionosonde measurements for the choice of the prior mean and covariance parameters, and use the Gaussian Markov random fields as a sparse matrix approximation for the numerical computations. This results in a computationally efficient and statistically clear inversion algorithm for tomography. We demonstrate how this method works with simultaneous beacon satellite and ionosonde measurements obtained in northern Scandinavia. The performance is compared with results obtained with a zero mean prior and with the prior mean taken from the International Reference Ionosphere 2007 model. In validating the results, we use EISCAT UHF incoherent scatter radar measurements as the ground truth for the ionization profile shape. We find that ionosonde measurements improve the reconstruction by adding accurate information about the absolute value and the height distribution of electron density, and outperforms the alternative prior information sources. With an ionosonde at continuous disposal, the presented method enhances stand-alone near real-time ionospheric tomography for the given conditions significantly.
Norberg, J.; Virtanen, I. I.; Roininen, L.; Vierinen, J.; Orispää, M.; Kauristie, K.; Lehtinen, M. S.
2015-09-01
We validate two-dimensional ionospheric tomography reconstructions against EISCAT incoherent scatter radar measurements. Our tomography method is based on Bayesian statistical inversion with prior distribution given by its mean and covariance. We employ ionosonde measurements for the choice of the prior mean and covariance parameters, and use the Gaussian Markov random fields as a sparse matrix approximation for the numerical computations. This results in a computationally efficient and statistically clear inversion algorithm for tomography. We demonstrate how this method works with simultaneous beacon satellite and ionosonde measurements obtained in northern Scandinavia. The performance is compared with results obtained with a zero mean prior and with the prior mean taken from the International Reference Ionosphere 2007 model. In validating the results, we use EISCAT UHF incoherent scatter radar measurements as the ground truth for the ionization profile shape. We find that ionosonde measurements improve the reconstruction by adding accurate information about the absolute value and the height distribution of electron density, and outperforms the alternative prior information sources. With an ionosonde at continuous disposal, the presented method enhances stand-alone near real-time ionospheric tomography for the given conditions significantly.
Advances in Bayesian Model Based Clustering Using Particle Learning
Energy Technology Data Exchange (ETDEWEB)
Merl, D M
2009-11-19
Recent work by Carvalho, Johannes, Lopes and Polson and Carvalho, Lopes, Polson and Taddy introduced a sequential Monte Carlo (SMC) alternative to traditional iterative Monte Carlo strategies (e.g. MCMC and EM) for Bayesian inference for a large class of dynamic models. The basis of SMC techniques involves representing the underlying inference problem as one of state space estimation, thus giving way to inference via particle filtering. The key insight of Carvalho et al was to construct the sequence of filtering distributions so as to make use of the posterior predictive distribution of the observable, a distribution usually only accessible in certain Bayesian settings. Access to this distribution allows a reversal of the usual propagate and resample steps characteristic of many SMC methods, thereby alleviating to a large extent many problems associated with particle degeneration. Furthermore, Carvalho et al point out that for many conjugate models the posterior distribution of the static variables can be parametrized in terms of [recursively defined] sufficient statistics of the previously observed data. For models where such sufficient statistics exist, particle learning as it is being called, is especially well suited for the analysis of streaming data do to the relative invariance of its algorithmic complexity with the number of data observations. Through a particle learning approach, a statistical model can be fit to data as the data is arriving, allowing at any instant during the observation process direct quantification of uncertainty surrounding underlying model parameters. Here we describe the use of a particle learning approach for fitting a standard Bayesian semiparametric mixture model as described in Carvalho, Lopes, Polson and Taddy. In Section 2 we briefly review the previously presented particle learning algorithm for the case of a Dirichlet process mixture of multivariate normals. In Section 3 we describe several novel extensions to the original
Story, Roger E.
1996-01-01
Discussion of the use of Latent Semantic Indexing to determine relevancy in information retrieval focuses on statistical regression and Bayesian methods. Topics include keyword searching; a multiple regression model; how the regression model can aid search methods; and limitations of this approach, including complexity, linearity, and…
Applications of Bayesian Statistics to Problems in Gamma-Ray Bursts
Meegan, Charles A.
1997-01-01
This presentation will describe two applications of Bayesian statistics to Gamma Ray Bursts (GRBS). The first attempts to quantify the evidence for a cosmological versus galactic origin of GRBs using only the observations of the dipole and quadrupole moments of the angular distribution of bursts. The cosmological hypothesis predicts isotropy, while the galactic hypothesis is assumed to produce a uniform probability distribution over positive values for these moments. The observed isotropic distribution indicates that the Bayes factor for the cosmological hypothesis over the galactic hypothesis is about 300. Another application of Bayesian statistics is in the estimation of chance associations of optical counterparts with galaxies. The Bayesian approach is preferred to frequentist techniques here because the Bayesian approach easily accounts for galaxy mass distributions and because one can incorporate three disjoint hypotheses: (1) bursts come from galactic centers, (2) bursts come from galaxies in proportion to luminosity, and (3) bursts do not come from external galaxies. This technique was used in the analysis of the optical counterpart to GRB970228.
Distributions with given marginals and statistical modelling
Fortiana, Josep; Rodriguez-Lallena, José
2002-01-01
This book contains a selection of the papers presented at the meeting `Distributions with given marginals and statistical modelling', held in Barcelona (Spain), July 17-20, 2000. In 24 chapters, this book covers topics such as the theory of copulas and quasi-copulas, the theory and compatibility of distributions, models for survival distributions and other well-known distributions, time series, categorical models, definition and estimation of measures of dependence, monotonicity and stochastic ordering, shape and separability of distributions, hidden truncation models, diagonal families, orthogonal expansions, tests of independence, and goodness of fit assessment. These topics share the use and properties of distributions with given marginals, this being the fourth specialised text on this theme. The innovative aspect of the book is the inclusion of statistical aspects such as modelling, Bayesian statistics, estimation, and tests.
Development of a Bayesian Belief Network Runway Incursion Model
Green, Lawrence L.
2014-01-01
In a previous paper, a statistical analysis of runway incursion (RI) events was conducted to ascertain their relevance to the top ten Technical Challenges (TC) of the National Aeronautics and Space Administration (NASA) Aviation Safety Program (AvSP). The study revealed connections to perhaps several of the AvSP top ten TC. That data also identified several primary causes and contributing factors for RI events that served as the basis for developing a system-level Bayesian Belief Network (BBN) model for RI events. The system-level BBN model will allow NASA to generically model the causes of RI events and to assess the effectiveness of technology products being developed under NASA funding. These products are intended to reduce the frequency of RI events in particular, and to improve runway safety in general. The development, structure and assessment of that BBN for RI events by a Subject Matter Expert panel are documented in this paper.
A SEMIPARAMETRIC BAYESIAN MODEL FOR CIRCULAR-LINEAR REGRESSION
We present a Bayesian approach to regress a circular variable on a linear predictor. The regression coefficients are assumed to have a nonparametric distribution with a Dirichlet process prior. The semiparametric Bayesian approach gives added flexibility to the model and is usefu...
Bayesball: A Bayesian hierarchical model for evaluating fielding in major league baseball
Jensen, Shane T.; Shirley, Kenneth E.; Wyner, Abraham J.
2008-01-01
The use of statistical modeling in baseball has received substantial attention recently in both the media and academic community. We focus on a relatively under-explored topic: the use of statistical models for the analysis of fielding based on high-resolution data consisting of on-field location of batted balls. We combine spatial modeling with a hierarchical Bayesian structure in order to evaluate the performance of individual fielders while sharing information between fielders at each posi...
Fine Mapping Causal Variants with an Approximate Bayesian Method Using Marginal Test Statistics.
Chen, Wenan; Larrabee, Beth R; Ovsyannikova, Inna G; Kennedy, Richard B; Haralambieva, Iana H; Poland, Gregory A; Schaid, Daniel J
2015-07-01
Two recently developed fine-mapping methods, CAVIAR and PAINTOR, demonstrate better performance over other fine-mapping methods. They also have the advantage of using only the marginal test statistics and the correlation among SNPs. Both methods leverage the fact that the marginal test statistics asymptotically follow a multivariate normal distribution and are likelihood based. However, their relationship with Bayesian fine mapping, such as BIMBAM, is not clear. In this study, we first show that CAVIAR and BIMBAM are actually approximately equivalent to each other. This leads to a fine-mapping method using marginal test statistics in the Bayesian framework, which we call CAVIAR Bayes factor (CAVIARBF). Another advantage of the Bayesian framework is that it can answer both association and fine-mapping questions. We also used simulations to compare CAVIARBF with other methods under different numbers of causal variants. The results showed that both CAVIARBF and BIMBAM have better performance than PAINTOR and other methods. Compared to BIMBAM, CAVIARBF has the advantage of using only marginal test statistics and takes about one-quarter to one-fifth of the running time. We applied different methods on two independent cohorts of the same phenotype. Results showed that CAVIARBF, BIMBAM, and PAINTOR selected the same top 3 SNPs; however, CAVIARBF and BIMBAM had better consistency in selecting the top 10 ranked SNPs between the two cohorts. Software is available at https://bitbucket.org/Wenan/caviarbf. PMID:25948564
Bayesian calibration of power plant models for accurate performance prediction
International Nuclear Information System (INIS)
Highlights: • Bayesian calibration is applied to power plant performance prediction. • Measurements from a plant in operation are used for model calibration. • A gas turbine performance model and steam cycle model are calibrated. • An integrated plant model is derived. • Part load efficiency is accurately predicted as a function of ambient conditions. - Abstract: Gas turbine combined cycles are expected to play an increasingly important role in the balancing of supply and demand in future energy markets. Thermodynamic modeling of these energy systems is frequently applied to assist in decision making processes related to the management of plant operation and maintenance. In most cases, model inputs, parameters and outputs are treated as deterministic quantities and plant operators make decisions with limited or no regard of uncertainties. As the steady integration of wind and solar energy into the energy market induces extra uncertainties, part load operation and reliability are becoming increasingly important. In the current study, methods are proposed to not only quantify various types of uncertainties in measurements and plant model parameters using measured data, but to also assess their effect on various aspects of performance prediction. The authors aim to account for model parameter and measurement uncertainty, and for systematic discrepancy of models with respect to reality. For this purpose, the Bayesian calibration framework of Kennedy and O’Hagan is used, which is especially suitable for high-dimensional industrial problems. The article derives a calibrated model of the plant efficiency as a function of ambient conditions and operational parameters, which is also accurate in part load. The article shows that complete statistical modeling of power plants not only enhances process models, but can also increases confidence in operational decisions
Consumption Model Calibration and Related Statistical Problems
Czech Academy of Sciences Publication Activity Database
Brabec, Marek; Malý, Marek; Pelikán, Emil; Konár, Ondřej
Athens: WSEAS Press, 2009 - (Perlovsky, L.; Dionysiou, D.; Kostic, L.; Gonzalez-Concepcion, C.; Jaberg, H.; Mastorakis, N.; Zaharim, A.; Sopian, K.), s. 141-146 ISBN 978-960-474-091-8. [AEBD '09. World Multiconference on Applied Economics, Business and Development . Tenerife (ES), 01.07.2009-03.07.2009] R&D Projects: GA AV ČR 1ET400300513 Institutional research plan: CEZ:AV0Z10300504 Keywords : linear calibration * natural gas consumption modeling * Bayesian approach * statistical model * time-varying calibration * state-space model Subject RIV: JE - Non-nuclear Energetics, Energy Consumption ; Use
Bayesian Model Selection for LISA Pathfinder
Karnesis, Nikolaos; Sopuerta, Carlos F; Gibert, Ferran; Armano, Michele; Audley, Heather; Congedo, Giuseppe; Diepholz, Ingo; Ferraioli, Luigi; Hewitson, Martin; Hueller, Mauro; Korsakova, Natalia; Plagnol, Eric; Vitale, and Stefano
2013-01-01
The main goal of the LISA Pathfinder (LPF) mission is to fully characterize the acceleration noise models and to test key technologies for future space-based gravitational-wave observatories similar to the LISA/eLISA concept. The Data Analysis (DA) team has developed complex three-dimensional models of the LISA Technology Package (LTP) experiment on-board LPF. These models are used for simulations, but more importantly, they will be used for parameter estimation purposes during flight operations. One of the tasks of the DA team is to identify the physical effects that contribute significantly to the properties of the instrument noise. A way of approaching to this problem is to recover the essential parameters of the LTP which describe the data. Thus, we want to define the simplest model that efficiently explains the observations. To do so, adopting a Bayesian framework, one has to estimate the so-called Bayes Factor between two competing models. In our analysis, we use three main different methods to estimate...
Determination of absolute structure using Bayesian statistics on Bijvoet differences
Hooft, R.W.W.; Straver, L.H.; Spek, A.L.
2008-01-01
A new probabilistic approach is introduced for the determination of the absolute structure of a compound which is known to be enantiopure based on Bijvoet-pair intensity differences. The new method provides relative probabilities for different models of the chiral composition of the structure. The o
Stochastic model updating utilizing Bayesian approach and Gaussian process model
Wan, Hua-Ping; Ren, Wei-Xin
2016-03-01
Stochastic model updating (SMU) has been increasingly applied in quantifying structural parameter uncertainty from responses variability. SMU for parameter uncertainty quantification refers to the problem of inverse uncertainty quantification (IUQ), which is a nontrivial task. Inverse problem solved with optimization usually brings about the issues of gradient computation, ill-conditionedness, and non-uniqueness. Moreover, the uncertainty present in response makes the inverse problem more complicated. In this study, Bayesian approach is adopted in SMU for parameter uncertainty quantification. The prominent strength of Bayesian approach for IUQ problem is that it solves IUQ problem in a straightforward manner, which enables it to avoid the previous issues. However, when applied to engineering structures that are modeled with a high-resolution finite element model (FEM), Bayesian approach is still computationally expensive since the commonly used Markov chain Monte Carlo (MCMC) method for Bayesian inference requires a large number of model runs to guarantee the convergence. Herein we reduce computational cost in two aspects. On the one hand, the fast-running Gaussian process model (GPM) is utilized to approximate the time-consuming high-resolution FEM. On the other hand, the advanced MCMC method using delayed rejection adaptive Metropolis (DRAM) algorithm that incorporates local adaptive strategy with global adaptive strategy is employed for Bayesian inference. In addition, we propose the use of the powerful variance-based global sensitivity analysis (GSA) in parameter selection to exclude non-influential parameters from calibration parameters, which yields a reduced-order model and thus further alleviates the computational burden. A simulated aluminum plate and a real-world complex cable-stayed pedestrian bridge are presented to illustrate the proposed framework and verify its feasibility.
Bayesian Degree-Corrected Stochastic Block Models for Community Detection
Peng, Lijun
2013-01-01
Community detection in networks has drawn much attention in diverse fields, especially social sciences. Given its significance, there has been a large body of literature among which many are not statistically based. In this paper, we propose a novel stochastic blockmodel based on a logistic regression setup with node correction terms to better address this problem. We follow a Bayesian approach that explicitly captures the community behavior via prior specification. We then adopt a data augmentation strategy with latent Polya-Gamma variables to obtain posterior samples. We conduct inference based on a canonically mapped centroid estimator that formally addresses label non-identifiability. We demonstrate the novel proposed model and estimation on real-world as well as simulated benchmark networks and show that the proposed model and estimator are more flexible, representative, and yield smaller error rates when compared to the MAP estimator from classical degree-corrected stochastic blockmodels.
Cunningham, A. C.; Wallinga, J.; Hobo, N.; Versendaal, A. J.; Makaske, B.; Middelkoop, H.
2015-01-01
The optically stimulated luminescence (OSL) signal from fluvial sediment often contains a remnant from the previous deposition cycle, leading to a partially bleached equivalent-dose distribution. Although identification of the burial dose is of primary concern, the degree of bleaching could potentially provide insights into sediment transport processes. However, comparison of bleaching between samples is complicated by sample-to-sample variation in aliquot size and luminescence sensitivity. Here we begin development of an age model to account for these effects. With measurement data from multi-grain aliquots, we use Bayesian computational statistics to estimate the burial dose and bleaching parameters of the single-grain dose distribution. We apply the model to 46 samples taken from fluvial sediment of Rhine branches in the Netherlands, and compare the results with environmental predictor variables (depositional environment, texture, sample depth, depth relative to mean water level, dose rate). Although obvious correlations with predictor variables are absent, there is some suggestion that the best-bleached samples are found close to the modern mean water level, and that the extent of bleaching has changed over the recent past. We hypothesise that sediment deposited near the transition of channel to overbank deposits receives the most sunlight exposure, due to local reworking after deposition. However, nearly all samples are inferred to have at least some well-bleached grains, suggesting that bleaching also occurs during fluvial transport.
Universal efficiency at optimal work with Bayesian statistics
Johal, Ramandeep S.
2010-01-01
If the work per cycle of a quantum heat engine is averaged over an appropriate prior distribution for an external parameter $a$, the work becomes optimal at Curzon-Ahlborn efficiency. More general priors of the form $\\Pi(a) \\propto 1/a^{\\gamma}$ yield optimal work at an efficiency which stays close to CA value, in particular near equilibrium the efficiency scales as one-half of the Carnot value. This feature is analogous to the one recently observed in literature for certain models of finite-...
Bayesian Test of Significance for Conditional Independence: The Multinomial Model
de Morais Andrade, Pablo; Stern, Julio; de Bragança Pereira, Carlos
2014-03-01
Conditional independence tests (CI tests) have received special attention lately in Machine Learning and Computational Intelligence related literature as an important indicator of the relationship among the variables used by their models. In the field of Probabilistic Graphical Models (PGM)--which includes Bayesian Networks (BN) models--CI tests are especially important for the task of learning the PGM structure from data. In this paper, we propose the Full Bayesian Significance Test (FBST) for tests of conditional independence for discrete datasets. FBST is a powerful Bayesian test for precise hypothesis, as an alternative to frequentist's significance tests (characterized by the calculation of the \\emph{p-value}).
Universal efficiency at optimal work with bayesian statistics.
Johal, Ramandeep S
2010-12-01
If the work per cycle of a quantum heat engine is averaged over an appropriate prior distribution for an external parameter a , the work becomes optimal at Curzon-Ahlborn (CA) efficiency. More general priors of the form Π(a) ∝ 1/a(γ) yield optimal work at an efficiency which stays close to CA value, in particular near equilibrium the efficiency scales as one-half of the Carnot value. This feature is analogous to the one recently observed in literature for certain models of finite-time thermodynamics. Further, the use of Bayes' theorem implies that the work estimated with posterior probabilities also bears close analogy with the classical formula. These findings suggest that the notion of prior information can be used to reveal thermodynamic features in quantum systems, thus pointing to a connection between thermodynamic behavior and the concept of information. PMID:21230650
Bayesian Nonparametrics in Topic Modeling: A Brief Tutorial
Spangher, Alexander
2015-01-01
Using nonparametric methods has been increasingly explored in Bayesian hierarchical modeling as a way to increase model flexibility. Although the field shows a lot of promise, inference in many models, including Hierachical Dirichlet Processes (HDP), remain prohibitively slow. One promising path forward is to exploit the submodularity inherent in Indian Buffet Process (IBP) to derive near-optimal solutions in polynomial time. In this work, I will present a brief tutorial on Bayesian nonparame...
Non-parametric Bayesian models of response function in dynamic image sequences
Czech Academy of Sciences Publication Activity Database
Tichý, Ondřej; Šmídl, Václav
-, - (2016). ISSN 1077-3142 R&D Projects: GA ČR GA13-29225S Institutional support: RVO:67985556 Keywords : Response function * Blind source separation * Dynamic medical imaging * Probabilistic models * Bayesian methods Subject RIV: BB - Applied Statistics, Operational Research Impact factor: 1.540, year: 2014 http://library.utia.cas.cz/separaty/2016/AS/tichy-0456983.pdf
Czech Academy of Sciences Publication Activity Database
Fernandes, R.; Millard, A.R.; Brabec, Marek; Nadeau, M.J.; Grootes, P.
2014-01-01
Roč. 9, č. 2 (2014), Art. no. e87436. E-ISSN 1932-6203 Institutional support: RVO:67985807 Keywords : ancienit diet reconstruction * stable isotope measurements * mixture model * Bayesian estimation * Dirichlet prior Subject RIV: BB - Applied Statistics, Operational Research Impact factor: 3.234, year: 2014
Two-Stage Bayesian Model Averaging in Endogenous Variable Models.
Lenkoski, Alex; Eicher, Theo S; Raftery, Adrian E
2014-01-01
Economic modeling in the presence of endogeneity is subject to model uncertainty at both the instrument and covariate level. We propose a Two-Stage Bayesian Model Averaging (2SBMA) methodology that extends the Two-Stage Least Squares (2SLS) estimator. By constructing a Two-Stage Unit Information Prior in the endogenous variable model, we are able to efficiently combine established methods for addressing model uncertainty in regression models with the classic technique of 2SLS. To assess the validity of instruments in the 2SBMA context, we develop Bayesian tests of the identification restriction that are based on model averaged posterior predictive p-values. A simulation study showed that 2SBMA has the ability to recover structure in both the instrument and covariate set, and substantially improves the sharpness of resulting coefficient estimates in comparison to 2SLS using the full specification in an automatic fashion. Due to the increased parsimony of the 2SBMA estimate, the Bayesian Sargan test had a power of 50 percent in detecting a violation of the exogeneity assumption, while the method based on 2SLS using the full specification had negligible power. We apply our approach to the problem of development accounting, and find support not only for institutions, but also for geography and integration as development determinants, once both model uncertainty and endogeneity have been jointly addressed. PMID:24223471
Bayesian model reduction and empirical Bayes for group (DCM) studies.
Friston, Karl J; Litvak, Vladimir; Oswal, Ashwini; Razi, Adeel; Stephan, Klaas E; van Wijk, Bernadette C M; Ziegler, Gabriel; Zeidman, Peter
2016-03-01
This technical note describes some Bayesian procedures for the analysis of group studies that use nonlinear models at the first (within-subject) level - e.g., dynamic causal models - and linear models at subsequent (between-subject) levels. Its focus is on using Bayesian model reduction to finesse the inversion of multiple models of a single dataset or a single (hierarchical or empirical Bayes) model of multiple datasets. These applications of Bayesian model reduction allow one to consider parametric random effects and make inferences about group effects very efficiently (in a few seconds). We provide the relatively straightforward theoretical background to these procedures and illustrate their application using a worked example. This example uses a simulated mismatch negativity study of schizophrenia. We illustrate the robustness of Bayesian model reduction to violations of the (commonly used) Laplace assumption in dynamic causal modelling and show how its recursive application can facilitate both classical and Bayesian inference about group differences. Finally, we consider the application of these empirical Bayesian procedures to classification and prediction. PMID:26569570
Sampling Techniques in Bayesian Finite Element Model Updating
Boulkaibet, I; Mthembu, L; Friswell, M I; Adhikari, S
2011-01-01
Recent papers in the field of Finite Element Model (FEM) updating have highlighted the benefits of Bayesian techniques. The Bayesian approaches are designed to deal with the uncertainties associated with complex systems, which is the main problem in the development and updating of FEMs. This paper highlights the complexities and challenges of implementing any Bayesian method when the analysis involves a complicated structural dynamic model. In such systems an analytical Bayesian formulation might not be available in an analytic form; therefore this leads to the use of numerical methods, i.e. sampling methods. The main challenge then is to determine an efficient sampling of the model parameter space. In this paper, three sampling techniques, the Metropolis-Hastings (MH) algorithm, Slice Sampling and the Hybrid Monte Carlo (HMC) technique, are tested by updating a structural beam model. The efficiency and limitations of each technique is investigated when the FEM updating problem is implemented using the Bayesi...
Bayesian modelling of the emission spectrum of the JET Li-BES system
Kwak, Sehyun; Brix, M; Ghim, Y -c; Contributors, JET
2015-01-01
A Bayesian model of the emission spectrum of the JET lithium beam has been developed to infer the intensity of the Li I (2p-2s) line radiation and associated uncertainties. The detected spectrum for each channel of the lithium beam emission spectroscopy (Li-BES) system is here modelled by a single Li line modified by an instrumental function, Bremsstrahlung background, instrumental offset, and interference filter curve. Both the instrumental function and the interference filter curve are modelled with non-parametric Gaussian processes. All free parameters of the model, the intensities of the Li line, Bremsstrahlung background, and instrumental offset, are inferred using Bayesian probability theory with a Gaussian likelihood for photon statistics and electronic background noise. The prior distributions of the free parameters are chosen as Gaussians. Given these assumptions, the intensity of the Li line and corresponding uncertainties are analytically available using a Bayesian linear inversion technique. The p...
Efficient Nonparametric Bayesian Modelling with Sparse Gaussian Process Approximations
Seeger, Matthias; Lawrence, Neil; Herbrich, Ralf
2006-01-01
Sparse approximations to Bayesian inference for nonparametric Gaussian Process models scale linearly in the number of training points, allowing for the application of powerful kernel-based models to large datasets. We present a general framework based on the informative vector machine (IVM) (Lawrence et.al., 2002) and show how the complete Bayesian task of inference and learning of free hyperparameters can be performed in a practically efficient manner. Our framework allows for arbitrary like...
Modelling biogeochemical cycles in forest ecosystems: a Bayesian approach
Bagnara, Maurizio
2015-01-01
Forest models are tools for explaining and predicting the dynamics of forest ecosystems. They simulate forest behavior by integrating information on the underlying processes in trees, soil and atmosphere. Bayesian calibration is the application of probability theory to parameter estimation. It is a method, applicable to all models, that quantifies output uncertainty and identifies key parameters and variables. This study aims at testing the Bayesian procedure for calibration to different t...
Modeling cosmic void statistics
Hamaus, Nico; Wandelt, Benjamin D
2014-01-01
Understanding the internal structure and spatial distribution of cosmic voids is crucial when considering them as probes of cosmology. We present recent advances in modeling void density- and velocity-profiles in real space, as well as void two-point statistics in redshift space, by examining voids identified via the watershed transform in state-of-the-art $\\Lambda$CDM n-body simulations and mock galaxy catalogs. The simple and universal characteristics that emerge from these statistics indicate the self-similarity of large-scale structure and suggest cosmic voids to be among the most pristine objects to consider for future studies on the nature of dark energy, dark matter and modified gravity.
Rubin, Donald B.
1981-01-01
The Bayesian bootstrap is the Bayesian analogue of the bootstrap. Instead of simulating the sampling distribution of a statistic estimating a parameter, the Bayesian bootstrap simulates the posterior distribution of the parameter; operationally and inferentially the methods are quite similar. Because both methods of drawing inferences are based on somewhat peculiar model assumptions and the resulting inferences are generally sensitive to these assumptions, neither method should be applied wit...
Polyhedral approach to statistical learning graphical models
Czech Academy of Sciences Publication Activity Database
Studený, Milan; Haws, D.; Hemmecke, R.; Lindner, S.
Singapore : World Scientific Press, 2012, s. 346-372. ISBN 978-981-4383-45-5. [The 2nd CREST-SBM International Conference "Harmony of Groebner Bases and the Modern Industrial Society". Osaka (JP), 28.06.2012-2.07.2012] R&D Projects: GA ČR GA201/08/0539 Institutional support: RVO:67985556 Keywords : Bayesian network stucture * standard imset * characteristic imset * polyhedral geometry Subject RIV: BA - General Mathematics http://library.utia.cas.cz/separaty/2012/MTR/studeny-polyhedral approach to statistical learning graphical models.pdf
Biagini, Francesca
2016-01-01
This book provides an introduction to elementary probability and to Bayesian statistics using de Finetti's subjectivist approach. One of the features of this approach is that it does not require the introduction of sample space – a non-intrinsic concept that makes the treatment of elementary probability unnecessarily complicate – but introduces as fundamental the concept of random numbers directly related to their interpretation in applications. Events become a particular case of random numbers and probability a particular case of expectation when it is applied to events. The subjective evaluation of expectation and of conditional expectation is based on an economic choice of an acceptable bet or penalty. The properties of expectation and conditional expectation are derived by applying a coherence criterion that the evaluation has to follow. The book is suitable for all introductory courses in probability and statistics for students in Mathematics, Informatics, Engineering, and Physics.
Hunting down the best model of inflation with Bayesian evidence
International Nuclear Information System (INIS)
We present the first calculation of the Bayesian evidence for different prototypical single field inflationary scenarios, including representative classes of small field and large field models. This approach allows us to compare inflationary models in a well-defined statistical way and to determine the current 'best model of inflation'. The calculation is performed numerically by interfacing the inflationary code FieldInf with MultiNest. We find that small field models are currently preferred, while large field models having a self-interacting potential of power p>4 are strongly disfavored. The class of small field models as a whole has posterior odds of approximately 3 ratio 1 when compared with the large field class. The methodology and results presented in this article are an additional step toward the construction of a full numerical pipeline to constrain the physics of the early Universe with astrophysical observations. More accurate data (such as the Planck data) and the techniques introduced here should allow us to identify conclusively the best inflationary model.
A Bayesian observer model constrained by efficient coding can explain 'anti-Bayesian' percepts.
Wei, Xue-Xin; Stocker, Alan A
2015-10-01
Bayesian observer models provide a principled account of the fact that our perception of the world rarely matches physical reality. The standard explanation is that our percepts are biased toward our prior beliefs. However, reported psychophysical data suggest that this view may be simplistic. We propose a new model formulation based on efficient coding that is fully specified for any given natural stimulus distribution. The model makes two new and seemingly anti-Bayesian predictions. First, it predicts that perception is often biased away from an observer's prior beliefs. Second, it predicts that stimulus uncertainty differentially affects perceptual bias depending on whether the uncertainty is induced by internal or external noise. We found that both model predictions match reported perceptual biases in perceived visual orientation and spatial frequency, and were able to explain data that have not been explained before. The model is general and should prove applicable to other perceptual variables and tasks. PMID:26343249
Statistical models for expert judgement and wear prediction
International Nuclear Information System (INIS)
This thesis studies the statistical analysis of expert judgements and prediction of wear. The point of view adopted is the one of information theory and Bayesian statistics. A general Bayesian framework for analyzing both the expert judgements and wear prediction is presented. Information theoretic interpretations are given for some averaging techniques used in the determination of consensus distributions. Further, information theoretic models are compared with a Bayesian model. The general Bayesian framework is then applied in analyzing expert judgements based on ordinal comparisons. In this context, the value of information lost in the ordinal comparison process is analyzed by applying decision theoretic concepts. As a generalization of the Bayesian framework, stochastic filtering models for wear prediction are formulated. These models utilize the information from condition monitoring measurements in updating the residual life distribution of mechanical components. Finally, the application of stochastic control models in optimizing operational strategies for inspected components are studied. Monte-Carlo simulation methods, such as the Gibbs sampler and the stochastic quasi-gradient method, are applied in the determination of posterior distributions and in the solution of stochastic optimization problems. (orig.) (57 refs., 7 figs., 1 tab.)
Modelling of JET diagnostics using Bayesian Graphical Models
Energy Technology Data Exchange (ETDEWEB)
Svensson, J. [IPP Greifswald, Greifswald (Germany); Ford, O. [Imperial College, London (United Kingdom); McDonald, D.; Hole, M.; Nessi, G. von; Meakins, A.; Brix, M.; Thomsen, H.; Werner, A.; Sirinelli, A.
2011-07-01
The mapping between physics parameters (such as densities, currents, flows, temperatures etc) defining the plasma 'state' under a given model and the raw observations of each plasma diagnostic will 1) depend on the particular physics model used, 2) is inherently probabilistic, from uncertainties on both observations and instrumental aspects of the mapping, such as calibrations, instrument functions etc. A flexible and principled way of modelling such interconnected probabilistic systems is through so called Bayesian graphical models. Being an amalgam between graph theory and probability theory, Bayesian graphical models can simulate the complex interconnections between physics models and diagnostic observations from multiple heterogeneous diagnostic systems, making it relatively easy to optimally combine the observations from multiple diagnostics for joint inference on parameters of the underlying physics model, which in itself can be represented as part of the graph. At JET about 10 diagnostic systems have to date been modelled in this way, and has lead to a number of new results, including: the reconstruction of the flux surface topology and q-profiles without any specific equilibrium assumption, using information from a number of different diagnostic systems; profile inversions taking into account the uncertainties in the flux surface positions and a substantial increase in accuracy of JET electron density and temperature profiles, including improved pedestal resolution, through the joint analysis of three diagnostic systems. It is believed that the Bayesian graph approach could potentially be utilised for very large sets of diagnostics, providing a generic data analysis framework for nuclear fusion experiments, that would be able to optimally utilize the information from multiple diagnostics simultaneously, and where the explicit graph representation of the connections to underlying physics models could be used for sophisticated model testing. This
Bayesian model discrimination for glucose-insulin homeostasis
DEFF Research Database (Denmark)
Andersen, Kim Emil; Brooks, Stephen P.; Højbjerre, Malene
the reformulation of existing deterministic models as stochastic state space models which properly accounts for both measurement and process variability. The analysis is further enhanced by Bayesian model discrimination techniques and model averaged parameter estimation which fully accounts for model as well......In this paper we analyse a set of experimental data on a number of healthy and diabetic patients and discuss a variety of models for describing the physiological processes involved in glucose absorption and insulin secretion within the human body. We adopt a Bayesian approach which facilitates...
Rubin, David; Barbary, Kyle; Boone, Kyle; Chappell, Greta; Currie, Miles; Deustua, Susana; Fagrelius, Parker; Fruchter, Andrew; Hayden, Brian; Lidman, Chris; Nordin, Jakob; Perlmutter, Saul; Saunders, Clare; Sofiatti, Caroline
2015-01-01
While recent supernova cosmology research has benefited from improved measurements, current analysis approaches are not statistically optimal and will prove insufficient for future surveys. This paper discusses the limitations of current supernova cosmological analyses in treating outliers, selection effects, shape- and color-standardization relations, intrinsic dispersion, and heterogeneous observations. We present a new Bayesian framework, called UNITY (Unified Nonlinear Inference for Type-Ia cosmologY), that incorporates significant improvements in our ability to confront these effects. We apply the framework to real supernova observations and demonstrate smaller statistical and systematic uncertainties. We verify earlier results that SNe Ia require nonlinear shape and color standardizations, but we now include these nonlinear relations in a statistically well-justified way. This analysis was blinded, in that the method was first validated on simulated data, and no analysis changes were made after transiti...
Using consensus bayesian network to model the reactive oxygen species regulatory pathway.
Directory of Open Access Journals (Sweden)
Liangdong Hu
Full Text Available Bayesian network is one of the most successful graph models for representing the reactive oxygen species regulatory pathway. With the increasing number of microarray measurements, it is possible to construct the bayesian network from microarray data directly. Although large numbers of bayesian network learning algorithms have been developed, when applying them to learn bayesian networks from microarray data, the accuracies are low due to that the databases they used to learn bayesian networks contain too few microarray data. In this paper, we propose a consensus bayesian network which is constructed by combining bayesian networks from relevant literatures and bayesian networks learned from microarray data. It would have a higher accuracy than the bayesian networks learned from one database. In the experiment, we validated the bayesian network combination algorithm on several classic machine learning databases and used the consensus bayesian network to model the Escherichia coli's ROS pathway.
Bayesian chronological modeling of SunWatch, a fort ancient village in Dayton, Ohio
Krus, A.M.; Cook, R.; Hamilton, W.D.
2015-01-01
Radiocarbon results from houses, pits, and burials at the SunWatch site, Dayton, Ohio, are presented within an interpretative Bayesian statistical framework. The primary model incorporates dates from archaeological features in an unordered phase and uses charcoal outlier modeling (Bronk Ramsey 2009b) to account for issues of wood charcoal 14C dates predating their context. The results of the primary model estimate occupation lasted for 1–245 yr (95% probability), starting in cal AD 1175–1385 ...
A flexible bayesian model for testing for transmission ratio distortion.
Casellas, Joaquim; Manunza, Arianna; Mercader, Anna; Quintanilla, Raquel; Amills, Marcel
2014-12-01
Current statistical approaches to investigate the nature and magnitude of transmission ratio distortion (TRD) are scarce and restricted to the most common experimental designs such as F2 populations and backcrosses. In this article, we describe a new Bayesian approach to check TRD within a given biallelic genetic marker in a diploid species, providing a highly flexible framework that can accommodate any kind of population structure. This model relies on the genotype of each offspring and thus integrates all available information from either the parents' genotypes or population-specific allele frequencies and yields TRD estimates that can be corroborated by the calculation of a Bayes factor (BF). This approach has been evaluated on simulated data sets with appealing statistical performance. As a proof of concept, we have also tested TRD in a porcine population with five half-sib families and 352 offspring. All boars and piglets were genotyped with the Porcine SNP60 BeadChip, whereas genotypes from the sows were not available. The SNP-by-SNP screening of the pig genome revealed 84 SNPs with decisive evidences of TRD (BF > 100) after accounting for multiple testing. Many of these regions contained genes related to biological processes (e.g., nucleosome assembly and co-organization, DNA conformation and packaging, and DNA complex assembly) that are critically associated with embryonic viability. The implementation of this method, which overcomes many of the limitations of previous approaches, should contribute to fostering research on TRD in both model and nonmodel organisms. PMID:25271302
Wu, Yuefeng; Hooker, Giles
2013-01-01
This paper introduces a hierarchical framework to incorporate Hellinger distance methods into Bayesian analysis. We propose to modify a prior over non-parametric densities with the exponential of twice the Hellinger distance between a candidate and a parametric density. By incorporating a prior over the parameters of the second density, we arrive at a hierarchical model in which a non-parametric model is placed between parameters and the data. The parameters of the family can then be estimate...
Bayesian Proteoform Modeling Improves Protein Quantification of Global Proteomic Measurements
Energy Technology Data Exchange (ETDEWEB)
Webb-Robertson, Bobbie-Jo M.; Matzke, Melissa M.; Datta, Susmita; Payne, Samuel H.; Kang, Jiyun; Bramer, Lisa M.; Nicora, Carrie D.; Shukla, Anil K.; Metz, Thomas O.; Rodland, Karin D.; Smith, Richard D.; Tardiff, Mark F.; McDermott, Jason E.; Pounds, Joel G.; Waters, Katrina M.
2014-12-01
As the capability of mass spectrometry-based proteomics has matured, tens of thousands of peptides can be measured simultaneously, which has the benefit of offering a systems view of protein expression. However, a major challenge is that with an increase in throughput, protein quantification estimation from the native measured peptides has become a computational task. A limitation to existing computationally-driven protein quantification methods is that most ignore protein variation, such as alternate splicing of the RNA transcript and post-translational modifications or other possible proteoforms, which will affect a significant fraction of the proteome. The consequence of this assumption is that statistical inference at the protein level, and consequently downstream analyses, such as network and pathway modeling, have only limited power for biomarker discovery. Here, we describe a Bayesian model (BP-Quant) that uses statistically derived peptides signatures to identify peptides that are outside the dominant pattern, or the existence of multiple over-expressed patterns to improve relative protein abundance estimates. It is a research-driven approach that utilizes the objectives of the experiment, defined in the context of a standard statistical hypothesis, to identify a set of peptides exhibiting similar statistical behavior relating to a protein. This approach infers that changes in relative protein abundance can be used as a surrogate for changes in function, without necessarily taking into account the effect of differential post-translational modifications, processing, or splicing in altering protein function. We verify the approach using a dilution study from mouse plasma samples and demonstrate that BP-Quant achieves similar accuracy as the current state-of-the-art methods at proteoform identification with significantly better specificity. BP-Quant is available as a MatLab ® and R packages at https://github.com/PNNL-Comp-Mass-Spec/BP-Quant.
Bayesian calibration of the Community Land Model using surrogates
Energy Technology Data Exchange (ETDEWEB)
Ray, Jaideep [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Hou, Zhangshuan [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States); Huang, Maoyi [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States); Swiler, Laura Painton [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
2014-02-01
We present results from the Bayesian calibration of hydrological parameters of the Community Land Model (CLM), which is often used in climate simulations and Earth system models. A statistical inverse problem is formulated for three hydrological parameters, conditional on observations of latent heat surface fluxes over 48 months. Our calibration method uses polynomial and Gaussian process surrogates of the CLM, and solves the parameter estimation problem using a Markov chain Monte Carlo sampler. Posterior probability densities for the parameters are developed for two sites with different soil and vegetation covers. Our method also allows us to examine the structural error in CLM under two error models. We find that surrogate models can be created for CLM in most cases. The posterior distributions are more predictive than the default parameter values in CLM. Climatologically averaging the observations does not modify the parameters' distributions significantly. The structural error model reveals a correlation time-scale which can be used to identify the physical process that could be contributing to it. While the calibrated CLM has a higher predictive skill, the calibration is under-dispersive.
Ensemble bayesian model averaging using markov chain Monte Carlo sampling
Energy Technology Data Exchange (ETDEWEB)
Vrugt, Jasper A [Los Alamos National Laboratory; Diks, Cees G H [NON LANL; Clark, Martyn P [NON LANL
2008-01-01
Bayesian model averaging (BMA) has recently been proposed as a statistical method to calibrate forecast ensembles from numerical weather models. Successful implementation of BMA however, requires accurate estimates of the weights and variances of the individual competing models in the ensemble. In their seminal paper (Raftery etal. Mon Weather Rev 133: 1155-1174, 2(05)) has recommended the Expectation-Maximization (EM) algorithm for BMA model training, even though global convergence of this algorithm cannot be guaranteed. In this paper, we compare the performance of the EM algorithm and the recently developed Differential Evolution Adaptive Metropolis (DREAM) Markov Chain Monte Carlo (MCMC) algorithm for estimating the BMA weights and variances. Simulation experiments using 48-hour ensemble data of surface temperature and multi-model stream-flow forecasts show that both methods produce similar results, and that their performance is unaffected by the length of the training data set. However, MCMC simulation with DREAM is capable of efficiently handling a wide variety of BMA predictive distributions, and provides useful information about the uncertainty associated with the estimated BMA weights and variances.
Forecasting unconventional resource productivity - A spatial Bayesian model
Montgomery, J.; O'sullivan, F.
2015-12-01
Today's low prices mean that unconventional oil and gas development requires ever greater efficiency and better development decision-making. Inter and intra-field variability in well productivity, which is a major contemporary driver of uncertainty regarding resource size and its economics is driven by factors including geological conditions, well and completion design (which companies vary as they seek to optimize their performance), and uncertainty about the nature of fracture propagation. Geological conditions are often not be well understood early on in development campaigns, but nevertheless critical assessments and decisions must be made regarding the value of drilling an area and the placement of wells. In these situations, location provides a reasonable proxy for geology and the "rock quality." We propose a spatial Bayesian model for forecasting acreage quality, which improves decision-making by leveraging available production data and provides a framework for statistically studying the influence of different parameters on well productivity. Our approach consists of subdividing a field into sections and forming prior distributions for productivity in each section based on knowledge about the overall field. Production data from wells is used to update these estimates in a Bayesian fashion, improving model accuracy far more rapidly and with less sensitivity to outliers than a model that simply establishes an "average" productivity in each section. Additionally, forecasts using this model capture the importance of uncertainty—either due to a lack of information or for areas that demonstrate greater geological risk. We demonstrate the forecasting utility of this method using public data and also provide examples of how information from this model can be combined with knowledge about a field's geology or changes in technology to better quantify development risk. This approach represents an important shift in the way that production data is used to guide
Lack of Confidence in Approximate Bayesian Computation Model Choice
Robert, Christian P.; Cornuet, Jean-Marie; Marin, Jean-Michel; Pillai, Natesh S.
2011-01-01
Approximate Bayesian computation (ABC) have become an essential tool for the analysis of complex stochastic models. Grelaud et al. [(2009) Bayesian Anal 3:427–442] advocated the use of ABC for model choice in the specific case of Gibbs random fields, relying on an intermodel sufficiency property to show that the approximation was legitimate. We implemented ABC model choice in a wide range of phylogenetic models in the Do It Yourself-ABC (DIY-ABC) software [Cornuet et al. (2008) Bioinformatics...
Assessing fit in Bayesian models for spatial processes
Jun, M.
2014-09-16
© 2014 John Wiley & Sons, Ltd. Gaussian random fields are frequently used to model spatial and spatial-temporal data, particularly in geostatistical settings. As much of the attention of the statistics community has been focused on defining and estimating the mean and covariance functions of these processes, little effort has been devoted to developing goodness-of-fit tests to allow users to assess the models\\' adequacy. We describe a general goodness-of-fit test and related graphical diagnostics for assessing the fit of Bayesian Gaussian process models using pivotal discrepancy measures. Our method is applicable for both regularly and irregularly spaced observation locations on planar and spherical domains. The essential idea behind our method is to evaluate pivotal quantities defined for a realization of a Gaussian random field at parameter values drawn from the posterior distribution. Because the nominal distribution of the resulting pivotal discrepancy measures is known, it is possible to quantitatively assess model fit directly from the output of Markov chain Monte Carlo algorithms used to sample from the posterior distribution on the parameter space. We illustrate our method in a simulation study and in two applications.
Li, Ke; Zhang, Qiuju; Wang, Kun; Chen, Peng; Wang, Huaqing
2016-01-01
A new fault diagnosis method for rotating machinery based on adaptive statistic test filter (ASTF) and Diagnostic Bayesian Network (DBN) is presented in this paper. ASTF is proposed to obtain weak fault features under background noise, ASTF is based on statistic hypothesis testing in the frequency domain to evaluate similarity between reference signal (noise signal) and original signal, and remove the component of high similarity. The optimal level of significance α is obtained using particle swarm optimization (PSO). To evaluate the performance of the ASTF, evaluation factor Ipq is also defined. In addition, a simulation experiment is designed to verify the effectiveness and robustness of ASTF. A sensitive evaluation method using principal component analysis (PCA) is proposed to evaluate the sensitiveness of symptom parameters (SPs) for condition diagnosis. By this way, the good SPs that have high sensitiveness for condition diagnosis can be selected. A three-layer DBN is developed to identify condition of rotation machinery based on the Bayesian Belief Network (BBN) theory. Condition diagnosis experiment for rolling element bearings demonstrates the effectiveness of the proposed method. PMID:26761006
On the Bayesian Nonparametric Generalization of IRT-Type Models
San Martin, Ernesto; Jara, Alejandro; Rolin, Jean-Marie; Mouchart, Michel
2011-01-01
We study the identification and consistency of Bayesian semiparametric IRT-type models, where the uncertainty on the abilities' distribution is modeled using a prior distribution on the space of probability measures. We show that for the semiparametric Rasch Poisson counts model, simple restrictions ensure the identification of a general…
Bayesian inference model for fatigue life of laminated composites
DEFF Research Database (Denmark)
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...
deBInfer: Bayesian inference for dynamical models of biological systems in R
Boersch-Supan, Philipp H.; Johnson, Leah R
2016-01-01
1. Differential equations (DEs) are commonly used to model the temporal evolution of biological systems, but statistical methods for comparing DE models to data and for parameter inference are relatively poorly developed. This is especially problematic in the context of biological systems where observations are often noisy and only a small number of time points may be available. 2. Bayesian approaches offer a coherent framework for parameter inference that can account for multiple sources of ...
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.
Modelling LGD for unsecured retail loans using Bayesian methods
Katarzyna Bijak; Thomas, Lyn C
2015-01-01
Loss Given Default (LGD) is the loss borne by the bank when a customer defaults on a loan. LGD for unsecured retail loans is often found difficult to model. In the frequentist (non-Bayesian) two-step approach, two separate regression models are estimated independently, which can be considered potentially problematic when trying to combine them to make predictions about LGD. The result is a point estimate of LGD for each loan. Alternatively, LGD can be modelled using Bayesian methods. In the B...
A Bayesian Matrix Factorization Model for Relational Data
Singh, Ajit P
2012-01-01
Relational learning can be used to augment one data source with other correlated sources of information, to improve predictive accuracy. We frame a large class of relational learning problems as matrix factorization problems, and propose a hierarchical Bayesian model. Training our Bayesian model using random-walk Metropolis-Hastings is impractically slow, and so we develop a block Metropolis- Hastings sampler which uses the gradient and Hessian of the likelihood to dynamically tune the proposal. We demonstrate that a predictive model of brain response to stimuli can be improved by augmenting it with side information about the stimuli.
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 inverse modeling at the hydrological surface-subsurface interface
Cucchi, K.; Rubin, Y.
2014-12-01
In systems where surface and subsurface hydrological domains are highly connected, modeling surface and subsurface flow jointly is essential to accurately represent the physical processes and come up with reliable predictions of flows in river systems or stream-aquifer exchange. The flow quantification at the interface merging the two hydrosystem components is a function of both surface and subsurface spatially distributed parameters. In the present study, we apply inverse modeling techniques to a synthetic catchment with connected surface and subsurface hydrosystems. The model is physically-based and implemented with the Gridded Surface Subsurface Hydrologic Analysis software. On the basis of hydrograph measurement at the catchment outlet, we estimate parameters such as saturated hydraulic conductivity, overland and channel roughness coefficients. We compare maximum likelihood estimates (ML) with the parameter distributions obtained using the Bayesian statistical framework for spatially random fields provided by the Method of Anchored Distributions (MAD). While ML estimates maximize the probability of observing the data and capture the global trend of the target variables, MAD focuses on obtaining a probability distribution for the random unknown parameters and the anchors are designed to capture local features. We check the consistency between the two approaches and evaluate the additional information provided by MAD on parameter distributions. We also assess the contribution of adding new types of measurements such as water table depth or soil conductivity to the reduction of parameter uncertainty.
The Bayesian Modelling Of Inflation Rate In Romania
Directory of Open Access Journals (Sweden)
Mihaela Simionescu (Bratu
2014-06-01
Full Text Available Bayesian econometrics knew a considerable increase in popularity in the last years, joining the interests of various groups of researchers in economic sciences and additional ones as specialists in econometrics, commerce, industry, marketing, finance, micro-economy, macro-economy and other domains. The purpose of this research is to achieve an introduction in Bayesian approach applied in economics, starting with Bayes theorem. For the Bayesian linear regression models the methodology of estimation was presented, realizing two empirical studies for data taken from the Romanian economy. Thus, an autoregressive model of order 2 and a multiple regression model were built for the index of consumer prices. The Gibbs sampling algorithm was used for estimation in R software, computing the posterior means and the standard deviations. The parameters’ stability proved to be greater than in the case of estimations based on the methods of classical Econometrics.
Involving Stakeholders in Building Integrated Fisheries Models Using Bayesian Methods
Haapasaari, Päivi; Mäntyniemi, Samu; Kuikka, Sakari
2013-06-01
A participatory Bayesian approach was used to investigate how the views of stakeholders could be utilized to develop models to help understand the Central Baltic herring fishery. In task one, we applied the Bayesian belief network methodology to elicit the causal assumptions of six stakeholders on factors that influence natural mortality, growth, and egg survival of the herring stock in probabilistic terms. We also integrated the expressed views into a meta-model using the Bayesian model averaging (BMA) method. In task two, we used influence diagrams to study qualitatively how the stakeholders frame the management problem of the herring fishery and elucidate what kind of causalities the different views involve. The paper combines these two tasks to assess the suitability of the methodological choices to participatory modeling in terms of both a modeling tool and participation mode. The paper also assesses the potential of the study to contribute to the development of participatory modeling practices. It is concluded that the subjective perspective to knowledge, that is fundamental in Bayesian theory, suits participatory modeling better than a positivist paradigm that seeks the objective truth. The methodology provides a flexible tool that can be adapted to different kinds of needs and challenges of participatory modeling. The ability of the approach to deal with small data sets makes it cost-effective in participatory contexts. However, the BMA methodology used in modeling the biological uncertainties is so complex that it needs further development before it can be introduced to wider use in participatory contexts.
Bayesian modeling and prediction of solar particles flux
Czech Academy of Sciences Publication Activity Database
Dedecius, Kamil; Kalová, J.
Praha: FJFI ČVUT v Praze, 2009 - (Štěpán, V.), s. 77-77 ISBN 978-80-01-04430-8. [XXXI. Dny radiační ochrany. Kouty nad Desnou, Hrubý Jeseník (CZ), 02.11.2009-06.11.2009] R&D Projects: GA MŠk 1M0572 Institutional research plan: CEZ:AV0Z10750506 Keywords : Bayesian model * solar particle * solar wind Subject RIV: IN - Informatics, Computer Science http://library.utia.cas.cz/separaty/2009/AS/dedecius-bayesian modeling and prediction of solar particle s flux.pdf
Research & development and growth: A Bayesian model averaging analysis
Czech Academy of Sciences Publication Activity Database
Horváth, Roman
2011-01-01
Roč. 28, č. 6 (2011), s. 2669-2673. ISSN 0264-9993. [Society for Non-linear Dynamics and Econometrics Annual Conferencen. Washington DC, 16.03.2011-18.03.2011] R&D Projects: GA ČR GA402/09/0965 Institutional research plan: CEZ:AV0Z10750506 Keywords : Research and development * Growth * Bayesian model averaging Subject RIV: AH - Economics Impact factor: 0.701, year: 2011 http://library.utia.cas.cz/separaty/2011/E/horvath-research & development and growth a bayesian model averaging analysis.pdf
Approximate Bayesian Recursive Estimation of Linear Model with Uniform Noise
Czech Academy of Sciences Publication Activity Database
Pavelková, Lenka; Kárný, Miroslav
Brussels: IFAC, 2012, s. 1803-1807. ISBN 978-3-902823-06-9. [16th IFAC Symposium on System Identification The International Federation of Automatic Control. Brussels (BE), 11.07.2012-13.07.2012] R&D Projects: GA TA ČR TA01030123 Institutional support: RVO:67985556 Keywords : recursive parameter estimation * bounded noise * Bayesian learning * autoregressive models Subject RIV: BC - Control System s Theory http://library.utia.cas.cz/separaty/2012/AS/pavelkova-approximate bayesian recursive estimation of linear model with uniform noise.pdf
Comparing Bayesian models for multisensory cue combination without mandatory integration
Beierholm, Ulrik R.; Shams, Ladan; Kording, Konrad P; Ma, Wei Ji
2009-01-01
Bayesian models of multisensory perception traditionally address the problem of estimating an underlying variable that is assumed to be the cause of the two sensory signals. The brain, however, has to solve a more general problem: it also has to establish which signals come from the same source and should be integrated, and which ones do not and should be segregated. In the last couple of years, a few models have been proposed to solve this problem in a Bayesian fashion. One of these ha...
Bayesian Model Comparison With the g-Prior
DEFF Research Database (Denmark)
Nielsen, Jesper Kjær; Christensen, Mads Græsbøll; Cemgil, Ali Taylan;
2014-01-01
Model comparison and selection is an important problem in many model-based signal processing applications. Often, very simple information criteria such as the Akaike information criterion or the Bayesian information criterion are used despite their shortcomings. Compared to these methods, Djuric’...
Bayesian Estimation of the DINA Model with Gibbs Sampling
Culpepper, Steven Andrew
2015-01-01
A Bayesian model formulation of the deterministic inputs, noisy "and" gate (DINA) model is presented. Gibbs sampling is employed to simulate from the joint posterior distribution of item guessing and slipping parameters, subject attribute parameters, and latent class probabilities. The procedure extends concepts in Béguin and Glas,…
Applications of Bayesian Model Selection to Cosmological Parameters
Trotta, R
2005-01-01
Bayesian evidence is a tool for model comparison which can be used to decide whether the introduction of a new parameter is warranted by data. I show that the usual sampling statistic rejection tests for a null hypothesis can be misleading, since they do not take into account the information content of the data. I review the Laplace approximation and the Savage-Dickey density ratio to compute Bayes factors, which avoid the need of carrying out a computationally demanding multi-dimensional integration. I present a new procedure to forecast the Bayes factor of a future observation by computing the Expected Posterior Odds (ExPO). As an illustration, I consider three key parameters for our understanding of the cosmological concordance model: the spectral tilt of scalar perturbations, the spatial curvature of the Universe and a CDM isocurvature component to the initial conditions which is totally (anti)correlated with the adiabatic mode. I find that current data are not informative enough to draw a conclusion on t...
Bayesian-MCMC-based parameter estimation of stealth aircraft RCS models
Xia, Wei; Dai, Xiao-Xia; Feng, Yuan
2015-12-01
When modeling a stealth aircraft with low RCS (Radar Cross Section), conventional parameter estimation methods may cause a deviation from the actual distribution, owing to the fact that the characteristic parameters are estimated via directly calculating the statistics of RCS. The Bayesian-Markov Chain Monte Carlo (Bayesian-MCMC) method is introduced herein to estimate the parameters so as to improve the fitting accuracies of fluctuation models. The parameter estimations of the lognormal and the Legendre polynomial models are reformulated in the Bayesian framework. The MCMC algorithm is then adopted to calculate the parameter estimates. Numerical results show that the distribution curves obtained by the proposed method exhibit improved consistence with the actual ones, compared with those fitted by the conventional method. The fitting accuracy could be improved by no less than 25% for both fluctuation models, which implies that the Bayesian-MCMC method might be a good candidate among the optimal parameter estimation methods for stealth aircraft RCS models. Project supported by the National Natural Science Foundation of China (Grant No. 61101173), the National Basic Research Program of China (Grant No. 613206), the National High Technology Research and Development Program of China (Grant No. 2012AA01A308), the State Scholarship Fund by the China Scholarship Council (CSC), and the Oversea Academic Training Funds, and University of Electronic Science and Technology of China (UESTC).
Bayesian approach to color-difference models based on threshold and constant-stimuli methods.
Brusola, Fernando; Tortajada, Ignacio; Lengua, Ismael; Jordá, Begoña; Peris, Guillermo
2015-06-15
An alternative approach based on statistical Bayesian inference is presented to deal with the development of color-difference models and the precision of parameter estimation. The approach was applied to simulated data and real data, the latter published by selected authors involved with the development of color-difference formulae using traditional methods. Our results show very good agreement between the Bayesian and classical approaches. Among other benefits, our proposed methodology allows one to determine the marginal posterior distribution of each random individual parameter of the color-difference model. In this manner, it is possible to analyze the effect of individual parameters on the statistical significance calculation of a color-difference equation. PMID:26193510
International Nuclear Information System (INIS)
This paper is intended to make researchers in reliability theory aware of a recently introduced Bayesian model with imprecise prior distributions for statistical inference on failure data, that can also be considered as a robust Bayesian model. The model consists of a multinomial distribution with Dirichlet priors, making the approach basically nonparametric. New results for the model are presented, related to right-censored observations, where estimation based on this model is closely related to the product-limit estimator, which is an important statistical method to deal with reliability or survival data including right-censored observations. As for the product-limit estimator, the model considered in this paper aims at not using any information other than that provided by observed data, but our model fits into the robust Bayesian context which has the advantage that all inferences can be based on probabilities or expectations, or bounds for probabilities or expectations. The model uses a finite partition of the time-axis, and as such it is also related to life-tables
Directory of Open Access Journals (Sweden)
Edson Sandoval-Castellanos
Full Text Available Inference of population demographic history has vastly improved in recent years due to a number of technological and theoretical advances including the use of ancient DNA. Approximate Bayesian computation (ABC stands among the most promising methods due to its simple theoretical fundament and exceptional flexibility. However, limited availability of user-friendly programs that perform ABC analysis renders it difficult to implement, and hence programming skills are frequently required. In addition, there is limited availability of programs able to deal with heterochronous data. Here we present the software BaySICS: Bayesian Statistical Inference of Coalescent Simulations. BaySICS provides an integrated and user-friendly platform that performs ABC analyses by means of coalescent simulations from DNA sequence data. It estimates historical demographic population parameters and performs hypothesis testing by means of Bayes factors obtained from model comparisons. Although providing specific features that improve inference from datasets with heterochronous data, BaySICS also has several capabilities making it a suitable tool for analysing contemporary genetic datasets. Those capabilities include joint analysis of independent tables, a graphical interface and the implementation of Markov-chain Monte Carlo without likelihoods.
Bayesian Joint Modelling for Object Localisation in Weakly Labelled Images.
Shi, Zhiyuan; Hospedales, Timothy M; Xiang, Tao
2015-10-01
We address the problem of localisation of objects as bounding boxes in images and videos with weak labels. This weakly supervised object localisation problem has been tackled in the past using discriminative models where each object class is localised independently from other classes. In this paper, a novel framework based on Bayesian joint topic modelling is proposed, which differs significantly from the existing ones in that: (1) All foreground object classes are modelled jointly in a single generative model that encodes multiple object co-existence so that "explaining away" inference can resolve ambiguity and lead to better learning and localisation. (2) Image backgrounds are shared across classes to better learn varying surroundings and "push out" objects of interest. (3) Our model can be learned with a mixture of weakly labelled and unlabelled data, allowing the large volume of unlabelled images on the Internet to be exploited for learning. Moreover, the Bayesian formulation enables the exploitation of various types of prior knowledge to compensate for the limited supervision offered by weakly labelled data, as well as Bayesian domain adaptation for transfer learning. Extensive experiments on the PASCAL VOC, ImageNet and YouTube-Object videos datasets demonstrate the effectiveness of our Bayesian joint model for weakly supervised object localisation. PMID:26340253
Cybis, Gabriela Bettella
2014-01-01
Combining models for phenotypic and molecular evolution can lead to powerful inference tools.Under the flexible framework of Bayesian phylogenetics, I develop statistical methods to address phylodynamic problems in this intersection.First, I present a hierarchical phylogeographic method that combines information across multiple datasets to draw inference on a common geographical spread process. Each dataset represents a parallel realization of this geographic process on a different group of ...
A note on Bayesian nonparametric priors derived from exponentially tilted Poisson-Kingman models
Cerquetti, Annalisa
2007-01-01
We derive the class of normalized generalized Gamma processes from Poisson-Kingman models (Pitman, 2003) with tempered alfa-stable mixing distribution. Relying on this construction it can be shown that in Bayesian nonparametrics, results on quantities of statistical interest under those priors, like the analogous of the Blackwell-MacQueen prediction rules or the distribution of the number of distinct elements observed in a sample, arise as immediate consequences of Pitman's results.
Bayesian Uncertainty Quantification for Subsurface Inversion Using a Multiscale Hierarchical Model
Mondal, Anirban
2014-07-03
We consider a Bayesian approach to nonlinear inverse problems in which the unknown quantity is a random field (spatial or temporal). The Bayesian approach contains a natural mechanism for regularization in the form of prior information, can incorporate information from heterogeneous sources and provide a quantitative assessment of uncertainty in the inverse solution. The Bayesian setting casts the inverse solution as a posterior probability distribution over the model parameters. The Karhunen-Loeve expansion is used for dimension reduction of the random field. Furthermore, we use a hierarchical Bayes model to inject multiscale data in the modeling framework. In this Bayesian framework, we show that this inverse problem is well-posed by proving that the posterior measure is Lipschitz continuous with respect to the data in total variation norm. Computational challenges in this construction arise from the need for repeated evaluations of the forward model (e.g., in the context of MCMC) and are compounded by high dimensionality of the posterior. We develop two-stage reversible jump MCMC that has the ability to screen the bad proposals in the first inexpensive stage. Numerical results are presented by analyzing simulated as well as real data from hydrocarbon reservoir. This article has supplementary material available online. © 2014 American Statistical Association and the American Society for Quality.
Asymptotically minimax Bayesian predictive densities for multinomial models
Komaki, Fumiyasu
2011-01-01
One-step ahead prediction for the multinomial model is considered. The performance of a predictive density is evaluated by the average Kullback-Leibler divergence from the true density to the predictive density. Asymptotic approximations of risk functions of Bayesian predictive densities based on Dirichlet priors are obtained. It is shown that a Bayesian predictive density based on a specific Dirichlet prior is asymptotically minimax. The asymptotically minimax prior is different from known objective priors such as the Jeffreys prior or the uniform prior.
Uncertainty Modeling Based on Bayesian Network in Ontology Mapping
Institute of Scientific and Technical Information of China (English)
LI Yuhua; LIU Tao; SUN Xiaolin
2006-01-01
How to deal with uncertainty is crucial in exact concept mapping between ontologies. This paper presents a new framework on modeling uncertainty in ontologies based on bayesian networks (BN). In our approach, ontology Web language (OWL) is extended to add probabilistic markups for attaching probability information, the source and target ontologies (expressed by patulous OWL) are translated into bayesian networks (BNs), the mapping between the two ontologies can be digged out by constructing the conditional probability tables (CPTs) of the BN using a improved algorithm named I-IPFP based on iterative proportional fitting procedure (IPFP). The basic idea of this framework and algorithm are validated by positive results from computer experiments.
Euler, Christoph
2015-01-01
Using Monte Carlo simulations of globular clusters we developed a method separating metallicity effects from age effects on observed integrated ugriz colors. We demonstrate that these colors do not evolve with time significantly after an age of 4 Gyr and use Bayesian statistics to calculate a probability distribution function of the metallicity. We tested the method using the M31 globular cluster system and then applied to explain the observed color bimodality in globular cluster sets and tidal effects on it. We show that the color bimodality is an effect of a nonlinearity in the color-metallicity relation caused by stellar dynamics on the Giant Branch, that colors including only the UV show a weaker bimodality than those subtracting from visual bands and that cluster sets with a distinct bimodality are in principle older than those with only a weak bimodal distribution. Furthermore a bimodal color distribution of coeval clusters implies a bimodal metallicity distribution, but a unimodal color distribution do...
Kim, Tae-Jeong; Kim, Ki-Young; Shin, Dong-Hoon; Kwon, Hyun-Han
2015-04-01
It has been widely acknowledged that the appropriate simulation of natural streamflow at ungauged sites is one of the fundamental challenges to hydrology community. In particular, the key to reliable runoff simulation in ungauged basins is a reliable rainfall-runoff model and a parameter estimation. In general, parameter estimation in rainfall-runoff models is a complex issue due to an insufficient hydrologic data. This study aims to regionalize the parameters of the continuous rainfall-runoff model in conjunction with Bayesian statistical techniques to facilitate uncertainty analysis. First, this study uses the Bayesian Markov Chain Monte Carlo scheme for the Sacramento rainfall-runoff model that has been widely used around the world. The Sacramento model is calibrated against daily runoff observation, and thirteen parameters of the model are optimized as well as posterior distributor distributions for each parameter are derived. Second, we applied Bayesian generalized linear regression model to set of the parameters with basin characteristics (e.g. area and slope), to obtain a functional relationship between pairs of variables. The proposed model was validated in two gauged watersheds in accordance with the efficiency criteria such as the Nash-Sutcliffe efficiency, coefficient of efficiency, index of agreement and coefficient of correlation. The future study will be further focused on uncertainty analysis to fully incorporate propagation of the uncertainty into the regionalization framework. KEYWORDS: Ungauge, Parameter, Sacramento, Generalized linear model, Regionalization Acknowledgement This research was supported by a Grant (13SCIPA01) from Smart Civil Infrastructure Research Program funded by the Ministry of Land, Infrastructure and Transport (MOLIT) of Korea government and the Korea Agency for Infrastructure Technology Advancement (KAIA).
cudaBayesreg: Parallel Implementation of a Bayesian Multilevel Model for fMRI Data Analysis
Directory of Open Access Journals (Sweden)
Adelino R. Ferreira da Silva
2011-10-01
Full Text Available Graphic processing units (GPUs are rapidly gaining maturity as powerful general parallel computing devices. A key feature in the development of modern GPUs has been the advancement of the programming model and programming tools. Compute Unified Device Architecture (CUDA is a software platform for massively parallel high-performance computing on Nvidia many-core GPUs. In functional magnetic resonance imaging (fMRI, the volume of the data to be processed, and the type of statistical analysis to perform call for high-performance computing strategies. In this work, we present the main features of the R-CUDA package cudaBayesreg which implements in CUDA the core of a Bayesian multilevel model for the analysis of brain fMRI data. The statistical model implements a Gibbs sampler for multilevel/hierarchical linear models with a normal prior. The main contribution for the increased performance comes from the use of separate threads for fitting the linear regression model at each voxel in parallel. The R-CUDA implementation of the Bayesian model proposed here has been able to reduce significantly the run-time processing of Markov chain Monte Carlo (MCMC simulations used in Bayesian fMRI data analyses. Presently, cudaBayesreg is only configured for Linux systems with Nvidia CUDA support.
Model Selection by Friedman Statistics
Adil Korkmaz; Muharrem Burak ONEMLI
2011-01-01
This study investigates an application of Friedman statistic as a model selection methodology on post estimation data. The Friedman statistic is employed for testing the possible differences between related samples by ranking the data. Similarly, we suggest ranking of competing models based on a specific multiple comparison procedure for identifying differences between models. As a non-parametric test statistic, it does not make assumptions regarding the underlying distribution of data, howe...
Bayesian Modelling of fMRI Time Series
DEFF Research Database (Denmark)
Højen-Sørensen, Pedro; Hansen, Lars Kai; Rasmussen, Carl Edward
2000-01-01
We present a Hidden Markov Model (HMM) for inferring the hidden psychological state (or neural activity) during single trial fMRI activation experiments with blocked task paradigms. Inference is based on Bayesian methodology, using a combination of analytical and a variety of Markov Chain Monte...
Bayesian Modelling of fMRI Time Series
DEFF Research Database (Denmark)
Højen-Sørensen, Pedro; Hansen, Lars Kai; Rasmussen, Carl Edward
We present a Hidden Markov Model (HMM) for inferring the hidden psychological state (or neural activity) during single trial fMRI activation experiments with blocked task paradigms. Inference is based on Bayesian methodology, using a combination of analytical and a variety of Markov Chain Monte...
Statistical Model for Content Extraction
DEFF Research Database (Denmark)
Qureshi, Pir Abdul Rasool; Memon, Nasrullah
2011-01-01
We present a statistical model for content extraction from HTML documents. The model operates on Document Object Model (DOM) tree of the corresponding HTML document. It evaluates each tree node and associated statistical features to predict significance of the node towards overall content...
Research on Bayesian Network Based User's Interest Model
Institute of Scientific and Technical Information of China (English)
ZHANG Weifeng; XU Baowen; CUI Zifeng; XU Lei
2007-01-01
It has very realistic significance for improving the quality of users' accessing information to filter and selectively retrieve the large number of information on the Internet. On the basis of analyzing the existing users' interest models and some basic questions of users' interest (representation, derivation and identification of users' interest), a Bayesian network based users' interest model is given. In this model, the users' interest reduction algorithm based on Markov Blanket model is used to reduce the interest noise, and then users' interested and not interested documents are used to train the Bayesian network. Compared to the simple model, this model has the following advantages like small space requirements, simple reasoning method and high recognition rate. The experiment result shows this model can more appropriately reflect the user's interest, and has higher performance and good usability.
Equifinality of formal (DREAM) and informal (GLUE) bayesian approaches in hydrologic modeling?
Energy Technology Data Exchange (ETDEWEB)
Vrugt, Jasper A [Los Alamos National Laboratory; Robinson, Bruce A [Los Alamos National Laboratory; Ter Braak, Cajo J F [NON LANL; Gupta, Hoshin V [NON LANL
2008-01-01
In recent years, a strong debate has emerged in the hydrologic literature regarding what constitutes an appropriate framework for uncertainty estimation. Particularly, there is strong disagreement whether an uncertainty framework should have its roots within a proper statistical (Bayesian) context, or whether such a framework should be based on a different philosophy and implement informal measures and weaker inference to summarize parameter and predictive distributions. In this paper, we compare a formal Bayesian approach using Markov Chain Monte Carlo (MCMC) with generalized likelihood uncertainty estimation (GLUE) for assessing uncertainty in conceptual watershed modeling. Our formal Bayesian approach is implemented using the recently developed differential evolution adaptive metropolis (DREAM) MCMC scheme with a likelihood function that explicitly considers model structural, input and parameter uncertainty. Our results demonstrate that DREAM and GLUE can generate very similar estimates of total streamflow uncertainty. This suggests that formal and informal Bayesian approaches have more common ground than the hydrologic literature and ongoing debate might suggest. The main advantage of formal approaches is, however, that they attempt to disentangle the effect of forcing, parameter and model structural error on total predictive uncertainty. This is key to improving hydrologic theory and to better understand and predict the flow of water through catchments.
Reliability of equipments and theory of frequency statistics and Bayesian decision
International Nuclear Information System (INIS)
The rapid development of Bayesian techniques use in the domain of industrial risk is a recent phenomenon linked to the development of powerful computers. These techniques involve a reasoning well adapted to experimental logics, based on the dynamical knowledge enrichment with experience data. In the framework of reliability studies and statistical decision making, these methods differ slightly from the methods commonly used to evaluate the reliability of systems and from classical theoretical frequency statistics. This particular approach is described in this book and illustrated with many examples of application (power plants, pressure vessels, industrial installations etc..). These examples generally concern the risk management in the cases where the application of rules and the respect of norms become insufficient. It is now well known that the risk cannot be reduced to zero and that its evaluation must be performed using statistics, taking into account the possible accident processes and also the investments necessary to avoid them (service life, failure, maintenance costs and availability of materials). The result is the optimizing of a decision process about rare or uncertain events. (J.S.)
Bayesian and maximin optimal designs for heteroscedastic regression models
Dette, Holger; Haines, Linda M.; Imhof, Lorens A.
2003-01-01
The problem of constructing standardized maximin D-optimal designs for weighted polynomial regression models is addressed. In particular it is shown that, by following the broad approach to the construction of maximin designs introduced recently by Dette, Haines and Imhof (2003), such designs can be obtained as weak limits of the corresponding Bayesian Φq-optimal designs. The approach is illustrated for two specific weighted polynomial models and also for a particular growth model.
Bayesian modeling growth curves for quail assuming skewness in errors
Directory of Open Access Journals (Sweden)
Robson Marcelo Rossi
2014-06-01
Full Text Available Bayesian modeling growth curves for quail assuming skewness in errors - To assume normal distributions in the data analysis is common in different areas of the knowledge. However we can make use of the other distributions that are capable to model the skewness parameter in the situations that is needed to model data with tails heavier than the normal. This article intend to present alternatives to the assumption of the normality in the errors, adding asymmetric distributions. A Bayesian approach is proposed to fit nonlinear models when the errors are not normal, thus, the distributions t, skew-normal and skew-t are adopted. The methodology is intended to apply to different growth curves to the quail body weights. It was found that the Gompertz model assuming skew-normal errors and skew-t errors, respectively for male and female, were the best fitted to the data.
Uncertainties in ozone concentrations predicted with a Lagrangian photochemical air quality model have been estimated using Bayesian Monte Carlo (BMC) analysis. Bayesian Monte Carlo analysis provides a means of combining subjective "prior" uncertainty estimates developed ...
Höhna, Sebastian; Landis, Michael J; Heath, Tracy A; Boussau, Bastien; Lartillot, Nicolas; Moore, Brian R; Huelsenbeck, John P; Ronquist, Fredrik
2016-07-01
Programs for Bayesian inference of phylogeny currently implement a unique and ﬁxed suite of models. Consequently, users of these software packages are simultaneously forced to use a number of programs for a given study, while also lacking the freedom to explore models that have not been implemented by the developers of those programs. We developed a new open-source software package, RevBayes, to address these problems. RevBayes is entirely based on probabilistic graphical models, a powerful generic framework for specifying and analyzing statistical models. Phylogenetic-graphical models can be speciﬁed interactively in RevBayes, piece by piece, using a new succinct and intuitive language called Rev. Rev is similar to the R language and the BUGS model-speciﬁcation language, and should be easy to learn for most users. The strength of RevBayes is the simplicity with which one can design, specify, and implement new and complex models. Fortunately, this tremendous ﬂexibility does not come at the cost of slower computation; as we demonstrate, RevBayes outperforms competing software for several standard analyses. Compared with other programs, RevBayes has fewer black-box elements. Users need to explicitly specify each part of the model and analysis. Although this explicitness may initially be unfamiliar, we are convinced that this transparency will improve understanding of phylogenetic models in our ﬁeld. Moreover, it will motivate the search for improvements to existing methods by brazenly exposing the model choices that we make to critical scrutiny. RevBayes is freely available at http://www.RevBayes.com [Bayesian inference; Graphical models; MCMC; statistical phylogenetics.]. PMID:27235697
Bayesian demography 250 years after Bayes.
Bijak, Jakub; Bryant, John
2016-01-01
Bayesian statistics offers an alternative to classical (frequentist) statistics. It is distinguished by its use of probability distributions to describe uncertain quantities, which leads to elegant solutions to many difficult statistical problems. Although Bayesian demography, like Bayesian statistics more generally, is around 250 years old, only recently has it begun to flourish. The aim of this paper is to review the achievements of Bayesian demography, address some misconceptions, and make the case for wider use of Bayesian methods in population studies. We focus on three applications: demographic forecasts, limited data, and highly structured or complex models. The key advantages of Bayesian methods are the ability to integrate information from multiple sources and to describe uncertainty coherently. Bayesian methods also allow for including additional (prior) information next to the data sample. As such, Bayesian approaches are complementary to many traditional methods, which can be productively re-expressed in Bayesian terms. PMID:26902889
Statistical Model of Extreme Shear
DEFF Research Database (Denmark)
Larsen, Gunner Chr.; Hansen, Kurt Schaldemose
2004-01-01
In order to continue cost-optimisation of modern large wind turbines, it is important to continously increase the knowledge on wind field parameters relevant to design loads. This paper presents a general statistical model that offers site-specific prediction of the probability density function...... model that, on a statistically consistent basis, describe the most likely spatial shape of an extreme wind shear event. Predictions from the model have been compared with results from an extreme value data analysis, based on a large number of high-sampled full-scale time series measurements. the...... consistent, given the inevitabel uncertainties associated with model as well as with the extreme value data analysis. Keywords: Statistical model, extreme wind conditions, statistical analysis, turbulence, wind loading, statistical analysis, turbulence, wind loading, wind shear, wind turbines....
Bayesian methods for proteomic biomarker development
Directory of Open Access Journals (Sweden)
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.
A Bayesian nonlinear mixed-effects disease progression model
Kim, Seongho; Jang, Hyejeong; Wu, Dongfeng; Abrams, Judith
2016-01-01
A nonlinear mixed-effects approach is developed for disease progression models that incorporate variation in age in a Bayesian framework. We further generalize the probability model for sensitivity to depend on age at diagnosis, time spent in the preclinical state and sojourn time. The developed models are then applied to the Johns Hopkins Lung Project data and the Health Insurance Plan for Greater New York data using Bayesian Markov chain Monte Carlo and are compared with the estimation method that does not consider random-effects from age. Using the developed models, we obtain not only age-specific individual-level distributions, but also population-level distributions of sensitivity, sojourn time and transition probability. PMID:26798562
Bayesian optimization for materials design
Frazier, Peter I.; Wang, Jialei
2015-01-01
We introduce Bayesian optimization, a technique developed for optimizing time-consuming engineering simulations and for fitting machine learning models on large datasets. Bayesian optimization guides the choice of experiments during materials design and discovery to find good material designs in as few experiments as possible. We focus on the case when materials designs are parameterized by a low-dimensional vector. Bayesian optimization is built on a statistical technique called Gaussian pro...
Bayesian Modelling in Machine Learning: A Tutorial Review
Seeger, Matthias
2006-01-01
Many facets of Bayesian Modelling are firmly established in Machine Learning and give rise to state-of-the-art solutions to application problems. The sheer number of techniques, ideas and models which have been proposed, and the terminology, can be bewildering. With this tutorial review, we aim to give a wide high-level overview over this important field, concentrating on central ideas and methods, and on their interconnections. The reader will gain a basic understanding of the topics and the...
Performance and prediction: Bayesian modelling of fallible choice in chess
Haworth, Guy McCrossan; Regan, Ken; Di Fatta, Giuseppe
2010-01-01
Evaluating agents in decision-making applications requires assessing their skill and predicting their behaviour. Both are well developed in Poker-like situations, but less so in more complex game and model domains. This paper addresses both tasks by using Bayesian inference in a benchmark space of reference agents. The concepts are explained and demonstrated using the game of chess but the model applies generically to any domain with quantifiable options and fallible choice. Demonstration ...
Bayesian modeling and prediction of solar particles flux
International Nuclear Information System (INIS)
An autoregression model was developed based on the Bayesian approach. Considering the solar wind non-homogeneity, the idea was applied of combining the pure autoregressive properties of the model with expert knowledge based on a similar behaviour of the various phenomena related to the flux properties. Examples of such situations include the hardening of the X-ray spectrum, which is often followed by coronal mass ejection and a significant increase in the particles flux intensity
Bayesian estimation of a DSGE model with inventories
Foerster, Marcel
2011-01-01
This paper introduces inventories in an otherwise standard Dynamic Stochastic General Equilibrium Model (DSGE) of the business cycle. Firms accumulate inventories to facilitate sales, but face a cost of doing so in terms of costly storage of intermediate goods. The paper's main contribution is to present a DSGE model with inventories that is estimated using Bayesian methods. Based on US data we show that accounting for inventory dynamics has a significant impact on parameter estimates and imp...
Organism-level models: When mechanisms and statistics fail us
International Nuclear Information System (INIS)
Purpose: To describe the unique characteristics of models that represent the entire course of radiation therapy at the organism level and to highlight the uses to which such models can be put. Methods: At the level of an organism, traditional model-building runs into severe difficulties. We do not have sufficient knowledge to devise a complete biochemistry-based model. Statistical model-building fails due to the vast number of variables and the inability to control many of them in any meaningful way. Finally, building surrogate models, such as animal-based models, can result in excluding some of the most critical variables. Bayesian probabilistic models (Bayesian networks) provide a useful alternative that have the advantages of being mathematically rigorous, incorporating the knowledge that we do have, and being practical. Results: Bayesian networks representing radiation therapy pathways for prostate cancer and head and neck cancer were used to highlight the important aspects of such models and some techniques of model-building. A more specific model representing the treatment of occult lymph nodes in head and neck cancer were provided as an example of how such a model can inform clinical decisions. A model of the possible role of PET imaging in brain cancer was used to illustrate the means by which clinical trials can be modelled in order to come up with a trial design that will have meaningful outcomes. Conclusions: Probabilistic models are currently the most useful approach to representing the entire therapy outcome process.
Markov Model of Wind Power Time Series UsingBayesian Inference of Transition Matrix
Chen, Peiyuan; Berthelsen, Kasper Klitgaard; Bak-Jensen, Birgitte; Chen, Zhe
2009-01-01
This paper proposes to use Bayesian inference of transition matrix when developing a discrete Markov model of a wind speed/power time series and 95% credible interval for the model verification. The Dirichlet distribution is used as a conjugate prior for the transition matrix. Three discrete Markov models are compared, i.e. the basic Markov model, the Bayesian Markov model and the birth-and-death Markov model. The proposed Bayesian Markov model shows the best accuracy in modeling the autocorr...
Foundational Issues in Statistical Modeling: Statistical Model Specification and Validation
Directory of Open Access Journals (Sweden)
Aris Spanos
2011-01-01
Full Text Available Statistical model specification and validation raise crucial foundational problems whose pertinent resolution holds the key to learning from data by securing the reliability of frequentist inference. The paper questions the judiciousness of several current practices, including the theory-driven approach, and the Akaike-type model selection procedures, arguing that they often lead to unreliable inferences. This is primarily due to the fact that goodness-of-fit/prediction measures and other substantive and pragmatic criteria are of questionable value when the estimated model is statistically misspecified. Foisting one's favorite model on the data often yields estimated models which are both statistically and substantively misspecified, but one has no way to delineate between the two sources of error and apportion blame. The paper argues that the error statistical approach can address this Duhemian ambiguity by distinguishing between statistical and substantive premises and viewing empirical modeling in a piecemeal way with a view to delineate the various issues more effectively. It is also argued that Hendry's general to specific procedures does a much better job in model selection than the theory-driven and the Akaike-type procedures primary because of its error statistical underpinnings.
Bayesian point event modeling in spatial and environmental epidemiology.
Lawson, Andrew B
2012-10-01
This paper reviews the current state of point event modeling in spatial epidemiology from a Bayesian perspective. Point event (or case event) data arise when geo-coded addresses of disease events are available. Often, this level of spatial resolution would not be accessible due to medical confidentiality constraints. However, for the examination of small spatial scales, it is important to be capable of examining point process data directly. Models for such data are usually formulated based on point process theory. In addition, special conditioning arguments can lead to simpler Bernoulli likelihoods and logistic spatial models. Goodness-of-fit diagnostics and Bayesian residuals are also considered. Applications within putative health hazard risk assessment, cluster detection, and linkage to environmental risk fields (misalignment) are considered. PMID:23035034
Statistical modelling with quantile functions
Gilchrist, Warren
2000-01-01
Galton used quantiles more than a hundred years ago in describing data. Tukey and Parzen used them in the 60s and 70s in describing populations. Since then, the authors of many papers, both theoretical and practical, have used various aspects of quantiles in their work. Until now, however, no one put all the ideas together to form what turns out to be a general approach to statistics.Statistical Modelling with Quantile Functions does just that. It systematically examines the entire process of statistical modelling, starting with using the quantile function to define continuous distributions. The author shows that by using this approach, it becomes possible to develop complex distributional models from simple components. A modelling kit can be developed that applies to the whole model - deterministic and stochastic components - and this kit operates by adding, multiplying, and transforming distributions rather than data.Statistical Modelling with Quantile Functions adds a new dimension to the practice of stati...
Bayesian networks modeling for thermal error of numerical control machine tools
Institute of Scientific and Technical Information of China (English)
Xin-hua YAO; Jian-zhong FU; Zi-chen CHEN
2008-01-01
The interaction between the heat source location,its intensity,thermal expansion coefficient,the machine system configuration and the running environment creates complex thermal behavior of a machine tool,and also makes thermal error prediction difficult.To address this issue,a novel prediction method for machine tool thermal error based on Bayesian networks (BNs) was presented.The method described causal relationships of factors inducing thermal deformation by graph theory and estimated the thermal error by Bayesian statistical techniques.Due to the effective combination of domain knowledge and sampled data,the BN method could adapt to the change of running state of machine,and obtain satisfactory prediction accuracy.Ex-periments on spindle thermal deformation were conducted to evaluate the modeling performance.Experimental results indicate that the BN method performs far better than the least squares(LS)analysis in terms of modeling estimation accuracy.
Bickel, David R
2011-01-01
In statistical practice, whether a Bayesian or frequentist approach is used in inference depends not only on the availability of prior information but also on the attitude taken toward partial prior information, with frequentists tending to be more cautious than Bayesians. The proposed framework defines that attitude in terms of a specified amount of caution, thereby enabling data analysis at the level of caution desired and on the basis of any prior information. The caution parameter represents the attitude toward partial prior information in much the same way as a loss function represents the attitude toward risk. When there is very little prior information and nonzero caution, the resulting inferences correspond to those of the candidate confidence intervals and p-values that are most similar to the credible intervals and hypothesis probabilities of the specified Bayesian posterior. On the other hand, in the presence of a known physical distribution of the parameter, inferences are based only on the corres...
Bayesian Statistics and Uncertainty Quantification for Safety Boundary Analysis in Complex Systems
He, Yuning; Davies, Misty Dawn
2014-01-01
The analysis of a safety-critical system often requires detailed knowledge of safe regions and their highdimensional non-linear boundaries. We present a statistical approach to iteratively detect and characterize the boundaries, which are provided as parameterized shape candidates. Using methods from uncertainty quantification and active learning, we incrementally construct a statistical model from only few simulation runs and obtain statistically sound estimates of the shape parameters for safety boundaries.
Bayesian Tracking of Emerging Epidemics Using Ensemble Optimal Statistical Interpolation (EnOSI)
Krishnamurthy, Ashok; Cobb, Loren; Mandel, Jan; Beezley, Jonathan
2010-01-01
We explore the use of the optimal statistical interpolation (OSI) data assimilation method for the statistical tracking of emerging epidemics and to study the spatial dynamics of a disease. The epidemic models that we used for this study are spatial variants of the common susceptible-infectious-removed (S-I-R) compartmental model of epidemiology. The spatial S-I-R epidemic model is illustrated by application to simulated spatial dynamic epidemic data from the historic "Black Death" plague of ...
Diffeomorphic Statistical Deformation Models
DEFF Research Database (Denmark)
Hansen, Michael Sass; Hansen, Mads/Fogtman; Larsen, Rasmus
2007-01-01
manifold and that the distance between two deformations are given by the metric introduced by the L2-norm in the parameter space. The chosen L2-norm is shown to have a clear and intuitive interpretation on the usual nonlinear manifold. Our model is validated on a set of MR images of corpus callosum with...
Bayesian Model Averaging for Ensemble-Based Estimates of Solvation Free Energies
Gosink, Luke J; Reehl, Sarah M; Whitney, Paul D; Mobley, David L; Baker, Nathan A
2016-01-01
This paper applies the Bayesian Model Averaging (BMA) statistical ensemble technique to estimate small molecule solvation free energies. There is a wide range methods for predicting solvation free energies, ranging from empirical statistical models to ab initio quantum mechanical approaches. Each of these methods are based on a set of conceptual assumptions that can affect a method's predictive accuracy and transferability. Using an iterative statistical process, we have selected and combined solvation energy estimates using an ensemble of 17 diverse methods from the SAMPL4 blind prediction study to form a single, aggregated solvation energy estimate. The ensemble design process evaluates the statistical information in each individual method as well as the performance of the aggregate estimate obtained from the ensemble as a whole. Methods that possess minimal or redundant information are pruned from the ensemble and the evaluation process repeats until aggregate predictive performance can no longer be improv...
A Statistical Programme Assignment Model
DEFF Research Database (Denmark)
Rosholm, Michael; Staghøj, Jonas; Svarer, Michael
When treatment effects of active labour market programmes are heterogeneous in an observable way across the population, the allocation of the unemployed into different programmes becomes a particularly important issue. In this paper, we present a statistical model designed to improve the present...... duration of unemployment spells may result if a statistical programme assignment model is introduced. We discuss several issues regarding the plementation of such a system, especially the interplay between the statistical model and case workers....
Application of Bayesian model averaging in modeling long-term wind speed distributions
Energy Technology Data Exchange (ETDEWEB)
Li, Gong; Shi, Jing [Department of Industrial and Manufacturing Engineering, North Dakota State University, Dept 2485, P.O. Box 6050, Fargo, ND 58108 (United States)
2010-06-15
Accurate estimation of wind speed distribution is critical to the assessment of wind energy potential, the site selection of wind farms, and the operations management of wind power conversion systems. This paper proposes a new approach for deriving more reliable and robust wind speed distributions than conventional statistical modeling approach. This approach combines Bayesian model averaging (BMA) and Markov Chain Monte Carlo (MCMC) sampling methods. The derived BMA probability density function (PDF) of the wind speed is an average of the model PDFs included in the model space weighted by their posterior probabilities over the sample data. MCMC method provides an effective way for numerically computing marginal likelihoods, which are essential for obtaining the posterior model probabilities. The approach is applied to multiple sites with high wind power potential in North Dakota. The wind speed data at these sites are the mean hourly wind speeds collected over two years. It is demonstrated that indeed none of the conventional statistical models such as Weibull distribution are universally plausible for all the sites. However, the BMA approach can provide comparative reliability and robustness in describing the long-term wind speed distributions for all sites, while making the traditional model comparison based on goodness-of-fit statistics unnecessary. (author)
A localization model to localize multiple sources using Bayesian inference
Dunham, Joshua Rolv
Accurate localization of a sound source in a room setting is important in both psychoacoustics and architectural acoustics. Binaural models have been proposed to explain how the brain processes and utilizes the interaural time differences (ITDs) and interaural level differences (ILDs) of sound waves arriving at the ears of a listener in determining source location. Recent work shows that applying Bayesian methods to this problem is proving fruitful. In this thesis, pink noise samples are convolved with head-related transfer functions (HRTFs) and compared to combinations of one and two anechoic speech signals convolved with different HRTFs or binaural room impulse responses (BRIRs) to simulate room positions. Through exhaustive calculation of Bayesian posterior probabilities and using a maximal likelihood approach, model selection will determine the number of sources present, and parameter estimation will result in azimuthal direction of the source(s).
Bayesian Inference and Forecasting in the Stationary Bilinear Model
Roberto Leon-Gonzalez; Fuyu Yang
2014-01-01
A stationary bilinear (SB) model can be used to describe processes with a time-varying degree of persistence that depends on past shocks. An example of such a process is inflation. This study develops methods for Bayesian inference, model comparison, and forecasting in the SB model. Using monthly U.K. inflation data, we find that the SB model outperforms the random walk and first order autoregressive AR(1) models in terms of root mean squared forecast errors for both the one-step-ahead and th...
Bayesian Age-Period-Cohort Modeling and Prediction - BAMP
Directory of Open Access Journals (Sweden)
Volker J. Schmid
2007-10-01
Full Text Available The software package BAMP provides a method of analyzing incidence or mortality data on the Lexis diagram, using a Bayesian version of an age-period-cohort model. A hierarchical model is assumed with a binomial model in the first-stage. As smoothing priors for the age, period and cohort parameters random walks of first and second order, with and without an additional unstructured component are available. Unstructured heterogeneity can also be included in the model. In order to evaluate the model fit, posterior deviance, DIC and predictive deviances are computed. By projecting the random walk prior into the future, future death rates can be predicted.
Bayesian analysis of recursive SVAR models with overidentifying restrictions
Kociecki, Andrzej; Rubaszek, Michał; Ca' Zorzi, Michele
2012-01-01
The paper provides a novel Bayesian methodological framework to estimate structural VAR (SVAR) models with recursive identification schemes that allows for the inclusion of over-identifying restrictions. The proposed framework enables the researcher to (i) elicit the prior on the non-zero contemporaneous relations between economic variables and to (ii) derive an analytical expression for the posterior distribution and marginal data density. We illustrate our methodological framework by estima...
Bayesian parsimonious covariance estimation for hierarchical linear mixed models
Frühwirth-Schnatter, Sylvia; Tüchler, Regina
2004-01-01
We considered a non-centered parameterization of the standard random-effects model, which is based on the Cholesky decomposition of the variance-covariance matrix. The regression type structure of the non-centered parameterization allows to choose a simple, conditionally conjugate normal prior on the Cholesky factor. Based on the non-centered parameterization, we search for a parsimonious variance-covariance matrix by identifying the non-zero elements of the Cholesky factors using Bayesian va...
Bayesian Methods for Neural Networks and Related Models
Titterington, D.M.
2004-01-01
Models such as feed-forward neural networks and certain other structures investigated in the computer science literature are not amenable to closed-form Bayesian analysis. The paper reviews the various approaches taken to overcome this difficulty, involving the use of Gaussian approximations, Markov chain Monte Carlo simulation routines and a class of non-Gaussian but “deterministic” approximations called variational approximations.
Bayesian network models in brain functional connectivity analysis
Ide, Jaime S.; Zhang, Sheng; Chiang-shan R. Li
2013-01-01
Much effort has been made to better understand the complex integration of distinct parts of the human brain using functional magnetic resonance imaging (fMRI). Altered functional connectivity between brain regions is associated with many neurological and mental illnesses, such as Alzheimer and Parkinson diseases, addiction, and depression. In computational science, Bayesian networks (BN) have been used in a broad range of studies to model complex data set in the presence of uncertainty and wh...
Bayesian Models of Learning and Reasoning with Relations
Chen, Dawn
2014-01-01
How do humans acquire relational concepts such as larger, which are essential for analogical inference and other forms of high-level reasoning? Are they necessarily innate, or can they be learned from non-relational inputs? Using comparative relations as a model domain, we show that structured relations can be learned from unstructured inputs of realistic complexity, applying bottom-up Bayesian learning mechanisms that make minimal assumptions about innate representations. First, we introduce...
Mixed deterministic statistical modelling of regional ozone air pollution
Kalenderski, Stoitchko Dimitrov
2011-03-17
We develop a physically motivated statistical model for regional ozone air pollution by separating the ground-level pollutant concentration field into three components, namely: transport, local production and large-scale mean trend mostly dominated by emission rates. The model is novel in the field of environmental spatial statistics in that it is a combined deterministic-statistical model, which gives a new perspective to the modelling of air pollution. The model is presented in a Bayesian hierarchical formalism, and explicitly accounts for advection of pollutants, using the advection equation. We apply the model to a specific case of regional ozone pollution-the Lower Fraser valley of British Columbia, Canada. As a predictive tool, we demonstrate that the model vastly outperforms existing, simpler modelling approaches. Our study highlights the importance of simultaneously considering different aspects of an air pollution problem as well as taking into account the physical bases that govern the processes of interest. © 2011 John Wiley & Sons, Ltd..
Directory of Open Access Journals (Sweden)
Kostas Alexandridis
2013-06-01
Full Text Available Assessing spatial model performance often presents challenges related to the choice and suitability of traditional statistical methods in capturing the true validity and dynamics of the predicted outcomes. The stochastic nature of many of our contemporary spatial models of land use change necessitate the testing and development of new and innovative methodologies in statistical spatial assessment. In many cases, spatial model performance depends critically on the spatially-explicit prior distributions, characteristics, availability and prevalence of the variables and factors under study. This study explores the statistical spatial characteristics of statistical model assessment of modeling land use change dynamics in a seven-county study area in South-Eastern Wisconsin during the historical period of 1963–1990. The artificial neural network-based Land Transformation Model (LTM predictions are used to compare simulated with historical land use transformations in urban/suburban landscapes. We introduce a range of Bayesian information entropy statistical spatial metrics for assessing the model performance across multiple simulation testing runs. Bayesian entropic estimates of model performance are compared against information-theoretic stochastic entropy estimates and theoretically-derived accuracy assessments. We argue for the critical role of informational uncertainty across different scales of spatial resolution in informing spatial landscape model assessment. Our analysis reveals how incorporation of spatial and landscape information asymmetry estimates can improve our stochastic assessments of spatial model predictions. Finally our study shows how spatially-explicit entropic classification accuracy estimates can work closely with dynamic modeling methodologies in improving our scientific understanding of landscape change as a complex adaptive system and process.
Bayesian model selection framework for identifying growth patterns in filamentous fungi.
Lin, Xiao; Terejanu, Gabriel; Shrestha, Sajan; Banerjee, Sourav; Chanda, Anindya
2016-06-01
This paper describes a rigorous methodology for quantification of model errors in fungal growth models. This is essential to choose the model that best describes the data and guide modeling efforts. Mathematical modeling of growth of filamentous fungi is necessary in fungal biology for gaining systems level understanding on hyphal and colony behaviors in different environments. A critical challenge in the development of these mathematical models arises from the indeterminate nature of their colony architecture, which is a result of processing diverse intracellular signals induced in response to a heterogeneous set of physical and nutritional factors. There exists a practical gap in connecting fungal growth models with measurement data. Here, we address this gap by introducing the first unified computational framework based on Bayesian inference that can quantify individual model errors and rank the statistical models based on their descriptive power against data. We show that this Bayesian model comparison is just a natural formalization of Occam׳s razor. The application of this framework is discussed in comparing three models in the context of synthetic data generated from a known true fungal growth model. This framework of model comparison achieves a trade-off between data fitness and model complexity and the quantified model error not only helps in calibrating and comparing the models, but also in making better predictions and guiding model refinements. PMID:27000772
Bayesian regression model for seasonal forecast of precipitation over Korea
Jo, Seongil; Lim, Yaeji; Lee, Jaeyong; Kang, Hyun-Suk; Oh, Hee-Seok
2012-08-01
In this paper, we apply three different Bayesian methods to the seasonal forecasting of the precipitation in a region around Korea (32.5°N-42.5°N, 122.5°E-132.5°E). We focus on the precipitation of summer season (June-July-August; JJA) for the period of 1979-2007 using the precipitation produced by the Global Data Assimilation and Prediction System (GDAPS) as predictors. Through cross-validation, we demonstrate improvement for seasonal forecast of precipitation in terms of root mean squared error (RMSE) and linear error in probability space score (LEPS). The proposed methods yield RMSE of 1.09 and LEPS of 0.31 between the predicted and observed precipitations, while the prediction using GDAPS output only produces RMSE of 1.20 and LEPS of 0.33 for CPC Merged Analyzed Precipitation (CMAP) data. For station-measured precipitation data, the RMSE and LEPS of the proposed Bayesian methods are 0.53 and 0.29, while GDAPS output is 0.66 and 0.33, respectively. The methods seem to capture the spatial pattern of the observed precipitation. The Bayesian paradigm incorporates the model uncertainty as an integral part of modeling in a natural way. We provide a probabilistic forecast integrating model uncertainty.
Application of Bayesian statistical decision theory for a maintenance optimization problem
International Nuclear Information System (INIS)
Reliability-centered maintenance (RCM) is a rational approach that can be used to identify the equipment of facilities that may turn out to be critical with respect to safety, to availability, or to maintenance costs. Is is dor these critical pieces of equipment alone that a corrective (one waits for a failure) or preventive (the type and frequency are specified) maintenance policy is established. But this approach has limitations: - when there is little operating feedback and it concerns rare events affecting a piece of equipment judged critical on a priori grounds (how is it possible, in this case, to decide whether or not it is critical, since there is conflict between the gravity of the potential failure and its frequency?); - when the aim is propose an optimal maintenance frequency for a critical piece of equipment - changing the maintenance frequency hitherto applied may cause a significant drift in the observed reliability of the equipment, an aspect not generally taken into account in the RCM approach. In these two situations, expert judgments can be combined with the available operating feedback (Bayesian approach) and the combination of risk of failure and economic consequences taken into account (statistical decision theory) to achieve a true optimization of maintenance policy choices. This paper presents an application on the maintenance of diesel generator component
AIC, BIC, Bayesian evidence against the interacting dark energy model
Energy Technology Data Exchange (ETDEWEB)
Szydlowski, Marek [Jagiellonian University, Astronomical Observatory, Krakow (Poland); Jagiellonian University, Mark Kac Complex Systems Research Centre, Krakow (Poland); Krawiec, Adam [Jagiellonian University, Institute of Economics, Finance and Management, Krakow (Poland); Jagiellonian University, Mark Kac Complex Systems Research Centre, Krakow (Poland); Kurek, Aleksandra [Jagiellonian University, Astronomical Observatory, Krakow (Poland); Kamionka, Michal [University of Wroclaw, Astronomical Institute, Wroclaw (Poland)
2015-01-01
Recent astronomical observations have indicated that the Universe is in a phase of accelerated expansion. While there are many cosmological models which try to explain this phenomenon, we focus on the interacting ΛCDM model where an interaction between the dark energy and dark matter sectors takes place. This model is compared to its simpler alternative - the ΛCDM model. To choose between these models the likelihood ratio test was applied as well as the model comparison methods (employing Occam's principle): the Akaike information criterion (AIC), the Bayesian information criterion (BIC) and the Bayesian evidence. Using the current astronomical data: type Ia supernova (Union2.1), h(z), baryon acoustic oscillation, the Alcock- Paczynski test, and the cosmic microwave background data, we evaluated both models. The analyses based on the AIC indicated that there is less support for the interacting ΛCDM model when compared to the ΛCDM model, while those based on the BIC indicated that there is strong evidence against it in favor of the ΛCDM model. Given the weak or almost non-existing support for the interacting ΛCDM model and bearing in mind Occam's razor we are inclined to reject this model. (orig.)
AIC, BIC, Bayesian evidence against the interacting dark energy model
Energy Technology Data Exchange (ETDEWEB)
Szydłowski, Marek, E-mail: marek.szydlowski@uj.edu.pl [Astronomical Observatory, Jagiellonian University, Orla 171, 30-244, Kraków (Poland); Mark Kac Complex Systems Research Centre, Jagiellonian University, Reymonta 4, 30-059, Kraków (Poland); Krawiec, Adam, E-mail: adam.krawiec@uj.edu.pl [Institute of Economics, Finance and Management, Jagiellonian University, Łojasiewicza 4, 30-348, Kraków (Poland); Mark Kac Complex Systems Research Centre, Jagiellonian University, Reymonta 4, 30-059, Kraków (Poland); Kurek, Aleksandra, E-mail: alex@oa.uj.edu.pl [Astronomical Observatory, Jagiellonian University, Orla 171, 30-244, Kraków (Poland); Kamionka, Michał, E-mail: kamionka@astro.uni.wroc.pl [Astronomical Institute, University of Wrocław, ul. Kopernika 11, 51-622, Wrocław (Poland)
2015-01-14
Recent astronomical observations have indicated that the Universe is in a phase of accelerated expansion. While there are many cosmological models which try to explain this phenomenon, we focus on the interacting ΛCDM model where an interaction between the dark energy and dark matter sectors takes place. This model is compared to its simpler alternative—the ΛCDM model. To choose between these models the likelihood ratio test was applied as well as the model comparison methods (employing Occam’s principle): the Akaike information criterion (AIC), the Bayesian information criterion (BIC) and the Bayesian evidence. Using the current astronomical data: type Ia supernova (Union2.1), h(z), baryon acoustic oscillation, the Alcock–Paczynski test, and the cosmic microwave background data, we evaluated both models. The analyses based on the AIC indicated that there is less support for the interacting ΛCDM model when compared to the ΛCDM model, while those based on the BIC indicated that there is strong evidence against it in favor of the ΛCDM model. Given the weak or almost non-existing support for the interacting ΛCDM model and bearing in mind Occam’s razor we are inclined to reject this model.
AIC, BIC, Bayesian evidence against the interacting dark energy model
International Nuclear Information System (INIS)
Recent astronomical observations have indicated that the Universe is in a phase of accelerated expansion. While there are many cosmological models which try to explain this phenomenon, we focus on the interacting ΛCDM model where an interaction between the dark energy and dark matter sectors takes place. This model is compared to its simpler alternative—the ΛCDM model. To choose between these models the likelihood ratio test was applied as well as the model comparison methods (employing Occam’s principle): the Akaike information criterion (AIC), the Bayesian information criterion (BIC) and the Bayesian evidence. Using the current astronomical data: type Ia supernova (Union2.1), h(z), baryon acoustic oscillation, the Alcock–Paczynski test, and the cosmic microwave background data, we evaluated both models. The analyses based on the AIC indicated that there is less support for the interacting ΛCDM model when compared to the ΛCDM model, while those based on the BIC indicated that there is strong evidence against it in favor of the ΛCDM model. Given the weak or almost non-existing support for the interacting ΛCDM model and bearing in mind Occam’s razor we are inclined to reject this model
A Bayesian approach to the semi-analytic model of galaxy formation: methodology
Lu, Yu; Weinberg, Martin D; Katz, Neal S
2010-01-01
We believe that a wide range of physical processes conspire to shape the observed galaxy population but we remain unsure of their detailed interactions. The semi-analytic model (SAM) of galaxy formation uses multi-dimensional parameterizations of the physical processes of galaxy formation and provides a tool to constrain these underlying physical interactions. Because of the high dimensionality, the parametric problem of galaxy formation may be profitably tackled with a Bayesian-inference based approach, which allows one to constrain theory with data in a statistically rigorous way. In this paper, we develop a generalized SAM using the framework of Bayesian inference. We show that, with a parallel implementation of an advanced Markov-Chain Monte-Carlo algorithm, it is now possible to rigorously sample the posterior distribution of the high-dimensional parameter space of typical SAMs. As an example, we characterize galaxy formation in the current $\\Lambda$CDM cosmology using stellar mass function of galaxies a...
Constraints on cosmic-ray propagation models from a global Bayesian analysis
Trotta, R; Moskalenko, I V; Porter, T A; de Austri, R Ruiz; Strong, A W
2010-01-01
Research in many areas of modern physics such as, e.g., indirect searches for dark matter and particle acceleration in SNR shocks, rely heavily on studies of cosmic rays (CRs) and associated diffuse emissions (radio, microwave, X-rays, gamma rays). While very detailed numerical models of CR propagation exist, a quantitative statistical analysis of such models has been so far hampered by the large computational effort that those models require. Although statistical analyses have been carried out before using semi-analytical models (where the computation is much faster), the evaluation of the results obtained from such models is difficult, as they necessarily suffer from many simplifying assumptions, The main objective of this paper is to present a working method for a full Bayesian parameter estimation for a numerical CR propagation model. For this study, we use the GALPROP code, the most advanced of its kind, that uses astrophysical information, nuclear and particle data as input to self-consistently predict ...
Sensometrics: Thurstonian and Statistical Models
DEFF Research Database (Denmark)
Christensen, Rune Haubo Bojesen
area of computational statistics, it is described how the Laplace approximation can be implemented on a case-by-case basis for flexible estimation of nonlinear mixed eects models with normally distributed response. The two R packages sensR and ordinal implement and support the methodological...... statistical package applicable to statistical problems far beyond sensometrics. A series of tutorials, user guides and reference manuals accompany these R packages. Finally, a number of chapters provide background theory on the development and computation of Thurstonian models for a range of binomial......This thesis is concerned with the development and bridging of Thurstonian and statistical models for sensory discrimination testing as applied in the scientific discipline of sensometrics. In sensory discrimination testing sensory differences between products are detected and quantified by the use...
Kwak, Sehyun; Svensson, J; Brix, M; Ghim, Y-C
2016-02-01
A Bayesian model of the emission spectrum of the JET lithium beam has been developed to infer the intensity of the Li I (2p-2s) line radiation and associated uncertainties. The detected spectrum for each channel of the lithium beam emission spectroscopy system is here modelled by a single Li line modified by an instrumental function, Bremsstrahlung background, instrumental offset, and interference filter curve. Both the instrumental function and the interference filter curve are modelled with non-parametric Gaussian processes. All free parameters of the model, the intensities of the Li line, Bremsstrahlung background, and instrumental offset, are inferred using Bayesian probability theory with a Gaussian likelihood for photon statistics and electronic background noise. The prior distributions of the free parameters are chosen as Gaussians. Given these assumptions, the intensity of the Li line and corresponding uncertainties are analytically available using a Bayesian linear inversion technique. The proposed approach makes it possible to extract the intensity of Li line without doing a separate background subtraction through modulation of the Li beam. PMID:26931843
Dissecting Magnetar Variability with Bayesian Hierarchical Models
Huppenkothen, Daniela; Brewer, Brendon J.; Hogg, David W.; Murray, Iain; Frean, Marcus; Elenbaas, Chris; Watts, Anna L.; Levin, Yuri; van der Horst, Alexander J.; Kouveliotou, Chryssa
2015-09-01
Neutron stars are a prime laboratory for testing physical processes under conditions of strong gravity, high density, and extreme magnetic fields. Among the zoo of neutron star phenomena, magnetars stand out for their bursting behavior, ranging from extremely bright, rare giant flares to numerous, less energetic recurrent bursts. The exact trigger and emission mechanisms for these bursts are not known; favored models involve either a crust fracture and subsequent energy release into the magnetosphere, or explosive reconnection of magnetic field lines. In the absence of a predictive model, understanding the physical processes responsible for magnetar burst variability is difficult. Here, we develop an empirical model that decomposes magnetar bursts into a superposition of small spike-like features with a simple functional form, where the number of model components is itself part of the inference problem. The cascades of spikes that we model might be formed by avalanches of reconnection, or crust rupture aftershocks. Using Markov Chain Monte Carlo sampling augmented with reversible jumps between models with different numbers of parameters, we characterize the posterior distributions of the model parameters and the number of components per burst. We relate these model parameters to physical quantities in the system, and show for the first time that the variability within a burst does not conform to predictions from ideas of self-organized criticality. We also examine how well the properties of the spikes fit the predictions of simplified cascade models for the different trigger mechanisms.
Dissecting magnetar variability with Bayesian hierarchical models
Huppenkothen, D; Hogg, D W; Murray, I; Frean, M; Elenbaas, C; Watts, A L; Levin, Y; van der Horst, A J; Kouveliotou, C
2015-01-01
Neutron stars are a prime laboratory for testing physical processes under conditions of strong gravity, high density, and extreme magnetic fields. Among the zoo of neutron star phenomena, magnetars stand out for their bursting behaviour, ranging from extremely bright, rare giant flares to numerous, less energetic recurrent bursts. The exact trigger and emission mechanisms for these bursts are not known; favoured models involve either a crust fracture and subsequent energy release into the magnetosphere, or explosive reconnection of magnetic field lines. In the absence of a predictive model, understanding the physical processes responsible for magnetar burst variability is difficult. Here, we develop an empirical model that decomposes magnetar bursts into a superposition of small spike-like features with a simple functional form, where the number of model components is itself part of the inference problem. The cascades of spikes that we model might be formed by avalanches of reconnection, or crust rupture afte...
Gordóvil-Merino, Amalia; Guàrdia-Olmos, Joan; Peró-Cebollero, Maribel; de la Fuente-Solanas, Emilia I
2010-04-01
The limitations inherent to classical estimation of the logistic regression models are known. The Bayesian approach in statistical analysis is an alternative to be considered, given that it makes it possible to introduce prior information about the phenomenon under study. The aim of the present work is to analyze binary and multinomial logistic regression simple models estimated by means of a Bayesian approach in comparison to classical estimation. To that effect, Child Attention Deficit Hyperactivity Disorder (ADHD) clinical data were analyzed. The sample included 286 participants of 6-12 years (78% boys, 22% girls) with ADHD positive diagnosis in 86.7% of the cases. The results show a reduction of standard errors associated to the coefficients obtained from the Bayesian analysis, thus bringing a greater stability to the coefficients. Complex models where parameter estimation may be easily compromised could benefit from this advantage. PMID:20524554
A Bayesian Network View on Nested Effects Models
Directory of Open Access Journals (Sweden)
Fröhlich Holger
2009-01-01
Full Text Available Nested effects models (NEMs are a class of probabilistic models that were designed to reconstruct a hidden signalling structure from a large set of observable effects caused by active interventions into the signalling pathway. We give a more flexible formulation of NEMs in the language of Bayesian networks. Our framework constitutes a natural generalization of the original NEM model, since it explicitly states the assumptions that are tacitly underlying the original version. Our approach gives rise to new learning methods for NEMs, which have been implemented in the /Bioconductor package nem. We validate these methods in a simulation study and apply them to a synthetic lethality dataset in yeast.
Probe Error Modeling Research Based on Bayesian Network
Institute of Scientific and Technical Information of China (English)
Wu Huaiqiang; Xing Zilong; Zhang Jian; Yan Yan
2015-01-01
Probe calibration is carried out under specific conditions; most of the error caused by the change of speed parameter has not been corrected. In order to reduce the measuring error influence on measurement accuracy, this article analyzes the relationship between speed parameter and probe error, and use Bayesian network to establish the model of probe error. Model takes account of prior knowledge and sample data, with the updating of data, which can reflect the change of the errors of the probe and constantly revised modeling results.
A Bayesian Model for Discovering Typological Implications
Daumé, Hal
2009-01-01
A standard form of analysis for linguistic typology is the universal implication. These implications state facts about the range of extant languages, such as ``if objects come after verbs, then adjectives come after nouns.'' Such implications are typically discovered by painstaking hand analysis over a small sample of languages. We propose a computational model for assisting at this process. Our model is able to discover both well-known implications as well as some novel implications that deserve further study. Moreover, through a careful application of hierarchical analysis, we are able to cope with the well-known sampling problem: languages are not independent.
Statistical Model of Extreme Shear
DEFF Research Database (Denmark)
Hansen, Kurt Schaldemose; Larsen, Gunner Chr.
2005-01-01
In order to continue cost-optimisation of modern large wind turbines, it is important to continuously increase the knowledge of wind field parameters relevant to design loads. This paper presents a general statistical model that offers site-specific prediction of the probability density function...... model that, on a statistically consistent basis, describes the most likely spatial shape of an extreme wind shear event. Predictions from the model have been compared with results from an extreme value data analysis, based on a large number of full-scale measurements recorded with a high sampling rate...
DPpackage: Bayesian Semi- and Nonparametric Modeling in R
Directory of Open Access Journals (Sweden)
Alejandro Jara
2011-04-01
Full Text Available Data analysis sometimes requires the relaxation of parametric assumptions in order to gain modeling flexibility and robustness against mis-specification of the probability model. In the Bayesian context, this is accomplished by placing a prior distribution on a function space, such as the space of all probability distributions or the space of all regression functions. Unfortunately, posterior distributions ranging over function spaces are highly complex and hence sampling methods play a key role. This paper provides an introduction to a simple, yet comprehensive, set of programs for the implementation of some Bayesian nonparametric and semiparametric models in R, DPpackage. Currently, DPpackage includes models for marginal and conditional density estimation, receiver operating characteristic curve analysis, interval-censored data, binary regression data, item response data, longitudinal and clustered data using generalized linear mixed models, and regression data using generalized additive models. The package also contains functions to compute pseudo-Bayes factors for model comparison and for eliciting the precision parameter of the Dirichlet process prior, and a general purpose Metropolis sampling algorithm. To maximize computational efficiency, the actual sampling for each model is carried out using compiled C, C++ or Fortran code.
KNET: Integrating Hypermedia and Bayesian Modeling
Chavez, R. Martin; Cooper, Gregory F.
2013-01-01
KNET is a general-purpose shell for constructing expert systems based on belief networks and decision networks. Such networks serve as graphical representations for decision models, in which the knowledge engineer must define clearly the alternatives, states, preferences, and relationships that constitute a decision basis. KNET contains a knowledge-engineering core written in Object Pascal and an interface that tightly integrates HyperCard, a hypertext authoring tool for the Apple Macintosh c...
International Nuclear Information System (INIS)
Classical methods of assessing the uncertainty associated with radiation doses estimated using cytogenetic techniques are now extremely well defined. However, several authors have suggested that a Bayesian approach to uncertainty estimation may be more suitable for cytogenetic data, which are inherently stochastic in nature. The Bayesian analysis framework focuses on identification of probability distributions (for yield of aberrations or estimated dose), which also means that uncertainty is an intrinsic part of the analysis, rather than an 'afterthought'. In this paper Bayesian, as well as some more advanced classical, data analysis methods for radiation cytogenetics are reviewed that have been proposed in the literature. A practical overview of Bayesian cytogenetic dose estimation is also presented, with worked examples from the literature. (authors)
Bayesian analysis of physiologically based toxicokinetic and toxicodynamic models.
Hack, C Eric
2006-04-17
Physiologically based toxicokinetic (PBTK) and toxicodynamic (TD) models of bromate in animals and humans would improve our ability to accurately estimate the toxic doses in humans based on available animal studies. These mathematical models are often highly parameterized and must be calibrated in order for the model predictions of internal dose to adequately fit the experimentally measured doses. Highly parameterized models are difficult to calibrate and it is difficult to obtain accurate estimates of uncertainty or variability in model parameters with commonly used frequentist calibration methods, such as maximum likelihood estimation (MLE) or least squared error approaches. The Bayesian approach called Markov chain Monte Carlo (MCMC) analysis can be used to successfully calibrate these complex models. Prior knowledge about the biological system and associated model parameters is easily incorporated in this approach in the form of prior parameter distributions, and the distributions are refined or updated using experimental data to generate posterior distributions of parameter estimates. The goal of this paper is to give the non-mathematician a brief description of the Bayesian approach and Markov chain Monte Carlo analysis, how this technique is used in risk assessment, and the issues associated with this approach. PMID:16466842
Macroeconomic Forecasts in Models with Bayesian Averaging of Classical Estimates
Directory of Open Access Journals (Sweden)
Piotr Białowolski
2012-03-01
Full Text Available The aim of this paper is to construct a forecasting model oriented on predicting basic macroeconomic variables, namely: the GDP growth rate, the unemployment rate, and the consumer price inflation. In order to select the set of the best regressors, Bayesian Averaging of Classical Estimators (BACE is employed. The models are atheoretical (i.e. they do not reflect causal relationships postulated by the macroeconomic theory and the role of regressors is played by business and consumer tendency survey-based indicators. Additionally, survey-based indicators are included with a lag that enables to forecast the variables of interest (GDP, unemployment, and inflation for the four forthcoming quarters without the need to make any additional assumptions concerning the values of predictor variables in the forecast period. Bayesian Averaging of Classical Estimators is a method allowing for full and controlled overview of all econometric models which can be obtained out of a particular set of regressors. In this paper authors describe the method of generating a family of econometric models and the procedure for selection of a final forecasting model. Verification of the procedure is performed by means of out-of-sample forecasts of main economic variables for the quarters of 2011. The accuracy of the forecasts implies that there is still a need to search for new solutions in the atheoretical modelling.
Bayesian joint modeling of longitudinal and spatial survival AIDS data.
Martins, Rui; Silva, Giovani L; Andreozzi, Valeska
2016-08-30
Joint analysis of longitudinal and survival data has received increasing attention in the recent years, especially for analyzing cancer and AIDS data. As both repeated measurements (longitudinal) and time-to-event (survival) outcomes are observed in an individual, a joint modeling is more appropriate because it takes into account the dependence between the two types of responses, which are often analyzed separately. We propose a Bayesian hierarchical model for jointly modeling longitudinal and survival data considering functional time and spatial frailty effects, respectively. That is, the proposed model deals with non-linear longitudinal effects and spatial survival effects accounting for the unobserved heterogeneity among individuals living in the same region. This joint approach is applied to a cohort study of patients with HIV/AIDS in Brazil during the years 2002-2006. Our Bayesian joint model presents considerable improvements in the estimation of survival times of the Brazilian HIV/AIDS patients when compared with those obtained through a separate survival model and shows that the spatial risk of death is the same across the different Brazilian states. Copyright © 2016 John Wiley & Sons, Ltd. PMID:26990773
Modeling operational risks of the nuclear industry with Bayesian networks
International Nuclear Information System (INIS)
Basically, planning a new industrial plant requires information on the industrial management, regulations, site selection, definition of initial and planned capacity, and on the estimation of the potential demand. However, this is far from enough to assure the success of an industrial enterprise. Unexpected and extremely damaging events may occur that deviates from the original plan. The so-called operational risks are not only in the system, equipment, process or human (technical or managerial) failures. They are also in intentional events such as frauds and sabotage, or extreme events like terrorist attacks or radiological accidents and even on public reaction to perceived environmental or future generation impacts. For the nuclear industry, it is a challenge to identify and to assess the operational risks and their various sources. Early identification of operational risks can help in preparing contingency plans, to delay the decision to invest or to approve a project that can, at an extreme, affect the public perception of the nuclear energy. A major problem in modeling operational risk losses is the lack of internal data that are essential, for example, to apply the loss distribution approach. As an alternative, methods that consider qualitative and subjective information can be applied, for example, fuzzy logic, neural networks, system dynamic or Bayesian networks. An advantage of applying Bayesian networks to model operational risk is the possibility to include expert opinions and variables of interest, to structure the model via causal dependencies among these variables, and to specify subjective prior and conditional probabilities distributions at each step or network node. This paper suggests a classification of operational risks in industry and discusses the benefits and obstacles of the Bayesian networks approach to model those risks. (author)
BAYESIAN LOCAL INFLUENCE ASSESSMENTS IN A GROWTH CURVE MODEL WITH GENERAL COVARIANCE STRUCTURE
Institute of Scientific and Technical Information of China (English)
2000-01-01
The objective of this paper is to present a Bayesian approach based on Kullback Leibler divergence for assessing local influence in a growth curve model with general covariance structure.Under certain prior distribution assumption,the Kullback-Leibler divergence is used to measure the influence of some minor perturbation on the posterior distribution of unknown parameter.This leads to the diagnostic statistic for detecting which response is locally influential.As an application,the common covariance-weighted perturbation scheme is thoroughly considered.
Beramendi-Orosco, Laura E.; Gonzalez-Hernandez, Galia; Urrutia-Fucugauchi, Jaime; Manzanilla, Linda R.; Soler-Arechalde, Ana M.; Goguitchaishvili, Avto; Jarboe, Nick
2009-03-01
A high-resolution 14C chronology for the Teopancazco archaeological site in the Teotihuacan urban center of Mesoamerica was generated by Bayesian analysis of 33 radiocarbon dates and detailed archaeological information related to occupation stratigraphy, pottery and archaeomagnetic dates. The calibrated intervals obtained using the Bayesian model are up to ca. 70% shorter than those obtained with individual calibrations. For some samples, this is a consequence of plateaus in the part of the calibration curve covered by the sample dates (2500 to 1450 14C yr BP). Effects of outliers are explored by comparing the results from a Bayesian model that incorporates radiocarbon data for two outlier samples with the same model excluding them. The effect of outliers was more significant than expected. Inclusion of radiocarbon dates from two altered contexts, 500 14C yr earlier than those for the first occupational phase, results in ages calculated by the model earlier than the archaeological records. The Bayesian chronology excluding these outliers separates the first two Teopancazco occupational phases and suggests that ending of the Xolalpan phase was around cal AD 550, 100 yr earlier than previously estimated and in accordance with previously reported archaeomagnetic dates from lime plasters for the same site.
Two-stage Bayesian models-application to ZEDB project
Energy Technology Data Exchange (ETDEWEB)
Bunea, C. [George Washington University, School of Applied Science, 1776 G Street, NW, Suite 108, Washington, DC 20052 (United States)]. E-mail: cornel@gwu.edu; Charitos, T. [Institute of Information and Computing Sciences, Padualaan 14, de Uithof, 3508 TB, Utrecht (Netherlands)]. E-mail: theodore@cs.uu.nl; Cooke, R.M. [Delft University of Technology, EWI Faculty, Mekelweg 4, 2628 CD, Delft (Netherlands)]. E-mail: r.m.cooke@ewi.tudelft.n1; Becker, G. [RISA, Krumme Str., Berlin 10627 (Germany)]. E-mail: guenter.becker@risa.de
2005-12-01
A well-known mathematical tool to analyze plant specific reliability data for nuclear power facilities is the two-stage Bayesian model. Such two-stage Bayesian models are standard practice nowadays, for example in the German ZEDB project or in the Swedish T-Book, although they may differ in their mathematical models and software implementation. In this paper, we review the mathematical model, its underlying assumptions and supporting arguments. Reasonable conditional assumptions are made to yield tractable and mathematically valid form for the failure rate at plant of interest, given failures and operational times at other plants in the population. The posterior probability of failure rate at plant of interest is sensitive to the choice of hyperprior parameters since the effect of hyperprior distribution will never be dominated by the effect of observation. The methods of Poern and Jeffrey for choosing distributions over hyperparameters are discussed. Furthermore, we will perform verification tasks associated with the theoretical model presented in this paper. The present software implementation produces good agreement with ZEDB results for various prior distributions. The difference between our results and those of ZEDB reflect differences that may arise from numerical implementation, as that would use different step size and truncation bounds.
Two-stage Bayesian models-application to ZEDB project
International Nuclear Information System (INIS)
A well-known mathematical tool to analyze plant specific reliability data for nuclear power facilities is the two-stage Bayesian model. Such two-stage Bayesian models are standard practice nowadays, for example in the German ZEDB project or in the Swedish T-Book, although they may differ in their mathematical models and software implementation. In this paper, we review the mathematical model, its underlying assumptions and supporting arguments. Reasonable conditional assumptions are made to yield tractable and mathematically valid form for the failure rate at plant of interest, given failures and operational times at other plants in the population. The posterior probability of failure rate at plant of interest is sensitive to the choice of hyperprior parameters since the effect of hyperprior distribution will never be dominated by the effect of observation. The methods of Poern and Jeffrey for choosing distributions over hyperparameters are discussed. Furthermore, we will perform verification tasks associated with the theoretical model presented in this paper. The present software implementation produces good agreement with ZEDB results for various prior distributions. The difference between our results and those of ZEDB reflect differences that may arise from numerical implementation, as that would use different step size and truncation bounds
Development of a cyber security risk model using Bayesian networks
International Nuclear Information System (INIS)
Cyber security is an emerging safety issue in the nuclear industry, especially in the instrumentation and control (I and C) field. To address the cyber security issue systematically, a model that can be used for cyber security evaluation is required. In this work, a cyber security risk model based on a Bayesian network is suggested for evaluating cyber security for nuclear facilities in an integrated manner. The suggested model enables the evaluation of both the procedural and technical aspects of cyber security, which are related to compliance with regulatory guides and system architectures, respectively. The activity-quality analysis model was developed to evaluate how well people and/or organizations comply with the regulatory guidance associated with cyber security. The architecture analysis model was created to evaluate vulnerabilities and mitigation measures with respect to their effect on cyber security. The two models are integrated into a single model, which is called the cyber security risk model, so that cyber security can be evaluated from procedural and technical viewpoints at the same time. The model was applied to evaluate the cyber security risk of the reactor protection system (RPS) of a research reactor and to demonstrate its usefulness and feasibility. - Highlights: • We developed the cyber security risk model can be find the weak point of cyber security integrated two cyber analysis models by using Bayesian Network. • One is the activity-quality model signifies how people and/or organization comply with the cyber security regulatory guide. • Other is the architecture model represents the probability of cyber-attack on RPS architecture. • The cyber security risk model can provide evidence that is able to determine the key element for cyber security for RPS of a research reactor
FRUITS for Fish: intake estimates of aquatic foods using a novel Bayesian model
Czech Academy of Sciences Publication Activity Database
Fernandes, R.; Brabec, Marek; Millard, A.; Nadeau, J.M.; Grootes, P.M.
University of Ghent, 2013. s. 110-111. [International Symposium 14C & Archaeology /14./. 08.04.2013-12.04.2013, Ghent] Institutional support: RVO:67985807 Keywords : Bayesian estimation * food consuption * archeology Subject RIV: BB - Applied Statistics, Operational Research
Radiative Transfer meets Bayesian statistics: where does your Galaxy's [CII] come from?
Accurso, Gioacchino; Bisbas, Thomas G; Viti, Serena
2016-01-01
The [CII] 158$\\mu$m emission line can arise in all phases of the ISM, therefore being able to disentangle the different contributions is an important yet unresolved problem when undertaking galaxy-wide, integrated [CII] observations. We present a new multi-phase 3D radiative transfer interface that couples Starburst99, a stellar spectrophotometric code, with the photoionisation and astrochemistry codes Mocassin and 3D-PDR. We model entire star forming regions, including the ionised, atomic and molecular phases of the ISM, and apply a Bayesian inference methodology to parametrise how the fraction of the [CII] emission originating from molecular regions, $f_{[CII],mol}$, varies as a function of typical integrated properties of galaxies in the local Universe. The main parameters responsible for the variations of $f_{[CII],mol}$ are specific star formation rate (sSFR), gas phase metallicity, HII region electron number density ($n_e$), and dust mass fraction. For example, $f_{[CII],mol}$ can increase from 60% to 8...
BAYESIAN ESTIMATION IN SHARED COMPOUND POISSON FRAILTY MODELS
Directory of Open Access Journals (Sweden)
David D. Hanagal
2015-06-01
Full Text Available In this paper, we study the compound Poisson distribution as the shared frailty distribution and two different baseline distributions namely Pareto and linear failure rate distributions for modeling survival data. We are using the Markov Chain Monte Carlo (MCMC technique to estimate parameters of the proposed models by introducing the Bayesian estimation procedure. In the present study, a simulation is done to compare the true values of parameters with the estimated values. We try to fit the proposed models to a real life bivariate survival data set of McGrilchrist and Aisbett (1991 related to kidney infection. Also, we present a comparison study for the same data by using model selection criterion, and suggest a better frailty model out of two proposed frailty models.
Experimental validation of a Bayesian model of visual acuity.
LENUS (Irish Health Repository)
Dalimier, Eugénie
2009-01-01
Based on standard procedures used in optometry clinics, we compare measurements of visual acuity for 10 subjects (11 eyes tested) in the presence of natural ocular aberrations and different degrees of induced defocus, with the predictions given by a Bayesian model customized with aberrometric data of the eye. The absolute predictions of the model, without any adjustment, show good agreement with the experimental data, in terms of correlation and absolute error. The efficiency of the model is discussed in comparison with image quality metrics and other customized visual process models. An analysis of the importance and customization of each stage of the model is also given; it stresses the potential high predictive power from precise modeling of ocular and neural transfer functions.
Assessing global vegetation activity using spatio-temporal Bayesian modelling
Mulder, Vera L.; van Eck, Christel M.; Friedlingstein, Pierre; Regnier, Pierre A. G.
2016-04-01
This work demonstrates the potential of modelling vegetation activity using a hierarchical Bayesian spatio-temporal model. This approach allows modelling changes in vegetation and climate simultaneous in space and time. Changes of vegetation activity such as phenology are modelled as a dynamic process depending on climate variability in both space and time. Additionally, differences in observed vegetation status can be contributed to other abiotic ecosystem properties, e.g. soil and terrain properties. Although these properties do not change in time, they do change in space and may provide valuable information in addition to the climate dynamics. The spatio-temporal Bayesian models were calibrated at a regional scale because the local trends in space and time can be better captured by the model. The regional subsets were defined according to the SREX segmentation, as defined by the IPCC. Each region is considered being relatively homogeneous in terms of large-scale climate and biomes, still capturing small-scale (grid-cell level) variability. Modelling within these regions is hence expected to be less uncertain due to the absence of these large-scale patterns, compared to a global approach. This overall modelling approach allows the comparison of model behavior for the different regions and may provide insights on the main dynamic processes driving the interaction between vegetation and climate within different regions. The data employed in this study encompasses the global datasets for soil properties (SoilGrids), terrain properties (Global Relief Model based on SRTM DEM and ETOPO), monthly time series of satellite-derived vegetation indices (GIMMS NDVI3g) and climate variables (Princeton Meteorological Forcing Dataset). The findings proved the potential of a spatio-temporal Bayesian modelling approach for assessing vegetation dynamics, at a regional scale. The observed interrelationships of the employed data and the different spatial and temporal trends support
Textual information access statistical models
Gaussier, Eric
2013-01-01
This book presents statistical models that have recently been developed within several research communities to access information contained in text collections. The problems considered are linked to applications aiming at facilitating information access:- information extraction and retrieval;- text classification and clustering;- opinion mining;- comprehension aids (automatic summarization, machine translation, visualization).In order to give the reader as complete a description as possible, the focus is placed on the probability models used in the applications
Directory of Open Access Journals (Sweden)
David Lunn
Full Text Available The advantages of Bayesian statistical approaches, such as flexibility and the ability to acknowledge uncertainty in all parameters, have made them the prevailing method for analysing the spread of infectious diseases in human or animal populations. We introduce a Bayesian approach to experimental host-pathogen systems that shares these attractive features. Since uncertainty in all parameters is acknowledged, existing information can be accounted for through prior distributions, rather than through fixing some parameter values. The non-linear dynamics, multi-factorial design, multiple measurements of responses over time and sampling error that are typical features of experimental host-pathogen systems can also be naturally incorporated. We analyse the dynamics of the free-living protozoan Paramecium caudatum and its specialist bacterial parasite Holospora undulata. Our analysis provides strong evidence for a saturable infection function, and we were able to reproduce the two waves of infection apparent in the data by separating the initial inoculum from the parasites released after the first cycle of infection. In addition, the parameter estimates from the hierarchical model can be combined to infer variations in the parasite's basic reproductive ratio across experimental groups, enabling us to make predictions about the effect of resources and host genotype on the ability of the parasite to spread. Even though the high level of variability between replicates limited the resolution of the results, this Bayesian framework has strong potential to be used more widely in experimental ecology.
One-Stage and Bayesian Two-Stage Optimal Designs for Mixture Models
Lin, Hefang
1999-01-01
In this research, Bayesian two-stage D-D optimal designs for mixture experiments with or without process variables under model uncertainty are developed. A Bayesian optimality criterion is used in the first stage to minimize the determinant of the posterior variances of the parameters. The second stage design is then generated according to an optimality procedure that collaborates with the improved model from first stage data. Our results show that the Bayesian two-stage D-D optimal design...
Uncovering Transcriptional Regulatory Networks by Sparse Bayesian Factor Model
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Qi Yuan(Alan
2010-01-01
Full Text Available Abstract The problem of uncovering transcriptional regulation by transcription factors (TFs based on microarray data is considered. A novel Bayesian sparse correlated rectified factor model (BSCRFM is proposed that models the unknown TF protein level activity, the correlated regulations between TFs, and the sparse nature of TF-regulated genes. The model admits prior knowledge from existing database regarding TF-regulated target genes based on a sparse prior and through a developed Gibbs sampling algorithm, a context-specific transcriptional regulatory network specific to the experimental condition of the microarray data can be obtained. The proposed model and the Gibbs sampling algorithm were evaluated on the simulated systems, and results demonstrated the validity and effectiveness of the proposed approach. The proposed model was then applied to the breast cancer microarray data of patients with Estrogen Receptor positive ( status and Estrogen Receptor negative ( status, respectively.
Efficient multilevel brain tumor segmentation with integrated bayesian model classification.
Corso, J J; Sharon, E; Dube, S; El-Saden, S; Sinha, U; Yuille, A
2008-05-01
We present a new method for automatic segmentation of heterogeneous image data that takes a step toward bridging the gap between bottom-up affinity-based segmentation methods and top-down generative model based approaches. The main contribution of the paper is a Bayesian formulation for incorporating soft model assignments into the calculation of affinities, which are conventionally model free. We integrate the resulting model-aware affinities into the multilevel segmentation by weighted aggregation algorithm, and apply the technique to the task of detecting and segmenting brain tumor and edema in multichannel magnetic resonance (MR) volumes. The computationally efficient method runs orders of magnitude faster than current state-of-the-art techniques giving comparable or improved results. Our quantitative results indicate the benefit of incorporating model-aware affinities into the segmentation process for the difficult case of glioblastoma multiforme brain tumor. PMID:18450536
Zhu, Yuda
2012-01-01
We propose and discuss two distinct and separate innovative Bayesian models. In the first model, we propose a replacement for standard statistical methodologies for longitudinal sexual behavior data. HIV intervention trials generally collect sexual behavior data repeatedly over time and involve multiple outcomes including the number of partners which are nested in subjects and the number of protected and unprotected sex acts with each partner which are inherently nested within partners. Th...
New Statistical Models for Copolymerization
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Martin S. Engler
2016-06-01
Full Text Available For many years, copolymerization has been studied using mathematical and statistical models. Here, we present new Markov chain models for copolymerization kinetics: the Bernoulli and Geometric models. They model copolymer synthesis as a random process and are based on a basic reaction scheme. In contrast to previous Markov chain approaches to copolymerization, both models take variable chain lengths and time-dependent monomer probabilities into account and allow for computing sequence likelihoods and copolymer fingerprints. Fingerprints can be computed from copolymer mass spectra, potentially allowing us to estimate the model parameters from measured fingerprints. We compare both models against Monte Carlo simulations. We find that computing the models is fast and memory efficient.
Emulation: A fast stochastic Bayesian method to eliminate model space
Roberts, Alan; Hobbs, Richard; Goldstein, Michael
2010-05-01
Joint inversion of large 3D datasets has been the goal of geophysicists ever since the datasets first started to be produced. There are two broad approaches to this kind of problem, traditional deterministic inversion schemes and more recently developed Bayesian search methods, such as MCMC (Markov Chain Monte Carlo). However, using both these kinds of schemes has proved prohibitively expensive, both in computing power and time cost, due to the normally very large model space which needs to be searched using forward model simulators which take considerable time to run. At the heart of strategies aimed at accomplishing this kind of inversion is the question of how to reliably and practicably reduce the size of the model space in which the inversion is to be carried out. Here we present a practical Bayesian method, known as emulation, which can address this issue. Emulation is a Bayesian technique used with considerable success in a number of technical fields, such as in astronomy, where the evolution of the universe has been modelled using this technique, and in the petroleum industry where history matching is carried out of hydrocarbon reservoirs. The method of emulation involves building a fast-to-compute uncertainty-calibrated approximation to a forward model simulator. We do this by modelling the output data from a number of forward simulator runs by a computationally cheap function, and then fitting the coefficients defining this function to the model parameters. By calibrating the error of the emulator output with respect to the full simulator output, we can use this to screen out large areas of model space which contain only implausible models. For example, starting with what may be considered a geologically reasonable prior model space of 10000 models, using the emulator we can quickly show that only models which lie within 10% of that model space actually produce output data which is plausibly similar in character to an observed dataset. We can thus much
An overview of component qualification using Bayesian statistics and energy methods.
Energy Technology Data Exchange (ETDEWEB)
Dohner, Jeffrey Lynn
2011-09-01
The below overview is designed to give the reader a limited understanding of Bayesian and Maximum Likelihood (MLE) estimation; a basic understanding of some of the mathematical tools to evaluate the quality of an estimation; an introduction to energy methods and a limited discussion of damage potential. This discussion then goes on to presented a limited presentation as to how energy methods and Bayesian estimation are used together to qualify components. Example problems with solutions have been supplied as a learning aid. Bold letters are used to represent random variables. Un-bolded letter represent deterministic values. A concluding section presents a discussion of attributes and concerns.
Improved model for statistical alignment
Energy Technology Data Exchange (ETDEWEB)
Miklos, I.; Toroczkai, Z. (Zoltan)
2001-01-01
The statistical approach to molecular sequence evolution involves the stochastic modeling of the substitution, insertion and deletion processes. Substitution has been modeled in a reliable way for more than three decades by using finite Markov-processes. Insertion and deletion, however, seem to be more difficult to model, and thc recent approaches cannot acceptably deal with multiple insertions and deletions. A new method based on a generating function approach is introduced to describe the multiple insertion process. The presented algorithm computes the approximate joint probability of two sequences in 0(13) running time where 1 is the geometric mean of the sequence lengths.
Perceptual decision making: Drift-diffusion model is equivalent to a Bayesian model
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Sebastian Bitzer
2014-02-01
Full Text Available Behavioural data obtained with perceptual decision making experiments are typically analysed with the drift-diffusion model. This parsimonious model accumulates noisy pieces of evidence towards a decision bound to explain the accuracy and reaction times of subjects. Recently, Bayesian models have been proposed to explain how the brain extracts information from noisy input as typically presented in perceptual decision making tasks. It has long been known that the drift-diffusion model is tightly linked with such functional Bayesian models but the precise relationship of the two mechanisms was never made explicit. Using a Bayesian model, we derived the equations which relate parameter values between these models. In practice we show that this equivalence is useful when fitting multi-subject data. We further show that the Bayesian model suggests different decision variables which all predict equal responses and discuss how these may be discriminated based on neural correlates of accumulated evidence. In addition, we discuss extensions to the Bayesian model which would be difficult to derive for the drift-diffusion model. We suggest that these and other extensions may be highly useful for deriving new experiments which test novel hypotheses.
MATHEMATICAL RISK ANALYSIS: VIA NICHOLAS RISK MODEL AND BAYESIAN ANALYSIS
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Anass BAYAGA
2010-07-01
Full Text Available The objective of this second part of a two-phased study was to explorethe predictive power of quantitative risk analysis (QRA method andprocess within Higher Education Institution (HEI. The method and process investigated the use impact analysis via Nicholas risk model and Bayesian analysis, with a sample of hundred (100 risk analysts in a historically black South African University in the greater Eastern Cape Province.The first findings supported and confirmed previous literature (KingIII report, 2009: Nicholas and Steyn, 2008: Stoney, 2007: COSA, 2004 that there was a direct relationship between risk factor, its likelihood and impact, certiris paribus. The second finding in relation to either controlling the likelihood or the impact of occurrence of risk (Nicholas risk model was that to have a brighter risk reward, it was important to control the likelihood ofoccurrence of risks as compared with its impact so to have a direct effect on entire University. On the Bayesian analysis, thus third finding, the impact of risk should be predicted along three aspects. These aspects included the human impact (decisions made, the property impact (students and infrastructural based and the business impact. Lastly, the study revealed that although in most business cases, where as business cycles considerably vary dependingon the industry and or the institution, this study revealed that, most impacts in HEI (University was within the period of one academic.The recommendation was that application of quantitative risk analysisshould be related to current legislative framework that affects HEI.
Baran, Sándor; Möller, Annette
2015-01-01
Forecast ensembles are typically employed to account for prediction uncertainties in numerical weather prediction models. However, ensembles often exhibit biases and dispersion errors, thus they require statistical post-processing to improve their predictive performance. Two popular univariate post-processing models are the Bayesian model averaging (BMA) and the ensemble model output statistics (EMOS). In the last few years increased interest has emerged in developing multivariate post-proces...
Factors contributing to academic achievement: a Bayesian structure equation modelling study
Payandeh Najafabadi, Amir T.; Omidi Najafabadi, Maryam; Farid-Rohani, Mohammad Reza
2013-06-01
In Iran, high school graduates enter university after taking a very difficult entrance exam called the Konkoor. Therefore, only the top-performing students are admitted by universities to continue their bachelor's education in statistics. Surprisingly, statistically, most of such students fall into the following categories: (1) do not succeed in their education despite their excellent performance on the Konkoor and in high school; (2) graduate with a grade point average (GPA) that is considerably lower than their high school GPA; (3) continue their master's education in majors other than statistics and (4) try to find jobs unrelated to statistics. This article employs the well-known and powerful statistical technique, the Bayesian structural equation modelling (SEM), to study the academic success of recent graduates who have studied statistics at Shahid Beheshti University in Iran. This research: (i) considered academic success as a latent variable, which was measured by GPA and other academic success (see below) of students in the target population; (ii) employed the Bayesian SEM, which works properly for small sample sizes and ordinal variables; (iii), which is taken from the literature, developed five main factors that affected academic success and (iv) considered several standard psychological tests and measured characteristics such as 'self-esteem' and 'anxiety'. We then study the impact of such factors on the academic success of the target population. Six factors that positively impact student academic success were identified in the following order of relative impact (from greatest to least): 'Teaching-Evaluation', 'Learner', 'Environment', 'Family', 'Curriculum' and 'Teaching Knowledge'. Particularly, influential variables within each factor have also been noted.
Bayesian meta-analysis models for microarray data: a comparative study
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Song Joon J
2007-03-01
Full Text Available Abstract Background With the growing abundance of microarray data, statistical methods are increasingly needed to integrate results across studies. Two common approaches for meta-analysis of microarrays include either combining gene expression measures across studies or combining summaries such as p-values, probabilities or ranks. Here, we compare two Bayesian meta-analysis models that are analogous to these methods. Results Two Bayesian meta-analysis models for microarray data have recently been introduced. The first model combines standardized gene expression measures across studies into an overall mean, accounting for inter-study variability, while the second combines probabilities of differential expression without combining expression values. Both models produce the gene-specific posterior probability of differential expression, which is the basis for inference. Since the standardized expression integration model includes inter-study variability, it may improve accuracy of results versus the probability integration model. However, due to the small number of studies typical in microarray meta-analyses, the variability between studies is challenging to estimate. The probability integration model eliminates the need to model variability between studies, and thus its implementation is more straightforward. We found in simulations of two and five studies that combining probabilities outperformed combining standardized gene expression measures for three comparison values: the percent of true discovered genes in meta-analysis versus individual studies; the percent of true genes omitted in meta-analysis versus separate studies, and the number of true discovered genes for fixed levels of Bayesian false discovery. We identified similar results when pooling two independent studies of Bacillus subtilis. We assumed that each study was produced from the same microarray platform with only two conditions: a treatment and control, and that the data sets
HDDM: Hierarchical Bayesian estimation of the Drift-Diffusion Model in Python
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Thomas V Wiecki
2013-08-01
Full Text Available The diffusion model is a commonly used tool to infer latent psychological processes underlying decision making, and to link them to neural mechanisms based on reaction times. Although efficient open source software has been made available to quantitatively fit the model to data, current estimation methods require an abundance of reaction time measurements to recover meaningful parameters, and only provide point estimates of each parameter. In contrast, hierarchical Bayesian parameter estimation methods are useful for enhancing statistical power, allowing for simultaneous estimation of individual subject parameters and the group distribution that they are drawn from, while also providing measures of uncertainty in these parameters in the posterior distribution. Here, we present a novel Python-based toolbox called HDDM (hierarchical drift diffusion model, which allows fast and flexible estimation of the the drift-diffusion model and the related linear ballistic accumulator model. HDDM requires fewer data per subject / condition than non-hierarchical method, allows for full Bayesian data analysis, and can handle outliers in the data. Finally, HDDM supports the estimation of how trial-by-trial measurements (e.g. fMRI influence decision making parameters. This paper will first describe the theoretical background of drift-diffusion model and Bayesian inference. We then illustrate usage of the toolbox on a real-world data set from our lab. Finally, parameter recovery studies show that HDDM beats alternative fitting methods like the chi-quantile method as well as maximum likelihood estimation. The software and documentation can be downloaded at: http://ski.clps.brown.edu/hddm_docs
Bayesian reduced-order models for multiscale dynamical systems
Koutsourelakis, P S
2010-01-01
While existing mathematical descriptions can accurately account for phenomena at microscopic scales (e.g. molecular dynamics), these are often high-dimensional, stochastic and their applicability over macroscopic time scales of physical interest is computationally infeasible or impractical. In complex systems, with limited physical insight on the coherent behavior of their constituents, the only available information is data obtained from simulations of the trajectories of huge numbers of degrees of freedom over microscopic time scales. This paper discusses a Bayesian approach to deriving probabilistic coarse-grained models that simultaneously address the problems of identifying appropriate reduced coordinates and the effective dynamics in this lower-dimensional representation. At the core of the models proposed lie simple, low-dimensional dynamical systems which serve as the building blocks of the global model. These approximate the latent, generating sources and parameterize the reduced-order dynamics. We d...
Extended Bayesian Information Criteria for Gaussian Graphical Models
Foygel, Rina
2010-01-01
Gaussian graphical models with sparsity in the inverse covariance matrix are of significant interest in many modern applications. For the problem of recovering the graphical structure, information criteria provide useful optimization objectives for algorithms searching through sets of graphs or for selection of tuning parameters of other methods such as the graphical lasso, which is a likelihood penalization technique. In this paper we establish the consistency of an extended Bayesian information criterion for Gaussian graphical models in a scenario where both the number of variables p and the sample size n grow. Compared to earlier work on the regression case, our treatment allows for growth in the number of non-zero parameters in the true model, which is necessary in order to cover connected graphs. We demonstrate the performance of this criterion on simulated data when used in conjunction with the graphical lasso, and verify that the criterion indeed performs better than either cross-validation or the ordi...
A Bayesian approach to the modelling of alpha Cen A
Bazot, M; Christensen-Dalsgaard, J
2012-01-01
Determining the physical characteristics of a star is an inverse problem consisting in estimating the parameters of models for the stellar structure and evolution, knowing certain observable quantities. We use a Bayesian approach to solve this problem for alpha Cen A, which allows us to incorporate prior information on the parameters to be estimated, in order to better constrain the problem. Our strategy is based on the use of a Markov Chain Monte Carlo (MCMC) algorithm to estimate the posterior probability densities of the stellar parameters: mass, age, initial chemical composition,... We use the stellar evolutionary code ASTEC to model the star. To constrain this model both seismic and non-seismic observations were considered. Several different strategies were tested to fit these values, either using two or five free parameters in ASTEC. We are thus able to show evidence that MCMC methods become efficient with respect to more classical grid-based strategies when the number of parameters increases. The resul...
A simulated annealing-based method for learning Bayesian networks from statistical data
Czech Academy of Sciences Publication Activity Database
Janžura, Martin; Nielsen, Jan
2006-01-01
Roč. 21, č. 3 (2006), s. 335-348. ISSN 0884-8173 R&D Projects: GA ČR GA201/03/0478 Institutional research plan: CEZ:AV0Z10750506 Keywords : Bayesian network * simulated annealing * Markov Chain Monte Carlo Subject RIV: BA - General Mathematics Impact factor: 0.429, year: 2006
Festa, Roberto
1992-01-01
According to the Bayesian view, scientific hypotheses must be appraised in terms of their posterior probabilities relative to the available experimental data. Such posterior probabilities are derived from the prior probabilities of the hypotheses by applying Bayes'theorem. One of the most important
Automated comparison of Bayesian reconstructions of experimental profiles with physical models
International Nuclear Information System (INIS)
In this work we developed an expert system that carries out in an integrated and fully automated way i) a reconstruction of plasma profiles from the measurements, using Bayesian analysis ii) a prediction of the reconstructed quantities, according to some models and iii) an intelligent comparison of the first two steps. This system includes systematic checking of the internal consistency of the reconstructed quantities, enables automated model validation and, if a well-validated model is used, can be applied to help detecting interesting new physics in an experiment. The work shows three applications of this quite general system. The expert system can successfully detect failures in the automated plasma reconstruction and provide (on successful reconstruction cases) statistics of agreement of the models with the experimental data, i.e. information on the model validity. (author)
Bayesian Analysis for Exponential Random Graph Models Using the Adaptive Exchange Sampler.
Jin, Ick Hoon; Yuan, Ying; Liang, Faming
2013-10-01
Exponential random graph models have been widely used in social network analysis. However, these models are extremely difficult to handle from a statistical viewpoint, because of the intractable normalizing constant and model degeneracy. In this paper, we consider a fully Bayesian analysis for exponential random graph models using the adaptive exchange sampler, which solves the intractable normalizing constant and model degeneracy issues encountered in Markov chain Monte Carlo (MCMC) simulations. The adaptive exchange sampler can be viewed as a MCMC extension of the exchange algorithm, and it generates auxiliary networks via an importance sampling procedure from an auxiliary Markov chain running in parallel. The convergence of this algorithm is established under mild conditions. The adaptive exchange sampler is illustrated using a few social networks, including the Florentine business network, molecule synthetic network, and dolphins network. The results indicate that the adaptive exchange algorithm can produce more accurate estimates than approximate exchange algorithms, while maintaining the same computational efficiency. PMID:24653788
Using Bayesian model averaging to estimate terrestrial evapotranspiration in China
Chen, Yang; Yuan, Wenping; Xia, Jiangzhou; Fisher, Joshua B.; Dong, Wenjie; Zhang, Xiaotong; Liang, Shunlin; Ye, Aizhong; Cai, Wenwen; Feng, Jinming
2015-09-01
Evapotranspiration (ET) is critical to terrestrial ecosystems as it links the water, carbon, and surface energy exchanges. Numerous ET models were developed for the ET estimations, but there are large model uncertainties. In this study, a Bayesian Model Averaging (BMA) method was used to merge eight satellite-based models, including five empirical and three process-based models, for improving the accuracy of ET estimates. At twenty-three eddy covariance flux towers, we examined the model performance on all possible combinations of eight models and found that an ensemble with four models (BMA_Best) showed the best model performance. The BMA_Best method can outperform the best of eight models, and the Kling-Gupta efficiency (KGE) value increased by 4% compared with the model with the highest KGE, and decreased RMSE by 4%. Although the correlation coefficient of BMA_Best is less than the best single model, the bias of BMA_Best is the smallest compared with the eight models. Moreover, based on the water balance principle over the river basin scale, the validation indicated the BMA_Best estimates can explain 86% variations. In general, the results showed BMA estimates will be very useful for future studies to characterize the regional water availability over long-time series.
Semi-parametric Bayesian Partially Identified Models based on Support Function
Liao, Yuan; De Simoni, Anna
2012-01-01
We provide a comprehensive semi-parametric study of Bayesian partially identified econometric models. While the existing literature on Bayesian partial identification has mostly focused on the structural parameter, our primary focus is on Bayesian credible sets (BCS's) of the unknown identified set and the posterior distribution of its support function. We construct a (two-sided) BCS based on the support function of the identified set. We prove the Bernstein-von Mises theorem for the posterio...
Williford, W. O.; Hsieh, P.; Carter, M. C.
1974-01-01
A Bayesian analysis of the two discrete probability models, the negative binomial and the modified negative binomial distributions, which have been used to describe thunderstorm activity at Cape Kennedy, Florida, is presented. The Bayesian approach with beta prior distributions is compared to the classical approach which uses a moment method of estimation or a maximum-likelihood method. The accuracy and simplicity of the Bayesian method is demonstrated.
Road network safety evaluation using Bayesian hierarchical joint model.
Wang, Jie; Huang, Helai
2016-05-01
Safety and efficiency are commonly regarded as two significant performance indicators of transportation systems. In practice, road network planning has focused on road capacity and transport efficiency whereas the safety level of a road network has received little attention in the planning stage. This study develops a Bayesian hierarchical joint model for road network safety evaluation to help planners take traffic safety into account when planning a road network. The proposed model establishes relationships between road network risk and micro-level variables related to road entities and traffic volume, as well as socioeconomic, trip generation and network density variables at macro level which are generally used for long term transportation plans. In addition, network spatial correlation between intersections and their connected road segments is also considered in the model. A road network is elaborately selected in order to compare the proposed hierarchical joint model with a previous joint model and a negative binomial model. According to the results of the model comparison, the hierarchical joint model outperforms the joint model and negative binomial model in terms of the goodness-of-fit and predictive performance, which indicates the reasonableness of considering the hierarchical data structure in crash prediction and analysis. Moreover, both random effects at the TAZ level and the spatial correlation between intersections and their adjacent segments are found to be significant, supporting the employment of the hierarchical joint model as an alternative in road-network-level safety modeling as well. PMID:26945109
Modelling of population dynamics of red king crab using Bayesian approach
Directory of Open Access Journals (Sweden)
Bakanev Sergey ...
2012-10-01
Modeling population dynamics based on the Bayesian approach enables to successfully resolve the above issues. The integration of the data from various studies into a unified model based on Bayesian parameter estimation method provides a much more detailed description of the processes occurring in the population.
Dynamic Bayesian Network Modeling of Game Based Diagnostic Assessments. CRESST Report 837
Levy, Roy
2014-01-01
Digital games offer an appealing environment for assessing student proficiencies, including skills and misconceptions in a diagnostic setting. This paper proposes a dynamic Bayesian network modeling approach for observations of student performance from an educational video game. A Bayesian approach to model construction, calibration, and use in…
Bayesian spatial semi-parametric modeling of HIV variation in Kenya.
Directory of Open Access Journals (Sweden)
Oscar Ngesa
Full Text Available Spatial statistics has seen rapid application in many fields, especially epidemiology and public health. Many studies, nonetheless, make limited use of the geographical location information and also usually assume that the covariates, which are related to the response variable, have linear effects. We develop a Bayesian semi-parametric regression model for HIV prevalence data. Model estimation and inference is based on fully Bayesian approach via Markov Chain Monte Carlo (McMC. The model is applied to HIV prevalence data among men in Kenya, derived from the Kenya AIDS indicator survey, with n = 3,662. Past studies have concluded that HIV infection has a nonlinear association with age. In this study a smooth function based on penalized regression splines is used to estimate this nonlinear effect. Other covariates were assumed to have a linear effect. Spatial references to the counties were modeled as both structured and unstructured spatial effects. We observe that circumcision reduces the risk of HIV infection. The results also indicate that men in the urban areas were more likely to be infected by HIV as compared to their rural counterpart. Men with higher education had the lowest risk of HIV infection. A nonlinear relationship between HIV infection and age was established. Risk of HIV infection increases with age up to the age of 40 then declines with increase in age. Men who had STI in the last 12 months were more likely to be infected with HIV. Also men who had ever used a condom were found to have higher likelihood to be infected by HIV. A significant spatial variation of HIV infection in Kenya was also established. The study shows the practicality and flexibility of Bayesian semi-parametric regression model in analyzing epidemiological data.
Technical Note: Approximate Bayesian parameterization of a complex tropical forest model
Directory of Open Access Journals (Sweden)
F. Hartig
2013-08-01
Full Text Available Inverse parameter estimation of process-based models is a long-standing problem in ecology and evolution. A key problem of inverse parameter estimation is to define a metric that quantifies how well model predictions fit to the data. Such a metric can be expressed by general cost or objective functions, but statistical inversion approaches are based on a particular metric, the probability of observing the data given the model, known as the likelihood. Deriving likelihoods for dynamic models requires making assumptions about the probability for observations to deviate from mean model predictions. For technical reasons, these assumptions are usually derived without explicit consideration of the processes in the simulation. Only in recent years have new methods become available that allow generating likelihoods directly from stochastic simulations. Previous applications of these approximate Bayesian methods have concentrated on relatively simple models. Here, we report on the application of a simulation-based likelihood approximation for FORMIND, a parameter-rich individual-based model of tropical forest dynamics. We show that approximate Bayesian inference, based on a parametric likelihood approximation placed in a conventional MCMC, performs well in retrieving known parameter values from virtual field data generated by the forest model. We analyze the results of the parameter estimation, examine the sensitivity towards the choice and aggregation of model outputs and observed data (summary statistics, and show results from using this method to fit the FORMIND model to field data from an Ecuadorian tropical forest. Finally, we discuss differences of this approach to Approximate Bayesian Computing (ABC, another commonly used method to generate simulation-based likelihood approximations. Our results demonstrate that simulation-based inference, which offers considerable conceptual advantages over more traditional methods for inverse parameter
Technical Note: Approximate Bayesian parameterization of a process-based tropical forest model
Hartig, F.; Dislich, C.; Wiegand, T.; Huth, A.
2014-02-01
Inverse parameter estimation of process-based models is a long-standing problem in many scientific disciplines. A key question for inverse parameter estimation is how to define the metric that quantifies how well model predictions fit to the data. This metric can be expressed by general cost or objective functions, but statistical inversion methods require a particular metric, the probability of observing the data given the model parameters, known as the likelihood. For technical and computational reasons, likelihoods for process-based stochastic models are usually based on general assumptions about variability in the observed data, and not on the stochasticity generated by the model. Only in recent years have new methods become available that allow the generation of likelihoods directly from stochastic simulations. Previous applications of these approximate Bayesian methods have concentrated on relatively simple models. Here, we report on the application of a simulation-based likelihood approximation for FORMIND, a parameter-rich individual-based model of tropical forest dynamics. We show that approximate Bayesian inference, based on a parametric likelihood approximation placed in a conventional Markov chain Monte Carlo (MCMC) sampler, performs well in retrieving known parameter values from virtual inventory data generated by the forest model. We analyze the results of the parameter estimation, examine its sensitivity to the choice and aggregation of model outputs and observed data (summary statistics), and demonstrate the application of this method by fitting the FORMIND model to field data from an Ecuadorian tropical forest. Finally, we discuss how this approach differs from approximate Bayesian computation (ABC), another method commonly used to generate simulation-based likelihood approximations. Our results demonstrate that simulation-based inference, which offers considerable conceptual advantages over more traditional methods for inverse parameter estimation
Technical Note: Approximate Bayesian parameterization of a complex tropical forest model
Hartig, F.; Dislich, C.; Wiegand, T.; Huth, A.
2013-08-01
Inverse parameter estimation of process-based models is a long-standing problem in ecology and evolution. A key problem of inverse parameter estimation is to define a metric that quantifies how well model predictions fit to the data. Such a metric can be expressed by general cost or objective functions, but statistical inversion approaches are based on a particular metric, the probability of observing the data given the model, known as the likelihood. Deriving likelihoods for dynamic models requires making assumptions about the probability for observations to deviate from mean model predictions. For technical reasons, these assumptions are usually derived without explicit consideration of the processes in the simulation. Only in recent years have new methods become available that allow generating likelihoods directly from stochastic simulations. Previous applications of these approximate Bayesian methods have concentrated on relatively simple models. Here, we report on the application of a simulation-based likelihood approximation for FORMIND, a parameter-rich individual-based model of tropical forest dynamics. We show that approximate Bayesian inference, based on a parametric likelihood approximation placed in a conventional MCMC, performs well in retrieving known parameter values from virtual field data generated by the forest model. We analyze the results of the parameter estimation, examine the sensitivity towards the choice and aggregation of model outputs and observed data (summary statistics), and show results from using this method to fit the FORMIND model to field data from an Ecuadorian tropical forest. Finally, we discuss differences of this approach to Approximate Bayesian Computing (ABC), another commonly used method to generate simulation-based likelihood approximations. Our results demonstrate that simulation-based inference, which offers considerable conceptual advantages over more traditional methods for inverse parameter estimation, can
Inversion of hierarchical Bayesian models using Gaussian processes.
Lomakina, Ekaterina I; Paliwal, Saee; Diaconescu, Andreea O; Brodersen, Kay H; Aponte, Eduardo A; Buhmann, Joachim M; Stephan, Klaas E
2015-09-01
Over the past decade, computational approaches to neuroimaging have increasingly made use of hierarchical Bayesian models (HBMs), either for inferring on physiological mechanisms underlying fMRI data (e.g., dynamic causal modelling, DCM) or for deriving computational trajectories (from behavioural data) which serve as regressors in general linear models. However, an unresolved problem is that standard methods for inverting the hierarchical Bayesian model are either very slow, e.g. Markov Chain Monte Carlo Methods (MCMC), or are vulnerable to local minima in non-convex optimisation problems, such as variational Bayes (VB). This article considers Gaussian process optimisation (GPO) as an alternative approach for global optimisation of sufficiently smooth and efficiently evaluable objective functions. GPO avoids being trapped in local extrema and can be computationally much more efficient than MCMC. Here, we examine the benefits of GPO for inverting HBMs commonly used in neuroimaging, including DCM for fMRI and the Hierarchical Gaussian Filter (HGF). Importantly, to achieve computational efficiency despite high-dimensional optimisation problems, we introduce a novel combination of GPO and local gradient-based search methods. The utility of this GPO implementation for DCM and HGF is evaluated against MCMC and VB, using both synthetic data from simulations and empirical data. Our results demonstrate that GPO provides parameter estimates with equivalent or better accuracy than the other techniques, but at a fraction of the computational cost required for MCMC. We anticipate that GPO will prove useful for robust and efficient inversion of high-dimensional and nonlinear models of neuroimaging data. PMID:26048619
A hierarchical bayesian model to quantify uncertainty of stream water temperature forecasts.
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Guillaume Bal
Full Text Available Providing generic and cost effective modelling approaches to reconstruct and forecast freshwater temperature using predictors as air temperature and water discharge is a prerequisite to understanding ecological processes underlying the impact of water temperature and of global warming on continental aquatic ecosystems. Using air temperature as a simple linear predictor of water temperature can lead to significant bias in forecasts as it does not disentangle seasonality and long term trends in the signal. Here, we develop an alternative approach based on hierarchical Bayesian statistical time series modelling of water temperature, air temperature and water discharge using seasonal sinusoidal periodic signals and time varying means and amplitudes. Fitting and forecasting performances of this approach are compared with that of simple linear regression between water and air temperatures using i an emotive simulated example, ii application to three French coastal streams with contrasting bio-geographical conditions and sizes. The time series modelling approach better fit data and does not exhibit forecasting bias in long term trends contrary to the linear regression. This new model also allows for more accurate forecasts of water temperature than linear regression together with a fair assessment of the uncertainty around forecasting. Warming of water temperature forecast by our hierarchical Bayesian model was slower and more uncertain than that expected with the classical regression approach. These new forecasts are in a form that is readily usable in further ecological analyses and will allow weighting of outcomes from different scenarios to manage climate change impacts on freshwater wildlife.
Statistical bootstrap model and annihilations
Möhring, H J
1974-01-01
The statistical bootstrap model (SBM) describes the decay of single, high mass, hadronic states (fireballs, clusters) into stable particles. Coupling constants B, one for each isospin multiplet of stable particles, are the only free parameter of the model. They are related to the maximum temperature parameter T/sub 0/. The various versions of the SMB can be classified into two groups: full statistical bootstrap models and linear ones. The main results of the model are the following: i) All momentum spectra are isotropic; especially the exclusive ones are described by invariant phase space. The inclusive and semi-inclusive single-particle distributions are asymptotically of pure exponential shape; the slope is governed by T /sub 0/ only. ii) The model parameter B for pions has been obtained by fitting the multiplicity distribution in pp and pn at rest, and corresponds to T/sub 0/=0.167 GeV in the full SBM with exotics. The average pi /sup -/ multiplicity for the linear and the full SBM (both with exotics) is c...
Modeling Land-Use Decision Behavior with Bayesian Belief Networks
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Inge Aalders
2008-06-01
Full Text Available The ability to incorporate and manage the different drivers of land-use change in a modeling process is one of the key challenges because they are complex and are both quantitative and qualitative in nature. This paper uses Bayesian belief networks (BBN to incorporate characteristics of land managers in the modeling process and to enhance our understanding of land-use change based on the limited and disparate sources of information. One of the two models based on spatial data represented land managers in the form of a quantitative variable, the area of individual holdings, whereas the other model included qualitative data from a survey of land managers. Random samples from the spatial data provided evidence of the relationship between the different variables, which I used to develop the BBN structure. The model was tested for four different posterior probability distributions, and results showed that the trained and learned models are better at predicting land use than the uniform and random models. The inference from the model demonstrated the constraints that biophysical characteristics impose on land managers; for older land managers without heirs, there is a higher probability of the land use being arable agriculture. The results show the benefits of incorporating a more complex notion of land managers in land-use models, and of using different empirical data sources in the modeling process. Future research should focus on incorporating more complex social processes into the modeling structure, as well as incorporating spatio-temporal dynamics in a BBN.
GPU Computing in Bayesian Inference of Realized Stochastic Volatility Model
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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
a Simplified Bayesian Network Model Applied in Crop or Animal Disease Diagnosis
Yu, Helong; Chen, Guifen; Liu, Dayou
Bayesian network is a powerful tool to represent and deal with uncertain knowledge. There exists much uncertainty in crop or animal disease. The construction of Bayesian network need much data and knowledge. But when data is scarce, some methods should be adopted to construct an effective Bayesian network. This paper introduces a disease diagnosis model based on Bayesian network, which is two-layered and obeys noisy-or assumption. Based on the two-layered structure, the relationship between nodes is obtained by domain knowledge. Based on the noisy-model, the conditional probability table is elicited by three methods, which are parameter learning, domain expert and the existing certainty factor model. In order to implement this model, a Bayesian network tool is developed. Finally, an example about cow disease diagnosis was implemented, which proved that the model discussed in this paper is an effective tool for some simple disease diagnosis in crop or animal field.
BONNSAI: a Bayesian tool for comparing stars with stellar evolution models
Schneider, Fabian R N; de Koter, Alex; Brott, Ines; Izzard, Robert G; Lau, Herbert H B
2014-01-01
Powerful telescopes equipped with multi-fibre or integral field spectrographs combined with detailed models of stellar atmospheres and automated fitting techniques allow for the analysis of large number of stars. These datasets contain a wealth of information that require new analysis techniques to bridge the gap between observations and stellar evolution models. To that end, we develop BONNSAI (BONN Stellar Astrophysics Interface), a Bayesian statistical method, that is capable of comparing all available observables simultaneously to stellar models while taking observed uncertainties and prior knowledge such as initial mass functions and distributions of stellar rotational velocities into account. BONNSAI can be used to (1) determine probability distributions of fundamental stellar parameters such as initial masses and stellar ages from complex datasets, (2) predict stellar parameters that were not yet observationally determined and (3) test stellar models to further advance our understanding of stellar evol...
Chen, Cong; Zhang, Guohui; Tarefder, Rafiqul; Ma, Jianming; Wei, Heng; Guan, Hongzhi
2015-07-01
Rear-end crash is one of the most common types of traffic crashes in the U.S. A good understanding of its characteristics and contributing factors is of practical importance. Previously, both multinomial Logit models and Bayesian network methods have been used in crash modeling and analysis, respectively, although each of them has its own application restrictions and limitations. In this study, a hybrid approach is developed to combine multinomial logit models and Bayesian network methods for comprehensively analyzing driver injury severities in rear-end crashes based on state-wide crash data collected in New Mexico from 2010 to 2011. A multinomial logit model is developed to investigate and identify significant contributing factors for rear-end crash driver injury severities classified into three categories: no injury, injury, and fatality. Then, the identified significant factors are utilized to establish a Bayesian network to explicitly formulate statistical associations between injury severity outcomes and explanatory attributes, including driver behavior, demographic features, vehicle factors, geometric and environmental characteristics, etc. The test results demonstrate that the proposed hybrid approach performs reasonably well. The Bayesian network reference analyses indicate that the factors including truck-involvement, inferior lighting conditions, windy weather conditions, the number of vehicles involved, etc. could significantly increase driver injury severities in rear-end crashes. The developed methodology and estimation results provide insights for developing effective countermeasures to reduce rear-end crash injury severities and improve traffic system safety performance. PMID:25888994
Estimating Parameters in Physical Models through Bayesian Inversion: A Complete Example
Allmaras, Moritz
2013-02-07
All mathematical models of real-world phenomena contain parameters that need to be estimated from measurements, either for realistic predictions or simply to understand the characteristics of the model. Bayesian statistics provides a framework for parameter estimation in which uncertainties about models and measurements are translated into uncertainties in estimates of parameters. This paper provides a simple, step-by-step example-starting from a physical experiment and going through all of the mathematics-to explain the use of Bayesian techniques for estimating the coefficients of gravity and air friction in the equations describing a falling body. In the experiment we dropped an object from a known height and recorded the free fall using a video camera. The video recording was analyzed frame by frame to obtain the distance the body had fallen as a function of time, including measures of uncertainty in our data that we describe as probability densities. We explain the decisions behind the various choices of probability distributions and relate them to observed phenomena. Our measured data are then combined with a mathematical model of a falling body to obtain probability densities on the space of parameters we seek to estimate. We interpret these results and discuss sources of errors in our estimation procedure. © 2013 Society for Industrial and Applied Mathematics.
Bayesian network models for error detection in radiotherapy plans
Kalet, Alan M.; Gennari, John H.; Ford, Eric C.; Phillips, Mark H.
2015-04-01
The purpose of this study is to design and develop a probabilistic network for detecting errors in radiotherapy plans for use at the time of initial plan verification. Our group has initiated a multi-pronged approach to reduce these errors. We report on our development of Bayesian models of radiotherapy plans. Bayesian networks consist of joint probability distributions that define the probability of one event, given some set of other known information. Using the networks, we find the probability of obtaining certain radiotherapy parameters, given a set of initial clinical information. A low probability in a propagated network then corresponds to potential errors to be flagged for investigation. To build our networks we first interviewed medical physicists and other domain experts to identify the relevant radiotherapy concepts and their associated interdependencies and to construct a network topology. Next, to populate the network’s conditional probability tables, we used the Hugin Expert software to learn parameter distributions from a subset of de-identified data derived from a radiation oncology based clinical information database system. These data represent 4990 unique prescription cases over a 5 year period. Under test case scenarios with approximately 1.5% introduced error rates, network performance produced areas under the ROC curve of 0.88, 0.98, and 0.89 for the lung, brain and female breast cancer error detection networks, respectively. Comparison of the brain network to human experts performance (AUC of 0.90 ± 0.01) shows the Bayes network model performs better than domain experts under the same test conditions. Our results demonstrate the feasibility and effectiveness of comprehensive probabilistic models as part of decision support systems for improved detection of errors in initial radiotherapy plan verification procedures.
Statistical models for seismic magnitude
Christoffersson, Anders
1980-02-01
In this paper some statistical models in connection with seismic magnitude are presented. Two main situations are treated. The first deals with the estimation of magnitude for an event, using a fixed network of stations and taking into account the detection and bias properties of the individual stations. The second treats the problem of estimating seismicity, and detection and bias properties of individual stations. The models are applied to analyze the magnitude bias effects for an earthquake aftershock sequence from Japan, as recorded by a hypothetical network of 15 stations. It is found that network magnitudes computed by the conventional averaging technique are considerably biased, and that a maximum likelihood approach using instantaneous noise-level estimates for non-detecting stations gives the most consistent magnitude estimates. Finally, the models are applied to evaluate the detection characteristics and associated seismicity as recorded by three VELA arrays: UBO (Uinta Basin), TFO (Tonto Forest) and WMO (Wichita Mountains).
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Highlights: • Deduce secondary structure content of intrinsically disordered proteins from IR spectra. • Bayesian analysis to infer conformations of disordered regions of proteins from IR. • Comparison of measured and calculated IR spectra to obtain thermodynamic weights. - Abstract: As it remains practically impossible to generate ergodic ensembles for large intrinsically disordered proteins (IDP) with molecular dynamics (MD) simulations, it becomes critical to compare spectroscopic characteristics of the theoretically generated ensembles to corresponding measurements. We develop a Bayesian framework to infer the ensemble properties of an IDP using a combination of conformations generated by MD simulations and its measured infrared spectrum. We performed 100 different MD simulations totaling more than 10 μs to characterize the conformational ensemble of α-synuclein, a prototypical IDP, in water. These conformations are clustered based on solvent accessibility and helical content. We compute the amide-I band for these clusters and predict the thermodynamic weights of each cluster given the measured amide-I band. Bayesian analysis produces a reproducible and non-redundant set of thermodynamic weights for each cluster, which can then be used to calculate the ensemble properties. In a rigorous validation, these weights reproduce measured chemical shifts
Bayesian methods for measures of agreement
Broemeling, Lyle D
2009-01-01
Using WinBUGS to implement Bayesian inferences of estimation and testing hypotheses, Bayesian Methods for Measures of Agreement presents useful methods for the design and analysis of agreement studies. It focuses on agreement among the various players in the diagnostic process.The author employs a Bayesian approach to provide statistical inferences based on various models of intra- and interrater agreement. He presents many examples that illustrate the Bayesian mode of reasoning and explains elements of a Bayesian application, including prior information, experimental information, the likelihood function, posterior distribution, and predictive distribution. The appendices provide the necessary theoretical foundation to understand Bayesian methods as well as introduce the fundamentals of programming and executing the WinBUGS software.Taking a Bayesian approach to inference, this hands-on book explores numerous measures of agreement, including the Kappa coefficient, the G coefficient, and intraclass correlation...
Bayesian modeling of ChIP-chip data using latent variables.
Wu, Mingqi
2009-10-26
BACKGROUND: The ChIP-chip technology has been used in a wide range of biomedical studies, such as identification of human transcription factor binding sites, investigation of DNA methylation, and investigation of histone modifications in animals and plants. Various methods have been proposed in the literature for analyzing the ChIP-chip data, such as the sliding window methods, the hidden Markov model-based methods, and Bayesian methods. Although, due to the integrated consideration of uncertainty of the models and model parameters, Bayesian methods can potentially work better than the other two classes of methods, the existing Bayesian methods do not perform satisfactorily. They usually require multiple replicates or some extra experimental information to parametrize the model, and long CPU time due to involving of MCMC simulations. RESULTS: In this paper, we propose a Bayesian latent model for the ChIP-chip data. The new model mainly differs from the existing Bayesian models, such as the joint deconvolution model, the hierarchical gamma mixture model, and the Bayesian hierarchical model, in two respects. Firstly, it works on the difference between the averaged treatment and control samples. This enables the use of a simple model for the data, which avoids the probe-specific effect and the sample (control/treatment) effect. As a consequence, this enables an efficient MCMC simulation of the posterior distribution of the model, and also makes the model more robust to the outliers. Secondly, it models the neighboring dependence of probes by introducing a latent indicator vector. A truncated Poisson prior distribution is assumed for the latent indicator variable, with the rationale being justified at length. CONCLUSION: The Bayesian latent method is successfully applied to real and ten simulated datasets, with comparisons with some of the existing Bayesian methods, hidden Markov model methods, and sliding window methods. The numerical results indicate that the
Bayesian modeling of ChIP-chip data using latent variables
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Tian Yanan
2009-10-01
Full Text Available Abstract Background The ChIP-chip technology has been used in a wide range of biomedical studies, such as identification of human transcription factor binding sites, investigation of DNA methylation, and investigation of histone modifications in animals and plants. Various methods have been proposed in the literature for analyzing the ChIP-chip data, such as the sliding window methods, the hidden Markov model-based methods, and Bayesian methods. Although, due to the integrated consideration of uncertainty of the models and model parameters, Bayesian methods can potentially work better than the other two classes of methods, the existing Bayesian methods do not perform satisfactorily. They usually require multiple replicates or some extra experimental information to parametrize the model, and long CPU time due to involving of MCMC simulations. Results In this paper, we propose a Bayesian latent model for the ChIP-chip data. The new model mainly differs from the existing Bayesian models, such as the joint deconvolution model, the hierarchical gamma mixture model, and the Bayesian hierarchical model, in two respects. Firstly, it works on the difference between the averaged treatment and control samples. This enables the use of a simple model for the data, which avoids the probe-specific effect and the sample (control/treatment effect. As a consequence, this enables an efficient MCMC simulation of the posterior distribution of the model, and also makes the model more robust to the outliers. Secondly, it models the neighboring dependence of probes by introducing a latent indicator vector. A truncated Poisson prior distribution is assumed for the latent indicator variable, with the rationale being justified at length. Conclusion The Bayesian latent method is successfully applied to real and ten simulated datasets, with comparisons with some of the existing Bayesian methods, hidden Markov model methods, and sliding window methods. The numerical results
Vrieze, Scott I.
2012-01-01
This article reviews the Akaike information criterion (AIC) and the Bayesian information criterion (BIC) in model selection and the appraisal of psychological theory. The focus is on latent variable models, given their growing use in theory testing and construction. Theoretical statistical results in regression are discussed, and more important…
Designing and testing inflationary models with Bayesian networks
Price, Layne C; Frazer, Jonathan; Easther, Richard
2015-01-01
Even simple inflationary scenarios have many free parameters. Beyond the variables appearing in the inflationary action, these include dynamical initial conditions, the number of fields, and couplings to other sectors. These quantities are often ignored but cosmological observables can depend on the unknown parameters. We use Bayesian networks to account for a large set of inflationary parameters, deriving generative models for the primordial spectra that are conditioned on a hierarchical set of prior probabilities describing the initial conditions, reheating physics, and other free parameters. We use $N_f$--quadratic inflation as an illustrative example, finding that the number of $e$-folds $N_*$ between horizon exit for the pivot scale and the end of inflation is typically the most important parameter, even when the number of fields, their masses and initial conditions are unknown, along with possible conditional dependencies between these parameters.
Designing and testing inflationary models with Bayesian networks
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Price, Layne C. [Carnegie Mellon Univ., Pittsburgh, PA (United States). Dept. of Physics; Auckland Univ. (New Zealand). Dept. of Physics; Peiris, Hiranya V. [Univ. College London (United Kingdom). Dept. of Physics and Astronomy; Frazer, Jonathan [DESY Hamburg (Germany). Theory Group; Univ. of the Basque Country, Bilbao (Spain). Dept. of Theoretical Physics; Basque Foundation for Science, Bilbao (Spain). IKERBASQUE; Easther, Richard [Auckland Univ. (New Zealand). Dept. of Physics
2015-11-15
Even simple inflationary scenarios have many free parameters. Beyond the variables appearing in the inflationary action, these include dynamical initial conditions, the number of fields, and couplings to other sectors. These quantities are often ignored but cosmological observables can depend on the unknown parameters. We use Bayesian networks to account for a large set of inflationary parameters, deriving generative models for the primordial spectra that are conditioned on a hierarchical set of prior probabilities describing the initial conditions, reheating physics, and other free parameters. We use N{sub f}-quadratic inflation as an illustrative example, finding that the number of e-folds N{sub *} between horizon exit for the pivot scale and the end of inflation is typically the most important parameter, even when the number of fields, their masses and initial conditions are unknown, along with possible conditional dependencies between these parameters.
Bazin, Eric; Dawson, Kevin J; Beaumont, Mark A
2010-06-01
We address the problem of finding evidence of natural selection from genetic data, accounting for the confounding effects of demographic history. In the absence of natural selection, gene genealogies should all be sampled from the same underlying distribution, often approximated by a coalescent model. Selection at a particular locus will lead to a modified genealogy, and this motivates a number of recent approaches for detecting the effects of natural selection in the genome as "outliers" under some models. The demographic history of a population affects the sampling distribution of genealogies, and therefore the observed genotypes and the classification of outliers. Since we cannot see genealogies directly, we have to infer them from the observed data under some model of mutation and demography. Thus the accuracy of an outlier-based approach depends to a greater or a lesser extent on the uncertainty about the demographic and mutational model. A natural modeling framework for this type of problem is provided by Bayesian hierarchical models, in which parameters, such as mutation rates and selection coefficients, are allowed to vary across loci. It has proved quite difficult computationally to implement fully probabilistic genealogical models with complex demographies, and this has motivated the development of approximations such as approximate Bayesian computation (ABC). In ABC the data are compressed into summary statistics, and computation of the likelihood function is replaced by simulation of data under the model. In a hierarchical setting one may be interested both in hyperparameters and parameters, and there may be very many of the latter--for example, in a genetic model, these may be parameters describing each of many loci or populations. This poses a problem for ABC in that one then requires summary statistics for each locus, which, if used naively, leads to a consequent difficulty in conditional density estimation. We develop a general method for applying
Bayesian analysis for exponential random graph models using the adaptive exchange sampler
Jin, Ick Hoon
2013-01-01
Exponential random graph models have been widely used in social network analysis. However, these models are extremely difficult to handle from a statistical viewpoint, because of the existence of intractable normalizing constants. In this paper, we consider a fully Bayesian analysis for exponential random graph models using the adaptive exchange sampler, which solves the issue of intractable normalizing constants encountered in Markov chain Monte Carlo (MCMC) simulations. The adaptive exchange sampler can be viewed as a MCMC extension of the exchange algorithm, and it generates auxiliary networks via an importance sampling procedure from an auxiliary Markov chain running in parallel. The convergence of this algorithm is established under mild conditions. The adaptive exchange sampler is illustrated using a few social networks, including the Florentine business network, molecule synthetic network, and dolphins network. The results indicate that the adaptive exchange algorithm can produce more accurate estimates than approximate exchange algorithms, while maintaining the same computational efficiency.
A unified Bayesian hierarchical model for MRI tissue classification.
Feng, Dai; Liang, Dong; Tierney, Luke
2014-04-15
Various works have used magnetic resonance imaging (MRI) tissue classification extensively to study a number of neurological and psychiatric disorders. Various noise characteristics and other artifacts make this classification a challenging task. Instead of splitting the procedure into different steps, we extend a previous work to develop a unified Bayesian hierarchical model, which addresses both the partial volume effect and intensity non-uniformity, the two major acquisition artifacts, simultaneously. We adopted a normal mixture model with the means and variances depending on the tissue types of voxels to model the observed intensity values. We modeled the relationship among the components of the index vector of tissue types by a hidden Markov model, which captures the spatial similarity of voxels. Furthermore, we addressed the partial volume effect by construction of a higher resolution image in which each voxel is divided into subvoxels. Finally, We achieved the bias field correction by using a Gaussian Markov random field model with a band precision matrix designed in light of image filtering. Sparse matrix methods and parallel computations based on conditional independence are exploited to improve the speed of the Markov chain Monte Carlo simulation. The unified model provides more accurate tissue classification results for both simulated and real data sets. PMID:24738112
Predictability of Regional Climate: A Bayesian Approach to Analysing a WRF Model Ensemble
Bruyere, C. L.; Mesquita, M. D. S.; Paimazumder, D.
2013-12-01
This study investigates aspects of climate predictability with a focus on climatic variables and different characteristics of extremes over nine North American climatic regions and two selected Atlantic sectors. An ensemble of state-of-the-art Weather Research and Forecasting Model (WRF) simulations is used for the analysis. The ensemble is comprised of a combination of various physics schemes, initial conditions, domain sizes, boundary conditions and breeding techniques. The main objectives of this research are: 1) to increase our understanding of the ability of WRF to capture regional climate information - both at the individual and collective ensemble members, 2) to investigate the role of different members and their synergy in reproducing regional climate 3) to estimate the associated uncertainty. In this study, we propose a Bayesian framework to study the predictability of extremes and associated uncertainties in order to provide a wealth of knowledge about WRF reliability and provide further clarity and understanding of the sensitivities and optimal combinations. The choice of the Bayesian model, as opposed to standard methods, is made because: a) this method has a mean square error that is less than standard statistics, which makes it a more robust method; b) it allows for the use of small sample sizes, which are typical in high-resolution modeling; c) it provides a probabilistic view of uncertainty, which is useful when making decisions concerning ensemble members.
Bayesian estimation in IRT models with missing values in background variables
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Christian Aßmann
2015-12-01
Full Text Available Large scale assessment studies typically aim at investigating the relationship between persons competencies and explaining variables. Individual competencies are often estimated by explicitly including explaining background variables into corresponding Item Response Theory models. Since missing values in background variables inevitably occur, strategies to handle the uncertainty related to missing values in parameter estimation are required. We propose to adapt a Bayesian estimation strategy based on Markov Chain Monte Carlo techniques. Sampling from the posterior distribution of parameters is thereby enriched by sampling from the full conditional distribution of the missing values. We consider non-parametric as well as parametric approximations for the full conditional distributions of missing values, thus allowing for a flexible incorporation of metric as well as categorical background variables. We evaluate the validity of our approach with respect to statistical accuracy by a simulation study controlling the missing values generating mechanism. We show that the proposed Bayesian strategy allows for effective comparison of nested model specifications via gauging highest posterior density intervals of all involved model parameters. An illustration of the suggested approach uses data from the National Educational Panel Study on mathematical competencies of fifth grade students.
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Gerhard Moser
2015-04-01
Full Text Available Gene discovery, estimation of heritability captured by SNP arrays, inference on genetic architecture and prediction analyses of complex traits are usually performed using different statistical models and methods, leading to inefficiency and loss of power. Here we use a Bayesian mixture model that simultaneously allows variant discovery, estimation of genetic variance explained by all variants and prediction of unobserved phenotypes in new samples. We apply the method to simulated data of quantitative traits and Welcome Trust Case Control Consortium (WTCCC data on disease and show that it provides accurate estimates of SNP-based heritability, produces unbiased estimators of risk in new samples, and that it can estimate genetic architecture by partitioning variation across hundreds to thousands of SNPs. We estimated that, depending on the trait, 2,633 to 9,411 SNPs explain all of the SNP-based heritability in the WTCCC diseases. The majority of those SNPs (>96% had small effects, confirming a substantial polygenic component to common diseases. The proportion of the SNP-based variance explained by large effects (each SNP explaining 1% of the variance varied markedly between diseases, ranging from almost zero for bipolar disorder to 72% for type 1 diabetes. Prediction analyses demonstrate that for diseases with major loci, such as type 1 diabetes and rheumatoid arthritis, Bayesian methods outperform profile scoring or mixed model approaches.
Statistical models for trisomic phenotypes
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Lamb, N.E.; Sherman, S.L.; Feingold, E. [Emory Univ., Atlanta, GA (United States)
1996-01-01
Certain genetic disorders are rare in the general population but more common in individuals with specific trisomies, which suggests that the genes involved in the etiology of these disorders may be located on the trisomic chromosome. As with all aneuploid syndromes, however, a considerable degree of variation exists within each phenotype so that any given trait is present only among a subset of the trisomic population. We have previously presented a simple gene-dosage model to explain this phenotypic variation and developed a strategy to map genes for such traits. The mapping strategy does not depend on the simple model but works in theory under any model that predicts that affected individuals have an increased likelihood of disomic homozygosity at the trait locus. This paper explores the robustness of our mapping method by investigating what kinds of models give an expected increase in disomic homozygosity. We describe a number of basic statistical models for trisomic phenotypes. Some of these are logical extensions of standard models for disomic phenotypes, and some are more specific to trisomy. Where possible, we discuss genetic mechanisms applicable to each model. We investigate which models and which parameter values give an expected increase in disomic homozygosity in individuals with the trait. Finally, we determine the sample sizes required to identify the increased disomic homozygosity under each model. Most of the models we explore yield detectable increases in disomic homozygosity for some reasonable range of parameter values, usually corresponding to smaller trait frequencies. It therefore appears that our mapping method should be effective for a wide variety of moderately infrequent traits, even though the exact mode of inheritance is unlikely to be known. 21 refs., 8 figs., 1 tab.
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A. E. Sikorska
2012-04-01
Full Text Available Urbanization and the resulting land-use change strongly affect the water cycle and runoff-processes in watersheds. Unfortunately, small urban watersheds, which are most affected by urban sprawl, are mostly ungauged. This makes it intrinsically difficult to assess the consequences of urbanization. Most of all, it is unclear how to reliably assess the predictive uncertainty given the structural deficits of the applied models. In this study, we therefore investigate the uncertainty of flood predictions in ungauged urban basins from structurally uncertain rainfall-runoff models. To this end, we suggest a procedure to explicitly account for input uncertainty and model structure deficits using Bayesian statistics with a continuous-time autoregressive error model. In addition, we propose a concise procedure to derive prior parameter distributions from base data and successfully apply the methodology to an urban catchment in Warsaw, Poland. Based on our results, we are able to demonstrate that the autoregressive error model greatly helps to meet the statistical assumptions and to compute reliable prediction intervals. In our study, we found that predicted peak flows were up to 7 times higher than observations. This was reduced to 5 times with Bayesian updating, using only few discharge measurements. In addition, our analysis suggests that imprecise rainfall information and model structure deficits contribute mostly to the total prediction uncertainty. In the future, flood predictions in ungauged basins will become more important due to ongoing urbanization as well as anthropogenic and climatic changes. Thus, providing reliable measures of uncertainty is crucial to support decision making.
Bayesian modeling of animal- and herd-level prevalences.
Branscum, A J; Gardner, I A; Johnson, W O
2004-12-15
We reviewed Bayesian approaches for animal-level and herd-level prevalence estimation based on cross-sectional sampling designs and demonstrated fitting of these models using the WinBUGS software. We considered estimation of infection prevalence based on use of a single diagnostic test applied to a single herd with binomial and hypergeometric sampling. We then considered multiple herds under binomial sampling with the primary goal of estimating the prevalence distribution and the proportion of infected herds. A new model is presented that can be used to estimate the herd-level prevalence in a region, including the posterior probability that all herds are non-infected. Using this model, inferences for the distribution of prevalences, mean prevalence in the region, and predicted prevalence of herds in the region (including the predicted probability of zero prevalence) are also available. In the models presented, both animal- and herd-level prevalences are modeled as mixture distributions to allow for zero infection prevalences. (If mixture models for the prevalences were not used, prevalence estimates might be artificially inflated, especially in herds and regions with low or zero prevalence.) Finally, we considered estimation of animal-level prevalence based on pooled samples. PMID:15579338
SU-E-T-51: Bayesian Network Models for Radiotherapy Error Detection
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Kalet, A; Phillips, M; Gennari, J [UniversityWashington, Seattle, WA (United States)
2014-06-01
Purpose: To develop a probabilistic model of radiotherapy plans using Bayesian networks that will detect potential errors in radiation delivery. Methods: Semi-structured interviews with medical physicists and other domain experts were employed to generate a set of layered nodes and arcs forming a Bayesian Network (BN) which encapsulates relevant radiotherapy concepts and their associated interdependencies. Concepts in the final network were limited to those whose parameters are represented in the institutional database at a level significant enough to develop mathematical distributions. The concept-relation knowledge base was constructed using the Web Ontology Language (OWL) and translated into Hugin Expert Bayes Network files via the the RHugin package in the R statistical programming language. A subset of de-identified data derived from a Mosaiq relational database representing 1937 unique prescription cases was processed and pre-screened for errors and then used by the Hugin implementation of the Estimation-Maximization (EM) algorithm for machine learning all parameter distributions. Individual networks were generated for each of several commonly treated anatomic regions identified by ICD-9 neoplasm categories including lung, brain, lymphoma, and female breast. Results: The resulting Bayesian networks represent a large part of the probabilistic knowledge inherent in treatment planning. By populating the networks entirely with data captured from a clinical oncology information management system over the course of several years of normal practice, we were able to create accurate probability tables with no additional time spent by experts or clinicians. These probabilistic descriptions of the treatment planning allow one to check if a treatment plan is within the normal scope of practice, given some initial set of clinical evidence and thereby detect for potential outliers to be flagged for further investigation. Conclusion: The networks developed here support the
SU-E-T-51: Bayesian Network Models for Radiotherapy Error Detection
International Nuclear Information System (INIS)
Purpose: To develop a probabilistic model of radiotherapy plans using Bayesian networks that will detect potential errors in radiation delivery. Methods: Semi-structured interviews with medical physicists and other domain experts were employed to generate a set of layered nodes and arcs forming a Bayesian Network (BN) which encapsulates relevant radiotherapy concepts and their associated interdependencies. Concepts in the final network were limited to those whose parameters are represented in the institutional database at a level significant enough to develop mathematical distributions. The concept-relation knowledge base was constructed using the Web Ontology Language (OWL) and translated into Hugin Expert Bayes Network files via the the RHugin package in the R statistical programming language. A subset of de-identified data derived from a Mosaiq relational database representing 1937 unique prescription cases was processed and pre-screened for errors and then used by the Hugin implementation of the Estimation-Maximization (EM) algorithm for machine learning all parameter distributions. Individual networks were generated for each of several commonly treated anatomic regions identified by ICD-9 neoplasm categories including lung, brain, lymphoma, and female breast. Results: The resulting Bayesian networks represent a large part of the probabilistic knowledge inherent in treatment planning. By populating the networks entirely with data captured from a clinical oncology information management system over the course of several years of normal practice, we were able to create accurate probability tables with no additional time spent by experts or clinicians. These probabilistic descriptions of the treatment planning allow one to check if a treatment plan is within the normal scope of practice, given some initial set of clinical evidence and thereby detect for potential outliers to be flagged for further investigation. Conclusion: The networks developed here support the
A Bayesian model of category-specific emotional brain responses.
Wager, Tor D; Kang, Jian; Johnson, Timothy D; Nichols, Thomas E; Satpute, Ajay B; Barrett, Lisa Feldman
2015-04-01
Understanding emotion is critical for a science of healthy and disordered brain function, but the neurophysiological basis of emotional experience is still poorly understood. We analyzed human brain activity patterns from 148 studies of emotion categories (2159 total participants) using a novel hierarchical Bayesian model. The model allowed us to classify which of five categories--fear, anger, disgust, sadness, or happiness--is engaged by a study with 66% accuracy (43-86% across categories). Analyses of the activity patterns encoded in the model revealed that each emotion category is associated with unique, prototypical patterns of activity across multiple brain systems including the cortex, thalamus, amygdala, and other structures. The results indicate that emotion categories are not contained within any one region or system, but are represented as configurations across multiple brain networks. The model provides a precise summary of the prototypical patterns for each emotion category, and demonstrates that a sufficient characterization of emotion categories relies on (a) differential patterns of involvement in neocortical systems that differ between humans and other species, and (b) distinctive patterns of cortical-subcortical interactions. Thus, these findings are incompatible with several contemporary theories of emotion, including those that emphasize emotion-dedicated brain systems and those that propose emotion is localized primarily in subcortical activity. They are consistent with componential and constructionist views, which propose that emotions are differentiated by a combination of perceptual, mnemonic, prospective, and motivational elements. Such brain-based models of emotion provide a foundation for new translational and clinical approaches. PMID:25853490
Bayesian Belief Networks Approach for Modeling Irrigation Behavior
Andriyas, S.; McKee, M.
2012-12-01
Canal operators need information to manage water deliveries to irrigators. Short-term irrigation demand forecasts can potentially valuable information for a canal operator who must manage an on-demand system. Such forecasts could be generated by using information about the decision-making processes of irrigators. Bayesian models of irrigation behavior can provide insight into the likely criteria which farmers use to make irrigation decisions. This paper develops a Bayesian belief network (BBN) to learn irrigation decision-making behavior of farmers and utilizes the resulting model to make forecasts of future irrigation decisions based on factor interaction and posterior probabilities. Models for studying irrigation behavior have been rarely explored in the past. The model discussed here was built from a combination of data about biotic, climatic, and edaphic conditions under which observed irrigation decisions were made. The paper includes a case study using data collected from the Canal B region of the Sevier River, near Delta, Utah. Alfalfa, barley and corn are the main crops of the location. The model has been tested with a portion of the data to affirm the model predictive capabilities. Irrigation rules were deduced in the process of learning and verified in the testing phase. It was found that most of the farmers used consistent rules throughout all years and across different types of crops. Soil moisture stress, which indicates the level of water available to the plant in the soil profile, was found to be one of the most significant likely driving forces for irrigation. Irrigations appeared to be triggered by a farmer's perception of soil stress, or by a perception of combined factors such as information about a neighbor irrigating or an apparent preference to irrigate on a weekend. Soil stress resulted in irrigation probabilities of 94.4% for alfalfa. With additional factors like weekend and irrigating when a neighbor irrigates, alfalfa irrigation
Statistical Modeling of Factors Influencind Breast-Milk PCDDs and PCDFs Exposure
Czech Academy of Sciences Publication Activity Database
Brabec, Marek; Bencko, V.; Černá, M.
Brusseles, 2008. s. 19-19. [CASCADE Annual Meeting /4./. 05.05.2008-05.07.2008, Brusseles] Institutional research plan: CEZ:AV0Z10300504 Keywords : PCDD/PCDF exposure estimation * Bayesian model * Breast milk Subject RIV: BB - Applied Statistics, Operational Research
Etienne, R.S.; Olff, H.
2005-01-01
Species abundances are undoubtedly the most widely available macroecological data, but can we use them to distinguish among several models of community structure? Here we present a Bayesian analysis of species-abundance data that yields a full joint probability distribution of each model's parameter
Etienne, RS; Olff, H
2005-01-01
Species abundances are undoubtedly the most widely available macroecological data, but can we use them to distinguish among several models of community structure? Here we present a Bayesian analysis of species-abundance data that yields a full joint probability distribution of each model's parameter
In this paper, the Genetic Algorithms (GA) and Bayesian model averaging (BMA) were combined to simultaneously conduct calibration and uncertainty analysis for the Soil and Water Assessment Tool (SWAT). In this hybrid method, several SWAT models with different structures are first selected; next GA i...
BSMac: a MATLAB toolbox implementing a Bayesian spatial model for brain activation and connectivity.
Zhang, Lijun; Agravat, Sanjay; Derado, Gordana; Chen, Shuo; McIntosh, Belinda J; Bowman, F DuBois
2012-02-15
We present a statistical and graphical visualization MATLAB toolbox for the analysis of functional magnetic resonance imaging (fMRI) data, called the Bayesian Spatial Model for activation and connectivity (BSMac). BSMac simultaneously performs whole-brain activation analyses at the voxel and region of interest (ROI) levels as well as task-related functional connectivity (FC) analyses using a flexible Bayesian modeling framework (Bowman et al., 2008). BSMac allows for inputting data in either Analyze or Nifti file formats. The user provides information pertaining to subgroup memberships, scanning sessions, and experimental tasks (stimuli), from which the design matrix is constructed. BSMac then performs parameter estimation based on Markov Chain Monte Carlo (MCMC) methods and generates plots for activation and FC, such as interactive 2D maps of voxel and region-level task-related changes in neural activity and animated 3D graphics of the FC results. The toolbox can be downloaded from http://www.sph.emory.edu/bios/CBIS/. We illustrate the BSMac toolbox through an application to an fMRI study of working memory in patients with schizophrenia. PMID:22101143
Optimizing the Amount of Models Taken into Consideration During Model Selection in Bayesian Networks
Castelo, J.R.; Siebes, Arno
1999-01-01
Graphical model selection from data embodies several difficulties. Among them, it is specially challenging the size of the sample space of models on which one should carry out model selection, even considering only a modest amount of variables. This becomes more severe when one works on those graphical models where some variables may be responses to other. This is the case of Bayesian Networks that are modeled by acyclic digraphs. In this paper we try to reduce the amount of models taken into...
Hill, T; Minier, V; Burton, M G; Cunningham, M R
2008-01-01
Concatenating data from the millimetre regime to the infrared, we have performed spectral energy distribution modelling for 227 of the 405 millimetre continuum sources of Hill et al. (2005) which are thought to contain young massive stars in the earliest stages of their formation. Three main parameters are extracted from the fits: temperature, mass and luminosity. The method employed was Bayesian inference, which allows a statistically probable range of suitable values for each parameter to be drawn for each individual protostellar candidate. This is the first application of this method to massive star formation. The cumulative distribution plots of the SED modelled parameters in this work indicate that collectively, the sources without methanol maser and/or radio continuum associations (MM-only cores) display similar characteristics to those of high mass star formation regions. Attributing significance to the marginal distinctions between the MM-only cores and the high-mass star formation sample we draw hypo...
Bayesian Analysis of Marginal Log-Linear Graphical Models for Three Way Contingency Tables
Ntzoufras, Ioannis; Tarantola, Claudia
2008-01-01
This paper deals with the Bayesian analysis of graphical models of marginal independence for three way contingency tables. We use a marginal log-linear parametrization, under which the model is defined through suitable zero-constraints on the interaction parameters calculated within marginal distributions. We undertake a comprehensive Bayesian analysis of these models, involving suitable choices of prior distributions, estimation, model determination, as well as the allied computational issue...
Bayesian Analysis of Graphical Models of Marginal Independence for Three Way Contingency Tables
Tarantola, Claudia; Ntzoufras, Ioannis
2012-01-01
This paper deals with the Bayesian analysis of graphical models of marginal independence for three way contingency tables. Each marginal independence model corresponds to a particular factorization of the cell probabilities and a conjugate analysis based on Dirichlet prior can be performed. We illustrate a comprehensive Bayesian analysis of such models, involving suitable choices of prior parameters, estimation, model determination, as well as the allied computational issues. The posterior di...
Bayesian Multi-Energy Computed Tomography reconstruction approaches based on decomposition models
International Nuclear Information System (INIS)
Multi-Energy Computed Tomography (MECT) makes it possible to get multiple fractions of basis materials without segmentation. In medical application, one is the soft-tissue equivalent water fraction and the other is the hard-matter equivalent bone fraction. Practical MECT measurements are usually obtained with polychromatic X-ray beams. Existing reconstruction approaches based on linear forward models without counting the beam poly-chromaticity fail to estimate the correct decomposition fractions and result in Beam-Hardening Artifacts (BHA). The existing BHA correction approaches either need to refer to calibration measurements or suffer from the noise amplification caused by the negative-log pre-processing and the water and bone separation problem. To overcome these problems, statistical DECT reconstruction approaches based on non-linear forward models counting the beam poly-chromaticity show great potential for giving accurate fraction images.This work proposes a full-spectral Bayesian reconstruction approach which allows the reconstruction of high quality fraction images from ordinary polychromatic measurements. This approach is based on a Gaussian noise model with unknown variance assigned directly to the projections without taking negative-log. Referring to Bayesian inferences, the decomposition fractions and observation variance are estimated by using the joint Maximum A Posteriori (MAP) estimation method. Subject to an adaptive prior model assigned to the variance, the joint estimation problem is then simplified into a single estimation problem. It transforms the joint MAP estimation problem into a minimization problem with a non-quadratic cost function. To solve it, the use of a monotone Conjugate Gradient (CG) algorithm with suboptimal descent steps is proposed.The performances of the proposed approach are analyzed with both simulated and experimental data. The results show that the proposed Bayesian approach is robust to noise and materials. It is also
Modeling of weak lensing statistics. II. Configuration-space statistics
Valageas, Patrick; Nishimichi, Takahiro
2011-01-01
We investigate the performance of an analytic model of the 3D matter distribution, which combines perturbation theory with halo models, for weak lensing configuration-space statistics. We compare our predictions for the weak lensing convergence two-point and three-point correlation functions with numerical simulations and fitting formulas proposed in previous works. We also consider the second and third-order moments of the smoothed convergence and of the aperture-mass. As in our previous study of Fourier-space weak lensing statistics, we find that our model provides better agreement with simulations than published fitting formulas. Moreover, we check that we recover the dependence on cosmology of these weak lensing statistics. This approach allows us to obtain the quantitative relationship between these integrated weak lensing statistics and the various contributions to the underlying 3D density fluctuations, decomposed over perturbative, 2-halo, or 1-halo terms.
Bayesian network model of crowd emotion and negative behavior
Ramli, Nurulhuda; Ghani, Noraida Abdul; Hatta, Zulkarnain Ahmad; Hashim, Intan Hashimah Mohd; Sulong, Jasni; Mahudin, Nor Diana Mohd; Rahman, Shukran Abd; Saad, Zarina Mat
2014-12-01
The effects of overcrowding have become a major concern for event organizers. One aspect of this concern has been the idea that overcrowding can enhance the occurrence of serious incidents during events. As one of the largest Muslim religious gathering attended by pilgrims from all over the world, Hajj has become extremely overcrowded with many incidents being reported. The purpose of this study is to analyze the nature of human emotion and negative behavior resulting from overcrowding during Hajj events from data gathered in Malaysian Hajj Experience Survey in 2013. The sample comprised of 147 Malaysian pilgrims (70 males and 77 females). Utilizing a probabilistic model called Bayesian network, this paper models the dependence structure between different emotions and negative behaviors of pilgrims in the crowd. The model included the following variables of emotion: negative, negative comfortable, positive, positive comfortable and positive spiritual and variables of negative behaviors; aggressive and hazardous acts. The study demonstrated that emotions of negative, negative comfortable, positive spiritual and positive emotion have a direct influence on aggressive behavior whereas emotion of negative comfortable, positive spiritual and positive have a direct influence on hazardous acts behavior. The sensitivity analysis showed that a low level of negative and negative comfortable emotions leads to a lower level of aggressive and hazardous behavior. Findings of the study can be further improved to identify the exact cause and risk factors of crowd-related incidents in preventing crowd disasters during the mass gathering events.
A Bayesian Semiparametric Model for Radiation Dose-Response Estimation.
Furukawa, Kyoji; Misumi, Munechika; Cologne, John B; Cullings, Harry M
2016-06-01
In evaluating the risk of exposure to health hazards, characterizing the dose-response relationship and estimating acceptable exposure levels are the primary goals. In analyses of health risks associated with exposure to ionizing radiation, while there is a clear agreement that moderate to high radiation doses cause harmful effects in humans, little has been known about the possible biological effects at low doses, for example, below 0.1 Gy, which is the dose range relevant to most radiation exposures of concern today. A conventional approach to radiation dose-response estimation based on simple parametric forms, such as the linear nonthreshold model, can be misleading in evaluating the risk and, in particular, its uncertainty at low doses. As an alternative approach, we consider a Bayesian semiparametric model that has a connected piece-wise-linear dose-response function with prior distributions having an autoregressive structure among the random slope coefficients defined over closely spaced dose categories. With a simulation study and application to analysis of cancer incidence data among Japanese atomic bomb survivors, we show that this approach can produce smooth and flexible dose-response estimation while reasonably handling the risk uncertainty at low doses and elsewhere. With relatively few assumptions and modeling options to be made by the analyst, the method can be particularly useful in assessing risks associated with low-dose radiation exposures. PMID:26581473
Bayesian parametrization of coarse-grain dissipative dynamics models
Dequidt, Alain; Solano Canchaya, Jose G.
2015-08-01
We introduce a new bottom-up method for the optimization of dissipative coarse-grain models. The method is based on Bayesian optimization of the likelihood to reproduce a coarse-grained reference trajectory obtained from analysis of a higher resolution molecular dynamics trajectory. This new method is related to force matching techniques, but using the total force on each grain averaged on a coarse time step instead of instantaneous forces. It has the advantage of not being limited to pairwise short-range interactions in the coarse-grain model and also yields an estimation of the friction parameter controlling the dynamics. The theory supporting the method is exposed in a practical perspective, with an analytical solution for the optimal set of parameters. The method was first validated by using it on a system with a known optimum. The new method was then tested on a simple system: n-pentane. The local molecular structure of the optimized model is in excellent agreement with the reference system. An extension of the method allows to get also an excellent agreement for the equilibrium density. As for the dynamic properties, they are also very satisfactory, but more sensitive to the choice of the coarse-grain representation. The quality of the final force field depends on the definition of the coarse grain degrees of freedom and interactions. We consider this method as a serious alternative to other methods like iterative Boltzmann inversion, force matching, and Green-Kubo formulae.
Cosmological parameter estimation and Bayesian model comparison using VSA data
Slosar, A; Cleary, K; Davies, R D; Davis, R J; Dickinson, C; Genova-Santos, R; Grainge, K; Gutíerrez, C M; Hafez, Y A; Hobson, M P; Jones, M E; Kneissl, R; Lancaster, K; Lasenby, A; Leahy, J P; Maisinger, K; Marshall, P J; Pooley, G G; Rebolo, R; Rubiño-Martín, J A; Rusholme, B A; Saunders, R D E; Savage, R; Scott, P F; Molina, P J S; Taylor, A C; Titterington, D; Waldram, E M; Watson, R A; Wilkinson, A; Slosar, Anze; Carreira, Pedro; Cleary, Kieran; Davies, Rod D.; Davis, Richard J.; Dickinson, Clive; Genova-Santos, Ricardo; Grainge, Keith; Gutierrez, Carlos M.; Hafez, Yaser A.; Hobson, Michael P.; Jones, Michael E.; Kneissl, Rudiger; Lancaster, Katy; Lasenby, Anthony; Maisinger, Klaus; Marshall, Phil J.; Pooley, Guy G.; Rebolo, Rafael; Rubino-Martin, Jose Alberto; Rusholme, Ben; Saunders, Richard D. E.; Savage, Richard; Scott, Paul F.; Molina, Pedro J. Sosa; Taylor, Angela C.; Titterington, David; Waldram, Elizabeth; Watson, Robert A.; Wilkinson, Althea
2003-01-01
We constrain the basic comological parameters using the first observations by the Very Small Array (VSA) in its extended configuration, together with existing cosmic microwave background data and other cosmological observations. We estimate cosmological parameters for four different models of increasing complexity. In each case, careful consideration is given to implied priors and the Bayesian evidence is calculated in order to perform model selection. We find that the data are most convincingly explained by a simple flat Lambda-CDM cosmology without tensor modes. In this case, combining just the VSA and COBE data sets yields the 68 per cent confidence intervals Omega_b h^2=0.034 (+0.007, -0.007), Omega_dm h^2 = 0.18 (+0.06, -0.04), h=0.72 (+0.15,-0.13), n_s=1.07 (+0.06,-0.06) and sigma_8=1.17 (+0.25, -0.20). The most general model considered includes spatial curvature, tensor modes, massive neutrinos and a parameterised equation of state for the dark energy. In this case, by combining all recent cosmological...
Institute of Scientific and Technical Information of China (English)
HU Zhao-yong
2005-01-01
Engineering diagnosis is essential to the operation of industrial equipment. The key to successful diagnosis is correct knowledge representation and reasoning. The Bayesian network is a powerful tool for it. This paper utilizes the Bayesian network to represent and reason diagnostic knowledge, named Bayesian diagnostic network. It provides a three-layer topologic structure based on operating conditions, possible faults and corresponding symptoms. The paper also discusses an approximate stochastic sampling algorithm. Then a practical Bayesian network for gas turbine diagnosis is constructed on a platform developed under a Visual C++ environment. It shows that the Bayesian network is a powerful model for representation and reasoning of diagnostic knowledge. The three-layer structure and the approximate algorithm are effective also.
Bayesian Influence Measures for Joint Models for Longitudinal and Survival Data
Zhu, Hongtu; Ibrahim, Joseph G.; Chi, Yueh-Yun; Tang, Niansheng
2012-01-01
This article develops a variety of influence measures for carrying out perturbation (or sensitivity) analysis to joint models of longitudinal and survival data (JMLS) in Bayesian analysis. A perturbation model is introduced to characterize individual and global perturbations to the three components of a Bayesian model, including the data points, the prior distribution, and the sampling distribution. Local influence measures are proposed to quantify the degree of these perturbations to the JML...
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
Modelling developmental instability as the joint action of noise and stability: a Bayesian approach
Directory of Open Access Journals (Sweden)
Lens Luc
2002-06-01
Full Text Available Abstract Background Fluctuating asymmetry is assumed to measure individual and population level developmental stability. The latter may in turn show an association with stress, which can be observed through asymmetry-stress correlations. However, the recent literature does not support an ubiquitous relationship. Very little is known why some studies show relatively strong associations while others completely fail to find such a correlation. We propose a new Bayesian statistical framework to examine these associations Results We are considering developmental stability – i.e. the individual buffering capacity – as the biologically relevant trait and show that (i little variation in developmental stability can explain observed variation in fluctuating asymmetry when the distribution of developmental stability is highly skewed, and (ii that a previously developed tool (i.e. the hypothetical repeatability of fluctuating asymmetry contains only limited information about variation in developmental stability, which stands in sharp contrast to the earlier established close association between the repeatability and developmental instability. Conclusion We provide tools to generate valuable information about the distribution of between-individual variation in developmental stability. A simple linear transformation of a previous model lead to completely different conclusions. Thus, theoretical modelling of asymmetry and stability appears to be very sensitive to the scale of inference. More research is urgently needed to get better insights in the developmental mechanisms of noise and stability. In spite of the fact that the model is likely to represent an oversimplification of reality, the accumulation of new insights could be incorporated in the Bayesian statistical approach to obtain more reliable estimation.
Directory of Open Access Journals (Sweden)
Wirichada Pan-ngum
Full Text Available BACKGROUND: Accuracy of rapid diagnostic tests for dengue infection has been repeatedly estimated by comparing those tests with reference assays. We hypothesized that those estimates might be inaccurate if the accuracy of the reference assays is not perfect. Here, we investigated this using statistical modeling. METHODS/PRINCIPAL FINDINGS: Data from a cohort study of 549 patients suspected of dengue infection presenting at Colombo North Teaching Hospital, Ragama, Sri Lanka, that described the application of our reference assay (a combination of Dengue IgM antibody capture ELISA and IgG antibody capture ELISA and of three rapid diagnostic tests (Panbio NS1 antigen, IgM antibody and IgG antibody rapid immunochromatographic cassette tests were re-evaluated using bayesian latent class models (LCMs. The estimated sensitivity and specificity of the reference assay were 62.0% and 99.6%, respectively. Prevalence of dengue infection (24.3%, and sensitivities and specificities of the Panbio NS1 (45.9% and 97.9%, IgM (54.5% and 95.5% and IgG (62.1% and 84.5% estimated by bayesian LCMs were significantly different from those estimated by assuming that the reference assay was perfect. Sensitivity, specificity, PPV and NPV for a combination of NS1, IgM and IgG cassette tests on admission samples were 87.0%, 82.8%, 62.0% and 95.2%, respectively. CONCLUSIONS: Our reference assay is an imperfect gold standard. In our setting, the combination of NS1, IgM and IgG rapid diagnostic tests could be used on admission to rule out dengue infection with a high level of accuracy (NPV 95.2%. Further evaluation of rapid diagnostic tests for dengue infection should include the use of appropriate statistical models.
Macroscopic Models of Clique Tree Growth for Bayesian Networks
National Aeronautics and Space Administration — In clique tree clustering, inference consists of propagation in a clique tree compiled from a Bayesian network. In this paper, we develop an analytical approach to...
Hierarchical Bayesian Spatio Temporal Model Comparison on the Earth Trapped Particle Forecast
International Nuclear Information System (INIS)
We compared two hierarchical Bayesian spatio temporal (HBST) results, Gaussian process (GP) and autoregressive (AR) models, on the Earth trapped particle forecast. Two models were employed on the South Atlantic Anomaly (SAA) region. Electron of >30 keV (mep0e1) from National Oceanic and Atmospheric Administration (NOAA) 15-18 satellites data was chosen as the particle modeled. We used two weeks data to perform the model fitting on a 5°x5° grid of longitude and latitude, and 31 August 2007 was set as the date of forecast. Three statistical validations were performed on the data, i.e. the root mean square error (RMSE), mean absolute percentage error (MAPE) and bias (BIAS). The statistical analysis showed that GP model performed better than AR with the average of RMSE = 0.38 and 0.63, MAPE = 11.98 and 17.30, and BIAS = 0.32 and 0.24, for GP and AR, respectively. Visual validation on both models with the NOAA map's also confirmed the superior of the GP than the AR. The variance of log flux minimum = 0.09 and 1.09, log flux maximum = 1.15 and 1.35, and in successively represents GP and AR
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.
Nitrate source apportionment in a subtropical watershed using Bayesian model
Energy Technology Data Exchange (ETDEWEB)
Yang, Liping; Han, Jiangpei; Xue, Jianlong; Zeng, Lingzao [College of Environmental and Natural Resource Sciences, Zhejiang Provincial Key Laboratory of Subtropical Soil and Plant Nutrition, Zhejiang University, Hangzhou, 310058 (China); Shi, Jiachun, E-mail: jcshi@zju.edu.cn [College of Environmental and Natural Resource Sciences, Zhejiang Provincial Key Laboratory of Subtropical Soil and Plant Nutrition, Zhejiang University, Hangzhou, 310058 (China); Wu, Laosheng, E-mail: laowu@zju.edu.cn [College of Environmental and Natural Resource Sciences, Zhejiang Provincial Key Laboratory of Subtropical Soil and Plant Nutrition, Zhejiang University, Hangzhou, 310058 (China); Jiang, Yonghai [State Key Laboratory of Environmental Criteria and Risk Assessment, Chinese Research Academy of Environmental Sciences, Beijing, 100012 (China)
2013-10-01
Nitrate (NO{sub 3}{sup −}) pollution in aquatic system is a worldwide problem. The temporal distribution pattern and sources of nitrate are of great concern for water quality. The nitrogen (N) cycling processes in a subtropical watershed located in Changxing County, Zhejiang Province, China were greatly influenced by the temporal variations of precipitation and temperature during the study period (September 2011 to July 2012). The highest NO{sub 3}{sup −} concentration in water was in May (wet season, mean ± SD = 17.45 ± 9.50 mg L{sup −1}) and the lowest concentration occurred in December (dry season, mean ± SD = 10.54 ± 6.28 mg L{sup −1}). Nevertheless, no water sample in the study area exceeds the WHO drinking water limit of 50 mg L{sup −1} NO{sub 3}{sup −}. Four sources of NO{sub 3}{sup −} (atmospheric deposition, AD; soil N, SN; synthetic fertilizer, SF; manure and sewage, M and S) were identified using both hydrochemical characteristics [Cl{sup −}, NO{sub 3}{sup −}, HCO{sub 3}{sup −}, SO{sub 4}{sup 2−}, Ca{sup 2+}, K{sup +}, Mg{sup 2+}, Na{sup +}, dissolved oxygen (DO)] and dual isotope approach (δ{sup 15}N–NO{sub 3}{sup −} and δ{sup 18}O–NO{sub 3}{sup −}). Both chemical and isotopic characteristics indicated that denitrification was not the main N cycling process in the study area. Using a Bayesian model (stable isotope analysis in R, SIAR), the contribution of each source was apportioned. Source apportionment results showed that source contributions differed significantly between the dry and wet season, AD and M and S contributed more in December than in May. In contrast, SN and SF contributed more NO{sub 3}{sup −} to water in May than that in December. M and S and SF were the major contributors in December and May, respectively. Moreover, the shortcomings and uncertainties of SIAR were discussed to provide implications for future works. With the assessment of temporal variation and sources of NO{sub 3}{sup −}, better
Nitrate source apportionment in a subtropical watershed using Bayesian model
International Nuclear Information System (INIS)
Nitrate (NO3−) pollution in aquatic system is a worldwide problem. The temporal distribution pattern and sources of nitrate are of great concern for water quality. The nitrogen (N) cycling processes in a subtropical watershed located in Changxing County, Zhejiang Province, China were greatly influenced by the temporal variations of precipitation and temperature during the study period (September 2011 to July 2012). The highest NO3− concentration in water was in May (wet season, mean ± SD = 17.45 ± 9.50 mg L−1) and the lowest concentration occurred in December (dry season, mean ± SD = 10.54 ± 6.28 mg L−1). Nevertheless, no water sample in the study area exceeds the WHO drinking water limit of 50 mg L−1 NO3−. Four sources of NO3− (atmospheric deposition, AD; soil N, SN; synthetic fertilizer, SF; manure and sewage, M and S) were identified using both hydrochemical characteristics [Cl−, NO3−, HCO3−, SO42−, Ca2+, K+, Mg2+, Na+, dissolved oxygen (DO)] and dual isotope approach (δ15N–NO3− and δ18O–NO3−). Both chemical and isotopic characteristics indicated that denitrification was not the main N cycling process in the study area. Using a Bayesian model (stable isotope analysis in R, SIAR), the contribution of each source was apportioned. Source apportionment results showed that source contributions differed significantly between the dry and wet season, AD and M and S contributed more in December than in May. In contrast, SN and SF contributed more NO3− to water in May than that in December. M and S and SF were the major contributors in December and May, respectively. Moreover, the shortcomings and uncertainties of SIAR were discussed to provide implications for future works. With the assessment of temporal variation and sources of NO3−, better agricultural management practices and sewage disposal programs can be implemented to sustain water quality in subtropical watersheds. - Highlights: • Nitrate concentration in water displayed
Bayesian auxiliary variable models for binary and multinomial regression
Holmes, C C; HELD, L.
2006-01-01
In this paper we discuss auxiliary variable approaches to Bayesian binary and multinomial regression. These approaches are ideally suited to automated Markov chain Monte Carlo simulation. In the first part we describe a simple technique using joint updating that improves the performance of the conventional probit regression algorithm. In the second part we discuss auxiliary variable methods for inference in Bayesian logistic regression, including covariate set uncertainty. Fina...
A Bayesian model of context-sensitive value attribution
Rigoli, Francesco; Friston, Karl J; Martinelli, Cristina; Selaković, Mirjana; Shergill, Sukhwinder S; Dolan, Raymond J
2016-01-01
Substantial evidence indicates that incentive value depends on an anticipation of rewards within a given context. However, the computations underlying this context sensitivity remain unknown. To address this question, we introduce a normative (Bayesian) account of how rewards map to incentive values. This assumes that the brain inverts a model of how rewards are generated. Key features of our account include (i) an influence of prior beliefs about the context in which rewards are delivered (weighted by their reliability in a Bayes-optimal fashion), (ii) the notion that incentive values correspond to precision-weighted prediction errors, (iii) and contextual information unfolding at different hierarchical levels. This formulation implies that incentive value is intrinsically context-dependent. We provide empirical support for this model by showing that incentive value is influenced by context variability and by hierarchically nested contexts. The perspective we introduce generates new empirical predictions that might help explaining psychopathologies, such as addiction. DOI: http://dx.doi.org/10.7554/eLife.16127.001 PMID:27328323
Visualizing statistical models and concepts
Farebrother, RW
2002-01-01
Examines classic algorithms, geometric diagrams, and mechanical principles for enhancing visualization of statistical estimation procedures and mathematical concepts in physics, engineering, and computer programming.
Complexity in Statistical Relational Learning : A Study on Learning Bayesian Logic Programs
Hagerf, Alexander
2015-01-01
Most work that is done within machine learning today uses statistical methods which assume that the data is identically and independently distributed. However, the problem domains that we face in the real world are often much more complicated and present both complex relational/logical parts as well as parts with uncertainty. Statistical relational learning (SRL) is a sub-ﬁeld of machine learning and A.I. that tries to solve these limitations by combining both relational and statistical learn...
Bayesian spatial modeling of cetacean sightings during a seismic acquisition survey.
Vilela, Raul; Pena, Ursula; Esteban, Ruth; Koemans, Robin
2016-08-15
A visual monitoring of marine mammals was carried out during a seismic acquisition survey performed in waters south of Portugal with the aim of assessing the likelihood of encountering Mysticeti species in this region as well as to determine the impact of the seismic activity upon encounter. Sightings and effort data were assembled with a range of environmental variables at different lags, and a Bayesian site-occupancy modeling approach was used to develop prediction maps and evaluate how species-specific habitat conditions evolved throughout the presence or not of seismic activity. No statistical evidence of a decrease in the sighting rates of Mysticeti by comparison to source activity was found. Indeed, it was found how Mysticeti distribution during the survey period was driven solely by environmental variables. Although further research is needed, possible explanations may include anthropogenic noise habituation and zone of seismic activity coincident with a naturally low density area. PMID:27210556
Mugnes, J-M
2015-01-01
Spectral analysis is a powerful tool to investigate stellar properties and it has been widely used for decades now. However, the methods considered to perform this kind of analysis are mostly based on iteration among a few diagnostic lines to determine the stellar parameters. While these methods are often simple and fast, they can lead to errors and large uncertainties due to the required assumptions. Here we present a method based on Bayesian statistics to find simultaneously the best combination of effective temperature, surface gravity, projected rotational velocity, and microturbulence velocity, using all the available spectral lines. Different tests are discussed to demonstrate the strength of our method, which we apply to 54 mid-resolution spectra of field and cluster B stars obtained at the Observatoire du Mont-M\\'egantic. We compare our results with those found in the literature. Differences are seen which are well explained by the different methods used. We conclude that the B-star microturbulence ve...
Directory of Open Access Journals (Sweden)
M.M. Mohie EL-Din
2016-03-01
Full Text Available In this paper, for Weibull subfamily of Morgenstern family, the joint density of the concomitants of generalized order statistics (GOS's is used to obtain the maximum likelihood estimates (MLE and Bayes estimates for the distribution parameters. Applications of these results for concomitants of order statistics are presented.
Bayesian Safety Risk Modeling of Human-Flightdeck Automation Interaction
Ancel, Ersin; Shih, Ann T.
2015-01-01
Usage of automatic systems in airliners has increased fuel efficiency, added extra capabilities, enhanced safety and reliability, as well as provide improved passenger comfort since its introduction in the late 80's. However, original automation benefits, including reduced flight crew workload, human errors or training requirements, were not achieved as originally expected. Instead, automation introduced new failure modes, redistributed, and sometimes increased workload, brought in new cognitive and attention demands, and increased training requirements. Modern airliners have numerous flight modes, providing more flexibility (and inherently more complexity) to the flight crew. However, the price to pay for the increased flexibility is the need for increased mode awareness, as well as the need to supervise, understand, and predict automated system behavior. Also, over-reliance on automation is linked to manual flight skill degradation and complacency in commercial pilots. As a result, recent accidents involving human errors are often caused by the interactions between humans and the automated systems (e.g., the breakdown in man-machine coordination), deteriorated manual flying skills, and/or loss of situational awareness due to heavy dependence on automated systems. This paper describes the development of the increased complexity and reliance on automation baseline model, named FLAP for FLightdeck Automation Problems. The model development process starts with a comprehensive literature review followed by the construction of a framework comprised of high-level causal factors leading to an automation-related flight anomaly. The framework was then converted into a Bayesian Belief Network (BBN) using the Hugin Software v7.8. The effects of automation on flight crew are incorporated into the model, including flight skill degradation, increased cognitive demand and training requirements along with their interactions. Besides flight crew deficiencies, automation system
Probing NWP model deficiencies by statistical postprocessing
DEFF Research Database (Denmark)
Rosgaard, Martin Haubjerg; Nielsen, Henrik Aalborg; Nielsen, Torben S.;
2016-01-01
The objective in this article is twofold. On one hand, a Model Output Statistics (MOS) framework for improved wind speed forecast accuracy is described and evaluated. On the other hand, the approach explored identifies unintuitive explanatory value from a diagnostic variable in an operational....... Based on the statistical model candidates inferred from the data, the lifted index NWP model diagnostic is consistently found among the NWP model predictors of the best performing statistical models across sites....
The Lumiere Project: Bayesian User Modeling for Inferring the Goals and Needs of Software Users
Horvitz, Eric J.; Breese, John S.; Heckerman, David; Hovel, David; Rommelse, Koos
2013-01-01
The Lumiere Project centers on harnessing probability and utility to provide assistance to computer software users. We review work on Bayesian user models that can be employed to infer a users needs by considering a user's background, actions, and queries. Several problems were tackled in Lumiere research, including (1) the construction of Bayesian models for reasoning about the time-varying goals of computer users from their observed actions and queries, (2) gaining access to a stream of eve...
Feroz, F.; Hobson, M. P.; Zwart, J T L; Saunders, R. D. E.; Grainge, K. J. B.
2008-01-01
We present a Bayesian approach to modelling galaxy clusters using multi-frequency pointed observations from telescopes that exploit the Sunyaev--Zel'dovich effect. We use the recently developed MultiNest technique (Feroz, Hobson & Bridges, 2008) to explore the high-dimensional parameter spaces and also to calculate the Bayesian evidence. This permits robust parameter estimation as well as model comparison. Tests on simulated Arcminute Microkelvin Imager observations of a cluster, in the prese...
Fernandes, Ricardo; Millard, Andrew R.; Brabec, Marek; Nadeau, Marie-Josée; Grootes, Pieter
2014-01-01
Human and animal diet reconstruction studies that rely on tissue chemical signatures aim at providing estimates on the relative intake of potential food groups. However, several sources of uncertainty need to be considered when handling data. Bayesian mixing models provide a natural platform to handle diverse sources of uncertainty while allowing the user to contribute with prior expert information. The Bayesian mixing model FRUITS (Food Reconstruction Using Isotopic Transferred Signals) was ...
Andrew Sanford; Imad Moosa
2015-01-01
This paper describes the development of a tool, based on a Bayesian network model, that provides posteriori predictions of operational risk events, aggregate operational loss distributions, and Operational Value-at-Risk, for a structured finance operations unit located within one of Australia's major banks. The Bayesian network, based on a previously developed causal framework, has been designed to model the smaller and more frequent, attritional operational loss events. Given the limited ava...
Cahill, N.; Kemp, A. C.; Horton, B. P.; Parnell, A.C.
2015-01-01
We present a holistic Bayesian hierarchical model for reconstructing the continuous and dynamic evolution of relative sea-level (RSL) change with fully quantified uncertainty. The reconstruction is produced from biological (foraminifera) and geochemical (δ13C) sea-level indicators preserved in dated cores of salt-marsh sediment. Our model is comprised of three modules: (1) A Bayesian transfer function for the calibration of foraminifera into tidal elevation,...
Cahill, Niamh; Kemp, Andrew C.; Horton, Benjamin P.; Andrew C Parnell
2016-01-01
We present a Bayesian hierarchical model for reconstructing the continuous and dynamic evolution of relative sea-level (RSL) change with quantified uncertainty. The reconstruction is produced from biological (foraminifera) and geochemical (δ13C) sea-level indicators preserved in dated cores of salt-marsh sediment. Our model is comprised of three modules: (1) a new Bayesian transfer (B-TF) function for the calibration of biological indicators into tidal elevation, which is fl...
A Bayesian approach for temporally scaling climate for modeling ecological systems.
Post van der Burg, Max; Anteau, Michael J; McCauley, Lisa A; Wiltermuth, Mark T
2016-05-01
With climate change becoming more of concern, many ecologists are including climate variables in their system and statistical models. The Standardized Precipitation Evapotranspiration Index (SPEI) is a drought index that has potential advantages in modeling ecological response variables, including a flexible computation of the index over different timescales. However, little development has been made in terms of the choice of timescale for SPEI. We developed a Bayesian modeling approach for estimating the timescale for SPEI and demonstrated its use in modeling wetland hydrologic dynamics in two different eras (i.e., historical [pre-1970] and contemporary [post-2003]). Our goal was to determine whether differences in climate between the two eras could explain changes in the amount of water in wetlands. Our results showed that wetland water surface areas tended to be larger in wetter conditions, but also changed less in response to climate fluctuations in the contemporary era. We also found that the average timescale parameter was greater in the historical period, compared with the contemporary period. We were not able to determine whether this shift in timescale was due to a change in the timing of wet-dry periods or whether it was due to changes in the way wetlands responded to climate. Our results suggest that perhaps some interaction between climate and hydrologic response may be at work, and further analysis is needed to determine which has a stronger influence. Despite this, we suggest that our modeling approach enabled us to estimate the relevant timescale for SPEI and make inferences from those estimates. Likewise, our approach provides a mechanism for using prior information with future data to assess whether these patterns may continue over time. We suggest that ecologists consider using temporally scalable climate indices in conjunction with Bayesian analysis for assessing the role of climate in ecological systems. PMID:27217947
A Bayesian approach for temporally scaling climate for modeling ecological systems
Post van der Burg, Max; Anteau, Michael J.; McCauley, Lisa A.; Wiltermuth, Mark T.
2016-01-01
With climate change becoming more of concern, many ecologists are including climate variables in their system and statistical models. The Standardized Precipitation Evapotranspiration Index (SPEI) is a drought index that has potential advantages in modeling ecological response variables, including a flexible computation of the index over different timescales. However, little development has been made in terms of the choice of timescale for SPEI. We developed a Bayesian modeling approach for estimating the timescale for SPEI and demonstrated its use in modeling wetland hydrologic dynamics in two different eras (i.e., historical [pre-1970] and contemporary [post-2003]). Our goal was to determine whether differences in climate between the two eras could explain changes in the amount of water in wetlands. Our results showed that wetland water surface areas tended to be larger in wetter conditions, but also changed less in response to climate fluctuations in the contemporary era. We also found that the average timescale parameter was greater in the historical period, compared with the contemporary period. We were not able to determine whether this shift in timescale was due to a change in the timing of wet–dry periods or whether it was due to changes in the way wetlands responded to climate. Our results suggest that perhaps some interaction between climate and hydrologic response may be at work, and further analysis is needed to determine which has a stronger influence. Despite this, we suggest that our modeling approach enabled us to estimate the relevant timescale for SPEI and make inferences from those estimates. Likewise, our approach provides a mechanism for using prior information with future data to assess whether these patterns may continue over time. We suggest that ecologists consider using temporally scalable climate indices in conjunction with Bayesian analysis for assessing the role of climate in ecological systems.
Enhanced Bayesian modelling in BAPS software for learning genetic structures of populations
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Sirén Jukka
2008-12-01
Full Text Available Abstract Background During the most recent decade many Bayesian statistical models and software for answering questions related to the genetic structure underlying population samples have appeared in the scientific literature. Most of these methods utilize molecular markers for the inferences, while some are also capable of handling DNA sequence data. In a number of earlier works, we have introduced an array of statistical methods for population genetic inference that are implemented in the software BAPS. However, the complexity of biological problems related to genetic structure analysis keeps increasing such that in many cases the current methods may provide either inappropriate or insufficient solutions. Results We discuss the necessity of enhancing the statistical approaches to face the challenges posed by the ever-increasing amounts of molecular data generated by scientists over a wide range of research areas and introduce an array of new statistical tools implemented in the most recent version of BAPS. With these methods it is possible, e.g., to fit genetic mixture models using user-specified numbers of clusters and to estimate levels of admixture under a genetic linkage model. Also, alleles representing a different ancestry compared to the average observed genomic positions can be tracked for the sampled individuals, and a priori specified hypotheses about genetic population structure can be directly compared using Bayes' theorem. In general, we have improved further the computational characteristics of the algorithms behind the methods implemented in BAPS facilitating the analyses of large and complex datasets. In particular, analysis of a single dataset can now be spread over multiple computers using a script interface to the software. Conclusion The Bayesian modelling methods introduced in this article represent an array of enhanced tools for learning the genetic structure of populations. Their implementations in the BAPS software are
Bayesian network as a modelling tool for risk management in agriculture
DEFF Research Database (Denmark)
Rasmussen, Svend; Madsen, Anders L.; Lund, Mogens
this paper we use Bayesian networks as an integrated modelling approach for representing uncertainty and analysing risk management in agriculture. It is shown how historical farm account data may be efficiently used to estimate conditional probabilities, which are the core elements in Bayesian network...... models. We further show how the Bayesian network model RiBay is used for stochastic simulation of farm income, and we demonstrate how RiBay can be used to simulate risk management at the farm level. It is concluded that the key strength of a Bayesian network is the transparency of assumptions, and that......The importance of risk management increases as farmers become more exposed to risk. But risk management is a difficult topic because income risk is the result of the complex interaction of multiple risk factors combined with the effect of an increasing array of possible risk management tools. In...
Gong, Maozhen
Selecting an appropriate prior distribution is a fundamental issue in Bayesian Statistics. In this dissertation, under the framework provided by Berger and Bernardo, I derive the reference priors for several models which include: Analysis of Variance (ANOVA)/Analysis of Covariance (ANCOVA) models with a categorical variable under common ordering constraints, the conditionally autoregressive (CAR) models and the simultaneous autoregressive (SAR) models with a spatial autoregression parameter rho considered. The performances of reference priors for ANOVA/ANCOVA models are evaluated by simulation studies with comparisons to Jeffreys' prior and Least Squares Estimation (LSE). The priors are then illustrated in a Bayesian model of the "Risk of Type 2 Diabetes in New Mexico" data, where the relationship between the type 2 diabetes risk (through Hemoglobin A1c) and different smoking levels is investigated. In both simulation studies and real data set modeling, the reference priors that incorporate internal order information show good performances and can be used as default priors. The reference priors for the CAR and SAR models are also illustrated in the "1999 SAT State Average Verbal Scores" data with a comparison to a Uniform prior distribution. Due to the complexity of the reference priors for both CAR and SAR models, only a portion (12 states in the Midwest) of the original data set is considered. The reference priors can give a different marginal posterior distribution compared to a Uniform prior, which provides an alternative for prior specifications for areal data in Spatial statistics.
Raje, D.; Krishnan, R.
2012-08-01
Macroscale hydrologic models (MHMs) were developed to study changes in land surface hydrology due to changing climate over large domains, such as continents or large river basins. However, there are many sources of uncertainty introduced in MHM hydrological simulation, such as model structure error, ineffective model parameters, and low-accuracy model input or validation data. It is hence important to model the uncertainty arising in projection results from an MHM. The objective of this study is to present a Bayesian statistical inference framework for parameter uncertainty modeling of a macroscale hydrologic model. The Bayesian approach implemented using Markov Chain Monte Carlo (MCMC) methods is used in this study to model uncertainty arising from calibration parameters of the Variable Infiltration Capacity (VIC) MHM. The study examines large-scale hydrologic impacts for Indian river basins and changes in discharges for three major river basins with distinct climatic and geographic characteristics, under climate change. Observed/reanalysis meteorological variables such as precipitation, temperature and wind speed are used to drive the VIC macroscale hydrologic model. An objective function describing the fit between observed and simulated discharges at four stations is used to compute the likelihood of the parameters. An MCMC approach using the Metropolis-Hastings algorithm is used to update probability distributions of the parameters. For future hydrologic simulations, bias-corrected GCM projections of climatic variables are used. The posterior distributions of VIC parameters are used for projection of 5th and 95th percentile discharge statistics at four stations, namely, Farakka, Jamtara, Garudeshwar, and Vijayawada for an ensemble of three GCMs and three scenarios, for two time slices. Spatial differences in uncertainty projections of runoff and evapotranspiration for years 2056-2065 for the a1b scenario at the 5th and 95th percentile levels are also projected
Development of a Bayesian Belief Network Runway Incursion and Excursion Model
Green, Lawrence L.
2014-01-01
In a previous work, a statistical analysis of runway incursion (RI) event data was conducted to ascertain the relevance of this data to the top ten Technical Challenges (TC) of the National Aeronautics and Space Administration (NASA) Aviation Safety Program (AvSP). The study revealed connections to several of the AvSP top ten TC and identified numerous primary causes and contributing factors of RI events. The statistical analysis served as the basis for developing a system-level Bayesian Belief Network (BBN) model for RI events, also previously reported. Through literature searches and data analysis, this RI event network has now been extended to also model runway excursion (RE) events. These RI and RE event networks have been further modified and vetted by a Subject Matter Expert (SME) panel. The combined system-level BBN model will allow NASA to generically model the causes of RI and RE events and to assess the effectiveness of technology products being developed under NASA funding. These products are intended to reduce the frequency of runway safety incidents/accidents, and to improve runway safety in general. The development and structure of the BBN for both RI and RE events are documented in this paper.
ESTIMATE OF THE HYPSOMETRIC RELATIONSHIP WITH NONLINEAR MODELS FITTED BY EMPIRICAL BAYESIAN METHODS
Directory of Open Access Journals (Sweden)
Monica Fabiana Bento Moreira
2015-09-01
Full Text Available In this paper we propose a Bayesian approach to solve the inference problem with restriction on parameters, regarding to nonlinear models used to represent the hypsometric relationship in clones of Eucalyptus sp. The Bayesian estimates are calculated using Monte Carlo Markov Chain (MCMC method. The proposed method was applied to different groups of actual data from which two were selected to show the results. These results were compared to the results achieved by the minimum square method, highlighting the superiority of the Bayesian approach, since this approach always generate the biologically consistent results for hipsometric relationship.
Predicting water main failures using Bayesian model averaging and survival modelling approach
International Nuclear Information System (INIS)
To develop an effective preventive or proactive repair and replacement action plan, water utilities often rely on water main failure prediction models. However, in predicting the failure of water mains, uncertainty is inherent regardless of the quality and quantity of data used in the model. To improve the understanding of water main failure, a Bayesian framework is developed for predicting the failure of water mains considering uncertainties. In this study, Bayesian model averaging method (BMA) is presented to identify the influential pipe-dependent and time-dependent covariates considering model uncertainties whereas Bayesian Weibull Proportional Hazard Model (BWPHM) is applied to develop the survival curves and to predict the failure rates of water mains. To accredit the proposed framework, it is implemented to predict the failure of cast iron (CI) and ductile iron (DI) pipes of the water distribution network of the City of Calgary, Alberta, Canada. Results indicate that the predicted 95% uncertainty bounds of the proposed BWPHMs capture effectively the observed breaks for both CI and DI water mains. Moreover, the performance of the proposed BWPHMs are better compare to the Cox-Proportional Hazard Model (Cox-PHM) for considering Weibull distribution for the baseline hazard function and model uncertainties. - Highlights: • Prioritize rehabilitation and replacements (R/R) strategies of water mains. • Consider the uncertainties for the failure prediction. • Improve the prediction capability of the water mains failure models. • Identify the influential and appropriate covariates for different models. • Determine the effects of the covariates on failure
Approximate Bayesian inference in semi-mechanistic models
Aderhold, Andrej; Husmeier, Dirk; Grzegorczyk, Marco
2016-01-01
Inference of interaction networks represented by systems of differential equations is a challenging problem in many scientific disciplines. In the present article, we follow a semi-mechanistic modelling approach based on gradient matching. We investigate the extent to which key factors, including the kinetic model, statistical formulation and numerical methods, impact upon performance at network reconstruction. We emphasize general lessons for computational statisticians when faced with the c...
Maximin and Bayesian Optimal Designs for Regression Models
Dette, Holger; Haines, Linda M.; Imhof, Lorens A.
2003-01-01
For many problems of statistical inference in regression modelling, the Fisher information matrix depends on certain nuisance parameters which are unknown and which enter the model nonlinearly. A common strategy to deal with this problem within the context of design is to construct maximin optimal designs as those designs which maximize the minimum value of a real valued (standardized) function of the Fisher information matrix, where the minimum is taken over a specified range of the unknown ...
Gilkey, Kelly M.; Myers, Jerry G.; McRae, Michael P.; Griffin, Elise A.; Kallrui, Aditya S.
2012-01-01
The Exploration Medical Capability project is creating a catalog of risk assessments using the Integrated Medical Model (IMM). The IMM is a software-based system intended to assist mission planners in preparing for spaceflight missions by helping them to make informed decisions about medical preparations and supplies needed for combating and treating various medical events using Probabilistic Risk Assessment. The objective is to use statistical analyses to inform the IMM decision tool with estimated probabilities of medical events occurring during an exploration mission. Because data regarding astronaut health are limited, Bayesian statistical analysis is used. Bayesian inference combines prior knowledge, such as data from the general U.S. population, the U.S. Submarine Force, or the analog astronaut population located at the NASA Johnson Space Center, with observed data for the medical condition of interest. The posterior results reflect the best evidence for specific medical events occurring in flight. Bayes theorem provides a formal mechanism for combining available observed data with data from similar studies to support the quantification process. The IMM team performed Bayesian updates on the following medical events: angina, appendicitis, atrial fibrillation, atrial flutter, dental abscess, dental caries, dental periodontal disease, gallstone disease, herpes zoster, renal stones, seizure, and stroke.
Bayesian Model Averaging of Artificial Intelligence Models for Hydraulic Conductivity Estimation
Nadiri, A.; Chitsazan, N.; Tsai, F. T.; Asghari Moghaddam, A.
2012-12-01
This research presents a Bayesian artificial intelligence model averaging (BAIMA) method that incorporates multiple artificial intelligence (AI) models to estimate hydraulic conductivity and evaluate estimation uncertainties. Uncertainty in the AI model outputs stems from error in model input as well as non-uniqueness in selecting different AI methods. Using one single AI model tends to bias the estimation and underestimate uncertainty. BAIMA employs Bayesian model averaging (BMA) technique to address the issue of using one single AI model for estimation. BAIMA estimates hydraulic conductivity by averaging the outputs of AI models according to their model weights. In this study, the model weights were determined using the Bayesian information criterion (BIC) that follows the parsimony principle. BAIMA calculates the within-model variances to account for uncertainty propagation from input data to AI model output. Between-model variances are evaluated to account for uncertainty due to model non-uniqueness. We employed Takagi-Sugeno fuzzy logic (TS-FL), artificial neural network (ANN) and neurofuzzy (NF) to estimate hydraulic conductivity for the Tasuj plain aquifer, Iran. BAIMA combined three AI models and produced better fitting than individual models. While NF was expected to be the best AI model owing to its utilization of both TS-FL and ANN models, the NF model is nearly discarded by the parsimony principle. The TS-FL model and the ANN model showed equal importance although their hydraulic conductivity estimates were quite different. This resulted in significant between-model variances that are normally ignored by using one AI model.
Bayesian Generalized Rating Curves
Helgi Sigurðarson 1985
2014-01-01
A rating curve is a curve or a model that describes the relationship between water elevation, or stage, and discharge in an observation site in a river. The rating curve is fit from paired observations of stage and discharge. The rating curve then predicts discharge given observations of stage and this methodology is applied as stage is substantially easier to directly observe than discharge. In this thesis a statistical rating curve model is proposed working within the framework of Bayesian...
Gelman, Andrew; Stern, Hal S; Dunson, David B; Vehtari, Aki; Rubin, Donald B
2013-01-01
FUNDAMENTALS OF BAYESIAN INFERENCEProbability and InferenceSingle-Parameter Models Introduction to Multiparameter Models Asymptotics and Connections to Non-Bayesian ApproachesHierarchical ModelsFUNDAMENTALS OF BAYESIAN DATA ANALYSISModel Checking Evaluating, Comparing, and Expanding ModelsModeling Accounting for Data Collection Decision AnalysisADVANCED COMPUTATION Introduction to Bayesian Computation Basics of Markov Chain Simulation Computationally Efficient Markov Chain Simulation Modal and Distributional ApproximationsREGRESSION MODELS Introduction to Regression Models Hierarchical Linear
Bayesian Network Based Fault Prognosis via Bond Graph Modeling of High-Speed Railway Traction Device
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Yunkai Wu
2015-01-01
component-level faults accurately for a high-speed railway traction system, a fault prognosis approach via Bayesian network and bond graph modeling techniques is proposed. The inherent structure of a railway traction system is represented by bond graph model, based on which a multilayer Bayesian network is developed for fault propagation analysis and fault prediction. For complete and incomplete data sets, two different parameter learning algorithms such as Bayesian estimation and expectation maximization (EM algorithm are adopted to determine the conditional probability table of the Bayesian network. The proposed prognosis approach using Pearl’s polytree propagation algorithm for joint probability reasoning can predict the failure probabilities of leaf nodes based on the current status of root nodes. Verification results in a high-speed railway traction simulation system can demonstrate the effectiveness of the proposed approach.
Bayesian log-periodic model for financial crashes
DEFF Research Database (Denmark)
Rodríguez-Caballero, Carlos Vladimir; Knapik, Oskar
2014-01-01
This paper introduces a Bayesian approach in econophysics literature about financial bubbles in order to estimate the most probable time for a financial crash to occur. To this end, we propose using noninformative prior distributions to obtain posterior distributions. Since these distributions...... part of the study, we analyze a well-known example of financial bubble – the S&P 500 1987 crash – to show the usefulness of the three methods under consideration and crashes of Merval-94, Bovespa-97, IPCMX-94, Hang Seng-97 using the simplest method. The novelty of this research is that the Bayesian...
Gustafson, Paul
2014-01-01
Partially identified models are characterized by the distribution of observables being compatible with a set of values for the target parameter, rather than a single value. This set is often referred to as an identification region. From a non-Bayesian point of view, the identification region is the object revealed to the investigator in the limit of increasing sample size. Conversely, a Bayesian analysis provides the identification region plus the limiting posterior distribution over this reg...
Bayesian inference of BWR model parameters by Markov chain Monte Carlo
International Nuclear Information System (INIS)
In this paper, the Markov chain Monte Carlo approach to Bayesian inference is applied for estimating the parameters of a reduced-order model of the dynamics of a boiling water reactor system. A Bayesian updating strategy is devised to progressively refine the estimates, as newly measured data become available. Finally, the technique is used for detecting parameter changes during the system lifetime, e.g. due to component degradation
Model Data Fusion: developing Bayesian inversion to constrain equilibrium and mode structure
Hole, M. J.; von Nessi, G.; Bertram, J; J. Svensson; Appel, L. C.; Blackwell, B. D.; Dewar, R L; Howard, J
2010-01-01
Recently, a new probabilistic "data fusion" framework based on Bayesian principles has been developed on JET and W7-AS. The Bayesian analysis framework folds in uncertainties and inter-dependencies in the diagnostic data and signal forward-models, together with prior knowledge of the state of the plasma, to yield predictions of internal magnetic structure. A feature of the framework, known as MINERVA (J. Svensson, A. Werner, Plasma Physics and Controlled Fusion 50, 085022, 2008), is the infer...
Gruber, Lutz F.; West, Mike
2016-01-01
The recently introduced class of simultaneous graphical dynamic linear models (SGDLMs) defines an ability to scale on-line Bayesian analysis and forecasting to higher-dimensional time series. This paper advances the methodology of SGDLMs, developing and embedding a novel, adaptive method of simultaneous predictor selection in forward filtering for on-line learning and forecasting. The advances include developments in Bayesian computation for scalability, and a case study in exploring the resu...
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Gao Shouguo
2011-08-01
Full Text Available Abstract Background Bayesian Network (BN is a powerful approach to reconstructing genetic regulatory networks from gene expression data. However, expression data by itself suffers from high noise and lack of power. Incorporating prior biological knowledge can improve the performance. As each type of prior knowledge on its own may be incomplete or limited by quality issues, integrating multiple sources of prior knowledge to utilize their consensus is desirable. Results We introduce a new method to incorporate the quantitative information from multiple sources of prior knowledge. It first uses the Naïve Bayesian classifier to assess the likelihood of functional linkage between gene pairs based on prior knowledge. In this study we included cocitation in PubMed and schematic similarity in Gene Ontology annotation. A candidate network edge reservoir is then created in which the copy number of each edge is proportional to the estimated likelihood of linkage between the two corresponding genes. In network simulation the Markov Chain Monte Carlo sampling algorithm is adopted, and samples from this reservoir at each iteration to generate new candidate networks. We evaluated the new algorithm using both simulated and real gene expression data including that from a yeast cell cycle and a mouse pancreas development/growth study. Incorporating prior knowledge led to a ~2 fold increase in the number of known transcription regulations recovered, without significant change in false positive rate. In contrast, without the prior knowledge BN modeling is not always better than a random selection, demonstrating the necessity in network modeling to supplement the gene expression data with additional information. Conclusion our new development provides a statistical means to utilize the quantitative information in prior biological knowledge in the BN modeling of gene expression data, which significantly improves the performance.
Directory of Open Access Journals (Sweden)
Mihaela Simionescu
2014-12-01
Full Text Available There are many types of econometric models used in predicting the inflation rate, but in this study we used a Bayesian shrinkage combination approach. This methodology is used in order to improve the predictions accuracy by including information that is not captured by the econometric models. Therefore, experts’ forecasts are utilized as prior information, for Romania these predictions being provided by Institute for Economic Forecasting (Dobrescu macromodel, National Commission for Prognosis and European Commission. The empirical results for Romanian inflation show the superiority of a fixed effects model compared to other types of econometric models like VAR, Bayesian VAR, simultaneous equations model, dynamic model, log-linear model. The Bayesian combinations that used experts’ predictions as priors, when the shrinkage parameter tends to infinite, improved the accuracy of all forecasts based on individual models, outperforming also zero and equal weights predictions and naïve forecasts.
Bayesian estimation of regularization parameters for deformable surface models
Energy Technology Data Exchange (ETDEWEB)
Cunningham, G.S.; Lehovich, A.; Hanson, K.M.
1999-02-20
In this article the authors build on their past attempts to reconstruct a 3D, time-varying bolus of radiotracer from first-pass data obtained by the dynamic SPECT imager, FASTSPECT, built by the University of Arizona. The object imaged is a CardioWest total artificial heart. The bolus is entirely contained in one ventricle and its associated inlet and outlet tubes. The model for the radiotracer distribution at a given time is a closed surface parameterized by 482 vertices that are connected to make 960 triangles, with nonuniform intensity variations of radiotracer allowed inside the surface on a voxel-to-voxel basis. The total curvature of the surface is minimized through the use of a weighted prior in the Bayesian framework, as is the weighted norm of the gradient of the voxellated grid. MAP estimates for the vertices, interior intensity voxels and background count level are produced. The strength of the priors, or hyperparameters, are determined by maximizing the probability of the data given the hyperparameters, called the evidence. The evidence is calculated by first assuming that the posterior is approximately normal in the values of the vertices and voxels, and then by evaluating the integral of the multi-dimensional normal distribution. This integral (which requires evaluating the determinant of a covariance matrix) is computed by applying a recent algorithm from Bai et. al. that calculates the needed determinant efficiently. They demonstrate that the radiotracer is highly inhomogeneous in early time frames, as suspected in earlier reconstruction attempts that assumed a uniform intensity of radiotracer within the closed surface, and that the optimal choice of hyperparameters is substantially different for different time frames.
Bayesian estimation of regularization parameters for deformable surface models
International Nuclear Information System (INIS)
In this article the authors build on their past attempts to reconstruct a 3D, time-varying bolus of radiotracer from first-pass data obtained by the dynamic SPECT imager, FASTSPECT, built by the University of Arizona. The object imaged is a CardioWest total artificial heart. The bolus is entirely contained in one ventricle and its associated inlet and outlet tubes. The model for the radiotracer distribution at a given time is a closed surface parameterized by 482 vertices that are connected to make 960 triangles, with nonuniform intensity variations of radiotracer allowed inside the surface on a voxel-to-voxel basis. The total curvature of the surface is minimized through the use of a weighted prior in the Bayesian framework, as is the weighted norm of the gradient of the voxellated grid. MAP estimates for the vertices, interior intensity voxels and background count level are produced. The strength of the priors, or hyperparameters, are determined by maximizing the probability of the data given the hyperparameters, called the evidence. The evidence is calculated by first assuming that the posterior is approximately normal in the values of the vertices and voxels, and then by evaluating the integral of the multi-dimensional normal distribution. This integral (which requires evaluating the determinant of a covariance matrix) is computed by applying a recent algorithm from Bai et. al. that calculates the needed determinant efficiently. They demonstrate that the radiotracer is highly inhomogeneous in early time frames, as suspected in earlier reconstruction attempts that assumed a uniform intensity of radiotracer within the closed surface, and that the optimal choice of hyperparameters is substantially different for different time frames
Mapping the Obesity in Iran by Bayesian Spatial Model
Directory of Open Access Journals (Sweden)
Maryam Farhadian
2013-06-01
Full Text Available Background: One of the methods used in the analysis of data related to diseases, and their underlying reasons is drawing geographical map. Mapping diseases is a valuable tool to determine the regions of high rate of infliction requiring therapeutic interventions. The objective of this study was to investigate obesity pattern in Iran by drawing geographical maps based on Bayesian spatial model to recognize the pattern of the understudy symptom more carefully.Methods: The data of this study consisted of the number of obese people in provinces of Iran in terms of sex based on the reports of non-contagious disease's risks in 30 provinces by the Iran MSRT disease center in 2007. The analysis of data was carried out by software R and Open BUGS. In addition, the data required for the adjacency matrix were produced by Geo bugs software.Results: The greatest percentage of obese people in all age ranges (15-64 is 17.8 for men in Mazandaran and the lowest is 4.9 in Sistan and Baluchestan. For women the highest and lowest are 29.9 and 11.9 in Mazandaran and Hormozgan, respectively. Mazandaran was considered the province of the greatest odds ratio of obesity for men and women.Conclusion: Recognizing the geographical distribution and the regions of high risk of obesity is the prerequisite of decision making in management and planning for health system of the country. The results can be applied in allocating correct resources between different regions of Iran.
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
Bayesian Analysis of Geostatistical Models With an Auxiliary Lattice
Park, Jincheol
2012-04-01
The Gaussian geostatistical model has been widely used for modeling spatial data. However, this model suffers from a severe difficulty in computation: it requires users to invert a large covariance matrix. This is infeasible when the number of observations is large. In this article, we propose an auxiliary lattice-based approach for tackling this difficulty. By introducing an auxiliary lattice to the space of observations and defining a Gaussian Markov random field on the auxiliary lattice, our model completely avoids the requirement of matrix inversion. It is remarkable that the computational complexity of our method is only O(n), where n is the number of observations. Hence, our method can be applied to very large datasets with reasonable computational (CPU) times. The numerical results indicate that our model can approximate Gaussian random fields very well in terms of predictions, even for those with long correlation lengths. For real data examples, our model can generally outperform conventional Gaussian random field models in both prediction errors and CPU times. Supplemental materials for the article are available online. © 2012 American Statistical Association, Institute of Mathematical Statistics, and Interface Foundation of North America.
A survey of Bayesian predictive methods for model assessment, selection and comparison
Directory of Open Access Journals (Sweden)
Aki Vehtari
2012-01-01
Full Text Available To date, several methods exist in the statistical literature formodel assessment, which purport themselves specifically as Bayesian predictive methods. The decision theoretic assumptions on which these methodsare based are not always clearly stated in the original articles, however.The aim of this survey is to provide a unified review of Bayesian predictivemodel assessment and selection methods, and of methods closely related tothem. We review the various assumptions that are made in this context anddiscuss the connections between different approaches, with an emphasis onhow each method approximates the expected utility of using a Bayesianmodel for the purpose of predicting future data.
Bayesian Soft Sensing in Cold Sheet Rolling
Czech Academy of Sciences Publication Activity Database
Dedecius, Kamil; Jirsa, Ladislav
Praha: ÚTIA AV ČR, v.v.i, 2010. s. 45-45. [6th International Workshop on Data–Algorithms–Decision Making. 2.12.2010-4.12.2010, Jindřichův Hradec] R&D Projects: GA MŠk(CZ) 7D09008 Institutional research plan: CEZ:AV0Z10750506 Keywords : soft sensor * bayesian statistics * bayesian model averaging Subject RIV: BB - Applied Statistics, Operational Research http://library.utia.cas.cz/separaty/2010/AS/dedecius-bayesian soft sensing in cold sheet rolling.pdf
A Bayesian approach for modeling origin-destination matrices
Perrakis, Konstantinos; Karlis, Dimitris; COOLS, Mario; JANSSENS, Davy; Vanhoof, Koen; Wets, Geert
2012-01-01
The majority of origin destination (OD) matrix estimation methods focus on situations where weak or partial information, derived from sample travel surveys, is available. Information derived from travel census studies, in contrast, covers the entire population of a specific study area of interest. In such cases where reliable historical data exist, statistical methodology may serve as a flexible alternative to traditional travel demand models by incorporating estimation of trip-generation, tr...
Approach to the Correlation Discovery of Chinese Linguistic Parameters Based on Bayesian Method
Institute of Scientific and Technical Information of China (English)
WANG Wei(王玮); CAI LianHong(蔡莲红)
2003-01-01
Bayesian approach is an important method in statistics. The Bayesian belief network is a powerful knowledge representation and reasoning tool under the conditions of uncertainty.It is a graphics model that encodes probabilistic relationships among variables of interest. In this paper, an approach to Bayesian network construction is given for discovering the Chinese linguistic parameter relationship in the corpus.
Bayesian Modeling of ChIP-chip Data Through a High-Order Ising Model
Mo, Qianxing
2010-01-29
ChIP-chip experiments are procedures that combine chromatin immunoprecipitation (ChIP) and DNA microarray (chip) technology to study a variety of biological problems, including protein-DNA interaction, histone modification, and DNA methylation. The most important feature of ChIP-chip data is that the intensity measurements of probes are spatially correlated because the DNA fragments are hybridized to neighboring probes in the experiments. We propose a simple, but powerful Bayesian hierarchical approach to ChIP-chip data through an Ising model with high-order interactions. The proposed method naturally takes into account the intrinsic spatial structure of the data and can be used to analyze data from multiple platforms with different genomic resolutions. The model parameters are estimated using the Gibbs sampler. The proposed method is illustrated using two publicly available data sets from Affymetrix and Agilent platforms, and compared with three alternative Bayesian methods, namely, Bayesian hierarchical model, hierarchical gamma mixture model, and Tilemap hidden Markov model. The numerical results indicate that the proposed method performs as well as the other three methods for the data from Affymetrix tiling arrays, but significantly outperforms the other three methods for the data from Agilent promoter arrays. In addition, we find that the proposed method has better operating characteristics in terms of sensitivities and false discovery rates under various scenarios. © 2010, The International Biometric Society.
Xiaoyin Wang
2015-01-01
The purpose of determining the relative importance of predictors is to expose the extent of the individual contribution of a predictor in the presence of other predictors within a selected model. The goal of this article is to expand the current research practice by developing a statistical paired comparison model with Two Sided Power (TSP) link function in the Bayesian framework to evaluate the relative importance of each predictor in a multiple regression model. Results from simulation stud...
Schöniger, A.; Nowak, W.; Wöhling, T.
2013-12-01
Bayesian model averaging (BMA) combines the predictive capabilities of alternative conceptual models into a robust best estimate and allows the quantification of conceptual uncertainty. The individual models are weighted with their posterior probability according to Bayes' theorem. Despite this rigorous procedure, we see four obstacles to robust model ranking: (1) The weights inherit uncertainty related to measurement noise in the calibration data set, which may compromise the reliability of model ranking. (2) Posterior weights rank the models only relative to each other, but do not contain information about the absolute model performance. (3) There is a lack of objective methods to assess whether the suggested models are practically distinguishable or very similar to each other, i.e., whether the individual models explore different regions of the model space. (4) No theory for optimal design (OD) of experiments exists that explicitly aims at maximum-confidence model discrimination. The goal of our study is to overcome these four shortcomings. We determine the robustness of weights against measurement noise (1) by repeatedly perturbing the observed data with random measurement errors and analyzing the variability in the obtained weights. Realizing that model weights have a probability distribution of their own, we introduce an additional term into the overall prediction uncertainty analysis scheme which we call 'weighting uncertainty'. We further assess an 'absolute distance' in performance of the model set from the truth (2) as seen through the eyes of the data by interpreting statistics of Bayesian model evidence. This analysis is of great value for modellers to decide, if the modelling task can be satisfactorily carried out with the model(s) at hand, or if more effort should be invested in extending the set with better performing models. As a further prerequisite for robust model selection, we scrutinize the ability of BMA to distinguish between the models in
Statistical Modeling of SAR Images: A Survey
Directory of Open Access Journals (Sweden)
Gui Gao
2010-01-01
Full Text Available Statistical modeling is essential to SAR (Synthetic Aperture Radar image interpretation. It aims to describe SAR images through statistical methods and reveal the characteristics of these images. Moreover, statistical modeling can provide a technical support for a comprehensive understanding of terrain scattering mechanism, which helps to develop algorithms for effective image interpretation and creditable image simulation. Numerous statistical models have been developed to describe SAR image data, and the purpose of this paper is to categorize and evaluate these models. We first summarize the development history and the current researching state of statistical modeling, then different SAR image models developed from the product model are mainly discussed in detail. Relevant issues are also discussed. Several promising directions for future research are concluded at last.
Frost, Andrew J.; Thyer, Mark A.; Srikanthan, R.; Kuczera, George
2007-07-01
SummaryMulti-site simulation of hydrological data are required for drought risk assessment of large multi-reservoir water supply systems. In this paper, a general Bayesian framework is presented for the calibration and evaluation of multi-site hydrological data at annual timescales. Models included within this framework are the hidden Markov model (HMM) and the widely used lag-1 autoregressive (AR(1)) model. These models are extended by the inclusion of a Box-Cox transformation and a spatial correlation function in a multi-site setting. Parameter uncertainty is evaluated using Markov chain Monte Carlo techniques. Models are evaluated by their ability to reproduce a range of important extreme statistics and compared using Bayesian model selection techniques which evaluate model probabilities. The case study, using multi-site annual rainfall data situated within catchments which contribute to Sydney's main water supply, provided the following results: Firstly, in terms of model probabilities and diagnostics, the inclusion of the Box-Cox transformation was preferred. Secondly the AR(1) and HMM performed similarly, while some other proposed AR(1)/HMM models with regionally pooled parameters had greater posterior probability than these two models. The practical significance of parameter and model uncertainty was illustrated using a case study involving drought security analysis for urban water supply. It was shown that ignoring parameter uncertainty resulted in a significant overestimate of reservoir yield and an underestimation of system vulnerability to severe drought.
Jain, Lakhmi
2012-01-01
Data mining is one of the most rapidly growing research areas in computer science and statistics. In Volume 2 of this three volume series, we have brought together contributions from some of the most prestigious researchers in theoretical data mining. Each of the chapters is self contained. Statisticians and applied scientists/ engineers will find this volume valuable. Additionally, it provides a sourcebook for graduate students interested in the current direction of research in data mining.
A population-based Bayesian approach to the minimal model of glucose and insulin homeostasis
DEFF Research Database (Denmark)
Andersen, Kim Emil; Højbjerre, Malene
2005-01-01
for a whole population. Traditionally it has been analysed in a deterministic set-up with only error terms on the measurements. In this work we adopt a Bayesian graphical model to describe the coupled minimal model that accounts for both measurement and process variability, and the model is extended...... to a population-based model. The estimation of the parameters are efficiently implemented in a Bayesian approach where posterior inference is made through the use of Markov chain Monte Carlo techniques. Hereby we obtain a powerful and flexible modelling framework for regularizing the ill-posed estimation problem...
Energy Technology Data Exchange (ETDEWEB)
Placek, Ben; Knuth, Kevin H. [Physics Department, University at Albany (SUNY), Albany, NY 12222 (United States); Angerhausen, Daniel, E-mail: bplacek@albany.edu, E-mail: kknuth@albany.edu, E-mail: daniel.angerhausen@gmail.com [Department of Physics, Applied Physics, and Astronomy, Rensselear Polytechnic Institute, Troy, NY 12180 (United States)
2014-11-10
EXONEST is an algorithm dedicated to detecting and characterizing the photometric signatures of exoplanets, which include reflection and thermal emission, Doppler boosting, and ellipsoidal variations. Using Bayesian inference, we can test between competing models that describe the data as well as estimate model parameters. We demonstrate this approach by testing circular versus eccentric planetary orbital models, as well as testing for the presence or absence of four photometric effects. In addition to using Bayesian model selection, a unique aspect of EXONEST is the potential capability to distinguish between reflective and thermal contributions to the light curve. A case study is presented using Kepler data recorded from the transiting planet KOI-13b. By considering only the nontransiting portions of the light curve, we demonstrate that it is possible to estimate the photometrically relevant model parameters of KOI-13b. Furthermore, Bayesian model testing confirms that the orbit of KOI-13b has a detectable eccentricity.
Parameterizing Bayesian network Representations of Social-Behavioral Models by Expert Elicitation
Energy Technology Data Exchange (ETDEWEB)
Walsh, Stephen J.; Dalton, Angela C.; Whitney, Paul D.; White, Amanda M.
2010-05-23
Bayesian networks provide a general framework with which to model many natural phenomena. The mathematical nature of Bayesian networks enables a plethora of model validation and calibration techniques: e.g parameter estimation, goodness of fit tests, and diagnostic checking of the model assumptions. However, they are not free of shortcomings. Parameter estimation from relevant extant data is a common approach to calibrating the model parameters. In practice it is not uncommon to find oneself lacking adequate data to reliably estimate all model parameters. In this paper we present the early development of a novel application of conjoint analysis as a method for eliciting and modeling expert opinions and using the results in a methodology for calibrating the parameters of a Bayesian network.
Bayesian analysis of overdispersed chromosome aberration data with the negative binomial model
International Nuclear Information System (INIS)
The usual assumption of a Poisson model for the number of chromosome aberrations in controlled calibration experiments implies variance equal to the mean. However, it is known that chromosome aberration data from experiments involving high linear energy transfer radiations can be overdispersed, i.e. the variance is greater than the mean. Present methods for dealing with overdispersed chromosome data rely on frequentist statistical techniques. In this paper, the problem of overdispersion is considered from a Bayesian standpoint. The Bayes Factor is used to compare Poisson and negative binomial models for two previously published calibration data sets describing the induction of dicentric chromosome aberrations by high doses of neutrons. Posterior densities for the model parameters, which characterise dose response and overdispersion are calculated and graphed. Calibrative densities are derived for unknown neutron doses from hypothetical radiation accident data to determine the impact of different model assumptions on dose estimates. The main conclusion is that an initial assumption of a negative binomial model is the conservative approach to chromosome dosimetry for high LET radiations. (author)
Mengersen, Kerrie
2016-01-01
Objectives To compare two Bayesian models capable of identifying unusual and unstable temporal patterns in spatiotemporal data. Setting Annual counts of mammography screening users from each statistical local area (SLA) in Brisbane, Australia, recorded between 1997 and 2008 inclusive. Primary outcome measures Mammography screening counts. Results The temporal trends of 91 SLAs (58%) were dissimilar from the overall common temporal trend. SLAs that followed the common temporal trend also tended to have stable temporal trends. SLAs with unstable temporal trends tended to be situated farther from the city and farther from mammography screening facilities. Conclusions This paper demonstrates the usefulness of the two models in identifying unusual and unstable temporal trends, and the synergy obtained when both models are applied to the same data set. An analysis of these models has provided interesting insights into the temporal trends of mammography screening counts and has shown several possible avenues for further research, such as extending the models to allow for multiple common temporal trends and accounting for additional spatiotemporal heterogeneity. PMID:27230999
Bayesian Analysis for Dynamic Generalized Linear Latent Model with Application to Tree Survival Rate
Directory of Open Access Journals (Sweden)
Yu-sheng Cheng
2014-01-01
Full Text Available Logistic regression model is the most popular regression technique, available for modeling categorical data especially for dichotomous variables. Classic logistic regression model is typically used to interpret relationship between response variables and explanatory variables. However, in real applications, most data sets are collected in follow-up, which leads to the temporal correlation among the data. In order to characterize the different variables correlations, a new method about the latent variables is introduced in this study. At the same time, the latent variables about AR (1 model are used to depict time dependence. In the framework of Bayesian analysis, parameters estimates and statistical inferences are carried out via Gibbs sampler with Metropolis-Hastings (MH algorithm. Model comparison, based on the Bayes factor, and forecasting/smoothing of the survival rate of the tree are established. A simulation study is conducted to assess the performance of the proposed method and a pika data set is analyzed to illustrate the real application. Since Bayes factor approaches vary significantly, efficiency tests have been performed in order to decide which solution provides a better tool for the analysis of real relational data sets.
Bayesian network modeling method based on case reasoning for emergency decision-making
Directory of Open Access Journals (Sweden)
XU Lei
2013-06-01
Full Text Available Bayesian network has the abilities of probability expression, uncertainty management and multi-information fusion.It can support emergency decision-making, which can improve the efficiency of decision-making.Emergency decision-making is highly time sensitive, which requires shortening the Bayesian Network modeling time as far as possible.Traditional Bayesian network modeling methods are clearly unable to meet that requirement.Thus, a Bayesian network modeling method based on case reasoning for emergency decision-making is proposed.The method can obtain optional cases through case matching by the functions of similarity degree and deviation degree.Then,new Bayesian network can be built through case adjustment by case merging and pruning.An example is presented to illustrate and test the proposed method.The result shows that the method does not have a huge search space or need sample data.The only requirement is the collection of expert knowledge and historical case models.Compared with traditional methods, the proposed method can reuse historical case models, which can reduce the modeling time and improve the efficiency.
Parameter Learning of Logic Programs for Symbolic-Statistical Modeling
Kameya, Y; 10.1613/jair.912
2011-01-01
We propose a logical/mathematical framework for statistical parameter learning of parameterized logic programs, i.e. definite clause programs containing probabilistic facts with a parameterized distribution. It extends the traditional least Herbrand model semantics in logic programming to distribution semantics, possible world semantics with a probability distribution which is unconditionally applicable to arbitrary logic programs including ones for HMMs, PCFGs and Bayesian networks. We also propose a new EM algorithm, the graphical EM algorithm, that runs for a class of parameterized logic programs representing sequential decision processes where each decision is exclusive and independent. It runs on a new data structure called support graphs describing the logical relationship between observations and their explanations, and learns parameters by computing inside and outside probability generalized for logic programs. The complexity analysis shows that when combined with OLDT search for all explanations for ...
Indian Academy of Sciences (India)
Wayan Suparta; Gusrizal
2014-08-01
We implement a hierarchical Bayesian spatiotemporal (HBST) model to forecast the daily trapped particle flux distribution over the South Atlantic Anomaly (SAA) region. The National Oceanic and Atmospheric Administration (NOAA)-15 data from 1–30 March 2008 with particle energies as < 30 keV (mep0e1) and < 300 keV (mep0e3) for electrons and 80–240 keV (mep0p2) and < 6900 keV (mep0p6) for protons were used as the model input to forecast the flux values on 31 March 2008. Data were transformed into logarithmic values and gridded in a 5° × 5° longitude and latitude size to fulfill the modeling precondition. A Monte Carlo Markov chain (MCMC) was then performed to solve the HBST Gaussian Process (GP) model by using the Gibbs sampling method. The result for this model was interpolated by a Kriging technique to achieve the whole distribution figure over the SAA region. Statistical results of the root mean square error (RMSE), mean absolute percentage error (MAPE), and bias (BIAS) showed a good indicator of the HBST method. The statistical validation also indicated the high variability of particle flux values in the SAA core area. The visual validation showed a powerful combination of HBST-GP model with Kriging interpolation technique. The Kriging also produced a good quality of the distribution map of particle flux over the SAA region as indicated by its small variance value. This suggests that the model can be applied in the development of a Low Earth Orbit (LEO)-Equatorial satellite for monitoring trapped particle radiation hazard.
The Bayesian statistical decision theory applied to the optimization of generating set maintenance
International Nuclear Information System (INIS)
The difficulty in RCM methodology is the allocation of a new periodicity of preventive maintenance on one equipment when a critical failure has been identified: until now this new allocation has been based on the engineer's judgment, and one must wait for a full cycle of feedback experience before to validate it. Statistical decision theory could be a more rational alternative for the optimization of preventive maintenance periodicity. This methodology has been applied to inspection and maintenance optimization of cylinders of diesel generator engines of 900 MW nuclear plants, and has shown that previous preventive maintenance periodicity can be extended. (authors). 8 refs., 5 figs
Actuarial statistics with generalized linear mixed models
K. Antonio; J. Beirlant
2007-01-01
Over the last decade the use of generalized linear models (GLMs) in actuarial statistics has received a lot of attention, starting from the actuarial illustrations in the standard text by McCullagh and Nelder [McCullagh, P., Nelder, J.A., 1989. Generalized linear models. In: Monographs on Statistics
A Bayesian Surrogate Model for Rapid Time Series Analysis and Application to Exoplanet Observations
Ford, Eric B; Veras, Dimitri
2011-01-01
We present a Bayesian surrogate model for the analysis of periodic or quasi-periodic time series data. We describe a computationally efficient implementation that enables Bayesian model comparison. We apply this model to simulated and real exoplanet observations. We discuss the results and demonstrate some of the challenges for applying our surrogate model to realistic exoplanet data sets. In particular, we find that analyses of real world data should pay careful attention to the effects of uneven spacing of observations and the choice of prior for the "jitter" parameter.
Statistical Models and Methods for Lifetime Data
Lawless, Jerald F
2011-01-01
Praise for the First Edition"An indispensable addition to any serious collection on lifetime data analysis and . . . a valuable contribution to the statistical literature. Highly recommended . . ."-Choice"This is an important book, which will appeal to statisticians working on survival analysis problems."-Biometrics"A thorough, unified treatment of statistical models and methods used in the analysis of lifetime data . . . this is a highly competent and agreeable statistical textbook."-Statistics in MedicineThe statistical analysis of lifetime or response time data is a key tool in engineering,
Schöniger, Anneli; Wöhling, Thomas; Samaniego, Luis; Nowak, Wolfgang
2014-12-01
Bayesian model selection or averaging objectively ranks a number of plausible, competing conceptual models based on Bayes' theorem. It implicitly performs an optimal trade-off between performance in fitting available data and minimum model complexity. The procedure requires determining Bayesian model evidence (BME), which is the likelihood of the observed data integrated over each model's parameter space. The computation of this integral is highly challenging because it is as high-dimensional as the number of model parameters. Three classes of techniques to compute BME are available, each with its own challenges and limitations: (1) Exact and fast analytical solutions are limited by strong assumptions. (2) Numerical evaluation quickly becomes unfeasible for expensive models. (3) Approximations known as information criteria (ICs) such as the AIC, BIC, or KIC (Akaike, Bayesian, or Kashyap information criterion, respectively) yield contradicting results with regard to model ranking. Our study features a theory-based intercomparison of these techniques. We further assess their accuracy in a simplistic synthetic example where for some scenarios an exact analytical solution exists. In more challenging scenarios, we use a brute-force Monte Carlo integration method as reference. We continue this analysis with a real-world application of hydrological model selection. This is a first-time benchmarking of the various methods for BME evaluation against true solutions. Results show that BME values from ICs are often heavily biased and that the choice of approximation method substantially influences the accuracy of model ranking. For reliable model selection, bias-free numerical methods should be preferred over ICs whenever computationally feasible.
Directory of Open Access Journals (Sweden)
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.
Holan, S.H.; Davis, G.M.; Wildhaber, M.L.; DeLonay, A.J.; Papoulias, D.M.
2009-01-01
The timing of spawning in fish is tightly linked to environmental factors; however, these factors are not very well understood for many species. Specifically, little information is available to guide recruitment efforts for endangered species such as the sturgeon. Therefore, we propose a Bayesian hierarchical model for predicting the success of spawning of the shovelnose sturgeon which uses both biological and behavioural (longitudinal) data. In particular, we use data that were produced from a tracking study that was conducted in the Lower Missouri River. The data that were produced from this study consist of biological variables associated with readiness to spawn along with longitudinal behavioural data collected by using telemetry and archival data storage tags. These high frequency data are complex both biologically and in the underlying behavioural process. To accommodate such complexity we developed a hierarchical linear regression model that uses an eigenvalue predictor, derived from the transition probability matrix of a two-state Markov switching model with generalized auto-regressive conditional heteroscedastic dynamics. Finally, to minimize the computational burden that is associated with estimation of this model, a parallel computing approach is proposed. ?? Journal compilation 2009 Royal Statistical Society.
A High Performance Bayesian Computing Framework for Spatiotemporal Uncertainty Modeling
Cao, G.
2015-12-01
All types of spatiotemporal measurements are subject to uncertainty. With spatiotemporal data becomes increasingly involved in scientific research and decision making, it is important to appropriately model the impact of uncertainty. Quantitatively modeling spatiotemporal uncertainty, however, is a challenging problem considering the complex dependence and dataheterogeneities.State-space models provide a unifying and intuitive framework for dynamic systems modeling. In this paper, we aim to extend the conventional state-space models for uncertainty modeling in space-time contexts while accounting for spatiotemporal effects and data heterogeneities. Gaussian Markov Random Field (GMRF) models, also known as conditional autoregressive models, are arguably the most commonly used methods for modeling of spatially dependent data. GMRF models basically assume that a geo-referenced variable primarily depends on its neighborhood (Markov property), and the spatial dependence structure is described via a precision matrix. Recent study has shown that GMRFs are efficient approximation to the commonly used Gaussian fields (e.g., Kriging), and compared with Gaussian fields, GMRFs enjoy a series of appealing features, such as fast computation and easily accounting for heterogeneities in spatial data (e.g, point and areal). This paper represents each spatial dataset as a GMRF and integrates them into a state-space form to statistically model the temporal dynamics. Different types of spatial measurements (e.g., categorical, count or continuous), can be accounted for by according link functions. A fast alternative to MCMC framework, so-called Integrated Nested Laplace Approximation (INLA), was adopted for model inference.Preliminary case studies will be conducted to showcase the advantages of the described framework. In the first case, we apply the proposed method for modeling the water table elevation of Ogallala aquifer over the past decades. In the second case, we analyze the
Mugnes, J.-M.; Robert, C.
2015-11-01
Spectral analysis is a powerful tool to investigate stellar properties and it has been widely used for decades now. However, the methods considered to perform this kind of analysis are mostly based on iteration among a few diagnostic lines to determine the stellar parameters. While these methods are often simple and fast, they can lead to errors and large uncertainties due to the required assumptions. Here, we present a method based on Bayesian statistics to find simultaneously the best combination of effective temperature, surface gravity, projected rotational velocity, and microturbulence velocity, using all the available spectral lines. Different tests are discussed to demonstrate the strength of our method, which we apply to 54 mid-resolution spectra of field and cluster B stars obtained at the Observatoire du Mont-Mégantic. We compare our results with those found in the literature. Differences are seen which are well explained by the different methods used. We conclude that the B-star microturbulence velocities are often underestimated. We also confirm the trend that B stars in clusters are on average faster rotators than field B stars.
International Nuclear Information System (INIS)
This paper is concerned with resistivity sounding measurements performed from single site (vertical sounding) or from several sites (profiles) within a bounded area. The objective is to present an accurate information about the study area and to estimate the likelihood of the produced quantitative models. The achievement of this objective obviously requires quite relevant data and processing methods. It also requires interpretation methods which should take into account the probable effect of an heterogeneous structure. In front of such difficulties, the interpretation of resistivity sounding data inevitably involves the use of inversion methods. We suggest starting the interpretation in simple situation (1-D approximation), and using the rough but correct model obtained as an a-priori model for any more refined interpretation. Related to this point of view, special attention should be paid for the inverse problem applied to the resistivity sounding data. This inverse problem is nonlinear, while linearity inherent in the functional response used to describe the physical experiment. Two different approaches are used to build an approximate but higher dimensional inversion of geoelectrical data: the linear approach and the bayesian statistical approach. Some illustrations of their application in resistivity sounding data acquired at Tritrivakely volcanic lake (single site) and at Mahitsy area (several sites) will be given. (author). 28 refs, 7 figs
2nd Bayesian Young Statisticians Meeting
Bitto, Angela; Kastner, Gregor; Posekany, Alexandra
2015-01-01
The Second Bayesian Young Statisticians Meeting (BAYSM 2014) and the research presented here facilitate connections among researchers using Bayesian Statistics by providing a forum for the development and exchange of ideas. WU Vienna University of Business and Economics hosted BAYSM 2014 from September 18th to 19th. The guidance of renowned plenary lecturers and senior discussants is a critical part of the meeting and this volume, which follows publication of contributions from BAYSM 2013. The meeting's scientific program reflected the variety of fields in which Bayesian methods are currently employed or could be introduced in the future. Three brilliant keynote lectures by Chris Holmes (University of Oxford), Christian Robert (Université Paris-Dauphine), and Mike West (Duke University), were complemented by 24 plenary talks covering the major topics Dynamic Models, Applications, Bayesian Nonparametrics, Biostatistics, Bayesian Methods in Economics, and Models and Methods, as well as a lively poster session ...
Directory of Open Access Journals (Sweden)
J. P. Werner
2015-03-01
Full Text Available Reconstructions of the late-Holocene climate rely heavily upon proxies that are assumed to be accurately dated by layer counting, such as measurements of tree rings, ice cores, and varved lake sediments. Considerable advances could be achieved if time-uncertain proxies were able to be included within these multiproxy reconstructions, and if time uncertainties were recognized and correctly modeled for proxies commonly treated as free of age model errors. Current approaches for accounting for time uncertainty are generally limited to repeating the reconstruction using each one of an ensemble of age models, thereby inflating the final estimated uncertainty – in effect, each possible age model is given equal weighting. Uncertainties can be reduced by exploiting the inferred space–time covariance structure of the climate to re-weight the possible age models. Here, we demonstrate how Bayesian hierarchical climate reconstruction models can be augmented to account for time-uncertain proxies. Critically, although a priori all age models are given equal probability of being correct, the probabilities associated with the age models are formally updated within the Bayesian framework, thereby reducing uncertainties. Numerical experiments show that updating the age model probabilities decreases uncertainty in the resulting reconstructions, as compared with the current de facto standard of sampling over all age models, provided there is sufficient information from other data sources in the spatial region of the time-uncertain proxy. This approach can readily be generalized to non-layer-counted proxies, such as those derived from marine sediments.
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
Statistical modelling of fish stocks
DEFF Research Database (Denmark)
Kvist, Trine
1999-01-01
for modelling the dynamics of a fish population is suggested. A new approach is introduced to analyse the sources of variation in age composition data, which is one of the most important sources of information in the cohort based models for estimation of stock abundancies and mortalities. The approach combines...... and it is argued that an approach utilising stochastic differential equations might be advantagous in fish stoch assessments....
Beam-R1. A Bayesian European archeomagnetic model for the past 2000 years
International Nuclear Information System (INIS)
Complete text of publication follows. Ongoing efforts are currently being made to enrich the available archeomagnetic database and to represent the data in space and time by means of Spherical Harmonic models. However, it is well known that the sparse spatial and temporal data distribution at the worldwide scale hampers the modeling to high resolutions. The data density is comparatively higher in Europe than in any other part of the world for the past 2000 yr. This situation offers a good opportunity to model the archeomagnetic field at spatial scales higher than permitted by spherical harmonics. In principle, such a regional modelling should give us the possibility of better exploring the reliability of the rapid spatial and time variations of the past magnetic field. We complement the recent regional modeling advances made by Pavon-Carrasco et al. (2009) with a new approach based on a Revised Spherical Cap Harmonic Analysis (R-SCHA2D; Thebault, 2008) and a Bayesian inversion scheme in order to process the most up-to-date archeomagnetic database for Europe. This allows us to solve non-linear inverse problems and to avoid the use of strong a priori information. We obtain the marginal probabilities of each regional parameter with a Monte Carlo Markov Chain at all epochs between 50BC and 1850AD. This helps us assessing the reliability of some time variations. Our method provides the maximum likelihood of the magnetic field components, their probability distribution, but also misfit histograms for all individual data. This exhaustive statistical information allow us to conclude that directional data are self-consistent in Europe but that important issues are faced when considering intensity data. By a comparison with other regional and global models, we conclude that our new Bayesian model represents the data to higher spatial resolutions than what is obtained by other techniques. However, given the data error and uncertainties, this does not necessarily lead to
Institute of Scientific and Technical Information of China (English)
Farid Zayeri; Masoud Salehi; Hasan Pirhosseini
2011-01-01
Objective:To present the geographical map of malaria and identify some of the important environmental factors of this disease in Sistan and Baluchistan province, Iran.Methods:We used the registered malaria data to compute the standard incidence rates (SIRs) of malaria in different areas of Sistan and Baluchistan province for a nine-year period (from 2001 to 2009). Statistical analyses consisted of two different parts: geographical mapping of malaria incidence rates, and modeling the environmental factors. The empirical Bayesian estimates of malaria SIRs were utilized for geographical mapping of malaria and a Poisson random effects model was used for assessing the effect of environmental factors on malaria SIRs.Results:In general, 64 926 new cases of malaria were registered in Sistan and Baluchistan Province from 2001 to 2009. Among them, 42 695 patients (65.8%) were male and 22 231 patients (34.2%) were female. Modeling the environmental factors showed that malaria incidence rates had positive relationship with humidity, elevation, average minimum temperature and average maximum temperature, while rainfall had negative effect on malaria SIRs in this province.Conclusions:The results of the present study reveals that malaria is still a serious health problem in Sistan and Baluchistan province, Iran. Geographical map and related environmental factors of malaria can help the health policy makers to intervene in high risk areas more efficiently and allocate the resources in a proper manner.
Directory of Open Access Journals (Sweden)
Brentani Helena
2004-08-01
Full Text Available Abstract Background An important challenge for transcript counting methods such as Serial Analysis of Gene Expression (SAGE, "Digital Northern" or Massively Parallel Signature Sequencing (MPSS, is to carry out statistical analyses that account for the within-class variability, i.e., variability due to the intrinsic biological differences among sampled individuals of the same class, and not only variability due to technical sampling error. Results We introduce a Bayesian model that accounts for the within-class variability by means of mixture distribution. We show that the previously available approaches of aggregation in pools ("pseudo-libraries" and the Beta-Binomial model, are particular cases of the mixture model. We illustrate our method with a brain tumor vs. normal comparison using SAGE data from public databases. We show examples of tags regarded as differentially expressed with high significance if the within-class variability is ignored, but clearly not so significant if one accounts for it. Conclusion Using available information about biological replicates, one can transform a list of candidate transcripts showing differential expression to a more reliable one. Our method is freely available, under GPL/GNU copyleft, through a user friendly web-based on-line tool or as R language scripts at supplemental web-site.
Maximum Likelihood Bayesian Averaging of Spatial Variability Models in Unsaturated Fractured Tuff
International Nuclear Information System (INIS)
Hydrologic analyses typically rely on a single conceptual-mathematical model. Yet hydrologic environments are open and complex, rendering them prone to multiple interpretations and mathematical descriptions. Adopting only one of these may lead to statistical bias and underestimation of uncertainty. Bayesian Model Averaging (BMA) provides an optimal way to combine the predictions of several competing models and to assess their joint predictive uncertainty. However, it tends to be computationally demanding and relies heavily on prior information about model parameters. We apply a maximum likelihood (ML) version of BMA (MLBMA) to seven alternative variogram models of log air permeability data from single-hole pneumatic injection tests in six boreholes at the Apache Leap Research Site (ALRS) in central Arizona. Unbiased ML estimates of variogram and drift parameters are obtained using Adjoint State Maximum Likelihood Cross Validation in conjunction with Universal Kriging and Generalized L east Squares. Standard information criteria provide an ambiguous ranking of the models, which does not justify selecting one of them and discarding all others as is commonly done in practice. Instead, we eliminate some of the models based on their negligibly small posterior probabilities and use the rest to project the measured log permeabilities by kriging onto a rock volume containing the six boreholes. We then average these four projections, and associated kriging variances, using the posterior probability of each model as weight. Finally, we cross-validate the results by eliminating from consideration all data from one borehole at a time, repeating the above process, and comparing the predictive capability of MLBMA with that of each individual model. We find that MLBMA is superior to any individual geostatistical model of log permeability among those we consider at the ALRS
Boulanger, Jean-Philippe; Martinez, Fernando; Segura, Enrique C.
2007-02-01
Evaluating the response of climate to greenhouse gas forcing is a major objective of the climate community, and the use of large ensemble of simulations is considered as a significant step toward that goal. The present paper thus discusses a new methodology based on neural network to mix ensemble of climate model simulations. Our analysis consists of one simulation of seven Atmosphere Ocean Global Climate Models, which participated in the IPCC Project and provided at least one simulation for the twentieth century (20c3m) and one simulation for each of three SRES scenarios: A2, A1B and B1. Our statistical method based on neural networks and Bayesian statistics computes a transfer function between models and observations. Such a transfer function was then used to project future conditions and to derive what we would call the optimal ensemble combination for twenty-first century climate change projections. Our approach is therefore based on one statement and one hypothesis. The statement is that an optimal ensemble projection should be built by giving larger weights to models, which have more skill in representing present climate conditions. The hypothesis is that our method based on neural network is actually weighting the models that way. While the statement is actually an open question, which answer may vary according to the region or climate signal under study, our results demonstrate that the neural network approach indeed allows to weighting models according to their skills. As such, our method is an improvement of existing Bayesian methods developed to mix ensembles of simulations. However, the general low skill of climate models in simulating precipitation mean climatology implies that the final projection maps (whatever the method used to compute them) may significantly change in the future as models improve. Therefore, the projection results for late twenty-first century conditions are presented as possible projections based on the “state-of-the-art” of
Quantile Probability and Statistical Data Modeling
Parzen, Emanuel
2004-01-01
Quantile and conditional quantile statistical thinking, as I have innovated it in my research since 1976, is outlined in this comprehensive survey and introductory course in quantile data analysis. We propose that a unification of the theory and practice of statistical methods of data modeling may be possible by a quantile perspective. Our broad range of topics of univariate and bivariate probability and statistics are best summarized by the key words. Two fascinating practical examples are g...
Tang, An-Min; Tang, Nian-Sheng
2015-02-28
We propose a semiparametric multivariate skew-normal joint model for multivariate longitudinal and multivariate survival data. One main feature of the posited model is that we relax the commonly used normality assumption for random effects and within-subject error by using a centered Dirichlet process prior to specify the random effects distribution and using a multivariate skew-normal distribution to specify the within-subject error distribution and model trajectory functions of longitudinal responses semiparametrically. A Bayesian approach is proposed to simultaneously obtain Bayesian estimates of unknown parameters, random effects and nonparametric functions by combining the Gibbs sampler and the Metropolis-Hastings algorithm. Particularly, a Bayesian local influence approach is developed to assess the effect of minor perturbations to within-subject measurement error and random effects. Several simulation studies and an example are presented to illustrate the proposed methodologies. PMID:25404574
Bayesian model selection applied to artificial neural networks used for water resources modeling
Kingston, Greer B.; Maier, Holger R.; Lambert, Martin F.
2008-04-01
Artificial neural networks (ANNs) have proven to be extremely valuable tools in the field of water resources engineering. However, one of the most difficult tasks in developing an ANN is determining the optimum level of complexity required to model a given problem, as there is no formal systematic model selection method. This paper presents a Bayesian model selection (BMS) method for ANNs that provides an objective approach for comparing models of varying complexity in order to select the most appropriate ANN structure. The approach uses Markov Chain Monte Carlo posterior simulations to estimate the evidence in favor of competing models and, in this study, three known methods for doing this are compared in terms of their suitability for being incorporated into the proposed BMS framework for ANNs. However, it is acknowledged that it can be particularly difficult to accurately estimate the evidence of ANN models. Therefore, the proposed BMS approach for ANNs incorporates a further check of the evidence results by inspecting the marginal posterior distributions of the hidden-to-output layer weights, which unambiguously indicate any redundancies in the hidden layer nodes. The fact that this check is available is one of the greatest advantages of the proposed approach over conventional model selection methods, which do not provide such a test and instead rely on the modeler's subjective choice of selection criterion. The advantages of a total Bayesian approach to ANN development, including training and model selection, are demonstrated on two synthetic and one real world water resources case study.
Uncertainty the soul of modeling, probability & statistics
Briggs, William
2016-01-01
This book presents a philosophical approach to probability and probabilistic thinking, considering the underpinnings of probabilistic reasoning and modeling, which effectively underlie everything in data science. The ultimate goal is to call into question many standard tenets and lay the philosophical and probabilistic groundwork and infrastructure for statistical modeling. It is the first book devoted to the philosophy of data aimed at working scientists and calls for a new consideration in the practice of probability and statistics to eliminate what has been referred to as the "Cult of Statistical Significance". The book explains the philosophy of these ideas and not the mathematics, though there are a handful of mathematical examples. The topics are logically laid out, starting with basic philosophy as related to probability, statistics, and science, and stepping through the key probabilistic ideas and concepts, and ending with statistical models. Its jargon-free approach asserts that standard methods, suc...
Statistical Model-Based Face Pose Estimation
Institute of Scientific and Technical Information of China (English)
GE Xinliang; YANG Jie; LI Feng; WANG Huahua
2007-01-01
A robust face pose estimation approach is proposed by using face shape statistical model approach and pose parameters are represented by trigonometric functions. The face shape statistical model is firstly built by analyzing the face shapes from different people under varying poses. The shape alignment is vital in the process of building the statistical model. Then, six trigonometric functions are employed to represent the face pose parameters. Lastly, the mapping function is constructed between face image and face pose by linearly relating different parameters. The proposed approach is able to estimate different face poses using a few face training samples. Experimental results are provided to demonstrate its efficiency and accuracy.
Automated statistical modeling of analytical measurement systems
International Nuclear Information System (INIS)
The statistical modeling of analytical measurement systems at the Idaho Chemical Processing Plant (ICPP) has been completely automated through computer software. The statistical modeling of analytical measurement systems is one part of a complete quality control program used by the Remote Analytical Laboratory (RAL) at the ICPP. The quality control program is an integration of automated data input, measurement system calibration, database management, and statistical process control. The quality control program and statistical modeling program meet the guidelines set forth by the American Society for Testing Materials and American National Standards Institute. A statistical model is a set of mathematical equations describing any systematic bias inherent in a measurement system and the precision of a measurement system. A statistical model is developed from data generated from the analysis of control standards. Control standards are samples which are made up at precise known levels by an independent laboratory and submitted to the RAL. The RAL analysts who process control standards do not know the values of those control standards. The object behind statistical modeling is to describe real process samples in terms of their bias and precision and, to verify that a measurement system is operating satisfactorily. The processing of control standards gives us this ability
Energy Technology Data Exchange (ETDEWEB)
Boulanger, Jean-Philippe [LODYC, UMR CNRS/IRD/UPMC, Tour 45-55/Etage 4/Case 100, UPMC, Paris Cedex 05 (France); University of Buenos Aires, Departamento de Ciencias de la Atmosfera y los Oceanos, Facultad de Ciencias Exactas y Naturales, Buenos Aires (Argentina); Martinez, Fernando; Segura, Enrique C. [University of Buenos Aires, Departamento de Computacion, Facultad de Ciencias Exactas y Naturales, Buenos Aires (Argentina)
2007-02-15
Evaluating the response of climate to greenhouse gas forcing is a major objective of the climate community, and the use of large ensemble of simulations is considered as a significant step toward that goal. The present paper thus discusses a new methodology based on neural network to mix ensemble of climate model simulations. Our analysis consists of one simulation of seven Atmosphere-Ocean Global Climate Models, which participated in the IPCC Project and provided at least one simulation for the twentieth century (20c3m) and one simulation for each of three SRES scenarios: A2, A1B and B1. Our statistical method based on neural networks and Bayesian statistics computes a transfer function between models and observations. Such a transfer function was then used to project future conditions and to derive what we would call the optimal ensemble combination for twenty-first century climate change projections. Our approach is therefore based on one statement and one hypothesis. The statement is that an optimal ensemble projection should be built by giving larger weights to models, which have more skill in representing present climate conditions. The hypothesis is that our method based on neural network is actually weighting the models that way. While the statement is actually an open question, which answer may vary according to the region or climate signal under study, our results demonstrate that the neural network approach indeed allows to weighting models according to their skills. As such, our method is an improvement of existing Bayesian methods developed to mix ensembles of simulations. However, the general low skill of climate models in simulating precipitation mean climatology implies that the final projection maps (whatever the method used to compute them) may significantly change in the future as models improve. Therefore, the projection results for late twenty-first century conditions are presented as possible projections based on the &apos
Chemical and statistical soot modeling
Blanquart, Guillaume
2008-01-01
The combustion of petroleum based fuels like kerosene, gasoline, or diesel leads to the formation of several kind of pollutants. Among them, soot particles are particularly bad for their severe consequences on human health. Over the past decades, strict regulations have been placed on car and aircraft engines in order to limit these particulate matter emissions. Designing low emission engines requires the use of predictive soot models which can be applied to the combustion of real fuels. ...
Energy Technology Data Exchange (ETDEWEB)
Vrugt, Jasper A [Los Alamos National Laboratory; Wohling, Thomas [NON LANL
2008-01-01
Most studies in vadose zone hydrology use a single conceptual model for predictive inference and analysis. Focusing on the outcome of a single model is prone to statistical bias and underestimation of uncertainty. In this study, we combine multi-objective optimization and Bayesian Model Averaging (BMA) to generate forecast ensembles of soil hydraulic models. To illustrate our method, we use observed tensiometric pressure head data at three different depths in a layered vadose zone of volcanic origin in New Zealand. A set of seven different soil hydraulic models is calibrated using a multi-objective formulation with three different objective functions that each measure the mismatch between observed and predicted soil water pressure head at one specific depth. The Pareto solution space corresponding to these three objectives is estimated with AMALGAM, and used to generate four different model ensembles. These ensembles are post-processed with BMA and used for predictive analysis and uncertainty estimation. Our most important conclusions for the vadose zone under consideration are: (1) the mean BMA forecast exhibits similar predictive capabilities as the best individual performing soil hydraulic model, (2) the size of the BMA uncertainty ranges increase with increasing depth and dryness in the soil profile, (3) the best performing ensemble corresponds to the compromise (or balanced) solution of the three-objective Pareto surface, and (4) the combined multi-objective optimization and BMA framework proposed in this paper is very useful to generate forecast ensembles of soil hydraulic models.
Different Manhattan project: automatic statistical model generation
Yap, Chee Keng; Biermann, Henning; Hertzmann, Aaron; Li, Chen; Meyer, Jon; Pao, Hsing-Kuo; Paxia, Salvatore
2002-03-01
We address the automatic generation of large geometric models. This is important in visualization for several reasons. First, many applications need access to large but interesting data models. Second, we often need such data sets with particular characteristics (e.g., urban models, park and recreation landscape). Thus we need the ability to generate models with different parameters. We propose a new approach for generating such models. It is based on a top-down propagation of statistical parameters. We illustrate the method in the generation of a statistical model of Manhattan. But the method is generally applicable in the generation of models of large geographical regions. Our work is related to the literature on generating complex natural scenes (smoke, forests, etc) based on procedural descriptions. The difference in our approach stems from three characteristics: modeling with statistical parameters, integration of ground truth (actual map data), and a library-based approach for texture mapping.
Lee, Sik-Yum
2012-01-01
This book provides clear instructions to researchers on how to apply Structural Equation Models (SEMs) for analyzing the inter relationships between observed and latent variables. Basic and Advanced Bayesian Structural Equation Modeling introduces basic and advanced SEMs for analyzing various kinds of complex data, such as ordered and unordered categorical data, multilevel data, mixture data, longitudinal data, highly non-normal data, as well as some of their combinations. In addition, Bayesian semiparametric SEMs to capture the true distribution of explanatory latent variables are introduce
DEFF Research Database (Denmark)
Dalgaard, Jens; Pena, Jose; Kocka, Tomas
2004-01-01
We propose a method to assist the user in the interpretation of the best Bayesian network model indu- ced from data. The method consists in extracting relevant features from the model (e.g. edges, directed paths and Markov blankets) and, then, assessing the con¯dence in them by studying multiple...
Bayesian interpolation in a dynamic sinusoidal model with application to packet-loss concealment
DEFF Research Database (Denmark)
Nielsen, Jesper Kjær; Christensen, Mads Græsbøll; Cemgil, Ali Taylan;
2010-01-01
a Bayesian inference scheme for the missing observations, hidden states and model parameters of the dynamic model. The inference scheme is based on a Markov chain Monte Carlo method known as Gibbs sampler. We illustrate the performance of the inference scheme to the application of packet-loss concealment...
Bayesian prediction of spatial count data using generalized linear mixed models
DEFF Research Database (Denmark)
Christensen, Ole Fredslund; Waagepetersen, Rasmus Plenge
2002-01-01
Spatial weed count data are modeled and predicted using a generalized linear mixed model combined with a Bayesian approach and Markov chain Monte Carlo. Informative priors for a data set with sparse sampling are elicited using a previously collected data set with extensive sampling. Furthermore, ...
Probabilistic Modelling of Fatigue Life of Composite Laminates Using Bayesian Inference
DEFF Research Database (Denmark)
Dimitrov, Nikolay Krasimirov; Kiureghian, Armen Der
2014-01-01
. Model parameters are estimated by Bayesian inference. The reference data used consists of constant-amplitude fatigue test results for a multi-directional laminate subjected to seven different load ratios. The paper describes the modelling techniques and the parameter estimation procedure, supported by...
A Bayesian Multi-Level Factor Analytic Model of Consumer Price Sensitivities across Categories
Duvvuri, Sri Devi; Gruca, Thomas S.
2010-01-01
Identifying price sensitive consumers is an important problem in marketing. We develop a Bayesian multi-level factor analytic model of the covariation among household-level price sensitivities across product categories that are substitutes. Based on a multivariate probit model of category incidence, this framework also allows the researcher to…
Markov Model of Wind Power Time Series UsingBayesian Inference of Transition Matrix
DEFF Research Database (Denmark)
Chen, Peiyuan; Berthelsen, Kasper Klitgaard; Bak-Jensen, Birgitte;
2009-01-01
This paper proposes to use Bayesian inference of transition matrix when developing a discrete Markov model of a wind speed/power time series and 95% credible interval for the model verification. The Dirichlet distribution is used as a conjugate prior for the transition matrix. Three discrete Markov...
Modelling the presence of disease under spatial misalignment using Bayesian latent Gaussian models.
Barber, Xavier; Conesa, David; Lladosa, Silvia; López-Quílez, Antonio
2016-01-01
Modelling patterns of the spatial incidence of diseases using local environmental factors has been a growing problem in the last few years. Geostatistical models have become popular lately because they allow estimating and predicting the underlying disease risk and relating it with possible risk factors. Our approach to these models is based on the fact that the presence/absence of a disease can be expressed with a hierarchical Bayesian spatial model that incorporates the information provided by the geographical and environmental characteristics of the region of interest. Nevertheless, our main interest here is to tackle the misalignment problem arising when information about possible covariates are partially (or totally) different than those of the observed locations and those in which we want to predict. As a result, we present two different models depending on the fact that there is uncertainty on the covariates or not. In both cases, Bayesian inference on the parameters and prediction of presence/absence in new locations are made by considering the model as a latent Gaussian model, which allows the use of the integrated nested Laplace approximation. In particular, the spatial effect is implemented with the stochastic partial differential equation approach. The methodology is evaluated on the presence of the Fasciola hepatica in Galicia, a North-West region of Spain. PMID:27087038
Energy Technology Data Exchange (ETDEWEB)
Chan, M.T. [Univ. of Southern California, Los Angeles, CA (United States); Herman, G.T. [Univ. of Pennsylvania, Philadelphia, PA (United States); Levitan, E. [Technion, Haifa (Israel)
1996-12-31
We demonstrate that (i) classical methods of image reconstruction from projections can be improved upon by considering the output of such a method as a distorted version of the original image and applying a Bayesian approach to estimate from it the original image (based on a model of distortion and on a Gibbs distribution as the prior) and (ii) by selecting an {open_quotes}image-modeling{close_quotes} prior distribution (i.e., one which is such that it is likely that a random sample from it shares important characteristics of the images of the application area) one can improve over another Gibbs prior formulated using only pairwise interactions. We illustrate our approach using simulated Positron Emission Tomography (PET) data from realistic brain phantoms. Since algorithm performance ultimately depends on the diagnostic task being performed. we examine a number of different medically relevant figures of merit to give a fair comparison. Based on a training-and-testing evaluation strategy, we demonstrate that statistically significant improvements can be obtained using the proposed approach.
Bayesian Modeling of MPSS Data: Gene Expression Analysis of Bovine Salmonella Infection
Dhavala, Soma S.
2010-09-01
Massively Parallel Signature Sequencing (MPSS) is a high-throughput, counting-based technology available for gene expression profiling. It produces output that is similar to Serial Analysis of Gene Expression and is ideal for building complex relational databases for gene expression. Our goal is to compare the in vivo global gene expression profiles of tissues infected with different strains of Salmonella obtained using the MPSS technology. In this article, we develop an exact ANOVA type model for this count data using a zero-inflatedPoisson distribution, different from existing methods that assume continuous densities. We adopt two Bayesian hierarchical models-one parametric and the other semiparametric with a Dirichlet process prior that has the ability to "borrow strength" across related signatures, where a signature is a specific arrangement of the nucleotides, usually 16-21 base pairs long. We utilize the discreteness of Dirichlet process prior to cluster signatures that exhibit similar differential expression profiles. Tests for differential expression are carried out using nonparametric approaches, while controlling the false discovery rate. We identify several differentially expressed genes that have important biological significance and conclude with a summary of the biological discoveries. This article has supplementary materials online. © 2010 American Statistical Association.
Topology for statistical modeling of petascale data.
Energy Technology Data Exchange (ETDEWEB)
Pascucci, Valerio (University of Utah, Salt Lake City, UT); Mascarenhas, Ajith Arthur; Rusek, Korben (Texas A& M University, College Station, TX); Bennett, Janine Camille; Levine, Joshua (University of Utah, Salt Lake City, UT); Pebay, Philippe Pierre; Gyulassy, Attila (University of Utah, Salt Lake City, UT); Thompson, David C.; Rojas, Joseph Maurice (Texas A& M University, College Station, TX)
2011-07-01
This document presents current technical progress and dissemination of results for the Mathematics for Analysis of Petascale Data (MAPD) project titled 'Topology for Statistical Modeling of Petascale Data', funded by the Office of Science Advanced Scientific Computing Research (ASCR) Applied Math program. Many commonly used algorithms for mathematical analysis do not scale well enough to accommodate the size or complexity of petascale data produced by computational simulations. The primary goal of this project is thus to develop new mathematical tools that address both the petascale size and uncertain nature of current data. At a high level, our approach is based on the complementary techniques of combinatorial topology and statistical modeling. In particular, we use combinatorial topology to filter out spurious data that would otherwise skew statistical modeling techniques, and we employ advanced algorithms from algebraic statistics to efficiently find globally optimal fits to statistical models. This document summarizes the technical advances we have made to date that were made possible in whole or in part by MAPD funding. These technical contributions can be divided loosely into three categories: (1) advances in the field of combinatorial topology, (2) advances in statistical modeling, and (3) new integrated topological and statistical methods.
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