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...
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...
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...
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
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...
Errata: A survey of Bayesian predictive methods for model assessment, selection and comparison
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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.
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.
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 Variable Selection for Logistic Models Using Auxiliary Mixture Sampling
Tüchler, Regina
2006-01-01
The paper presents an Markov Chain Monte Carlo algorithm for both variable and covariance selection in the context of logistic mixed effects models. This algorithm allows us to sample solely from standard densities, with no additional tuning being needed. We apply a stochastic search variable approach to select explanatory variables as well as to determine the structure of the random effects covariance matrix. For logistic mixed effects models prior determination of explanatory variables and ...
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.
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.
Bayesian Model Selection and Prediction with Empirical Applications
Phillips, Peter C.B.
1992-01-01
This paper builds on some recent work by the author and Werner Ploberger (1991, 1994) on the development of "Bayes models" for time series and on the authors' model selection criterion "PIC." The PIC criterion is used in this paper to determine the lag order, the trend degree, and the presence or absence of a unit root in an autoregression with deterministic trend. A new forecast encompassing test for Bayes models is developed which allows one Bayes model to be compared with another on the ba...
Elsheikh, Ahmed H.
2014-02-01
A Hybrid Nested Sampling (HNS) algorithm is proposed for efficient Bayesian model calibration and prior model selection. The proposed algorithm combines, Nested Sampling (NS) algorithm, Hybrid Monte Carlo (HMC) sampling and gradient estimation using Stochastic Ensemble Method (SEM). NS is an efficient sampling algorithm that can be used for Bayesian calibration and estimating the Bayesian evidence for prior model selection. Nested sampling has the advantage of computational feasibility. Within the nested sampling algorithm, a constrained sampling step is performed. For this step, we utilize HMC to reduce the correlation between successive sampled states. HMC relies on the gradient of the logarithm of the posterior distribution, which we estimate using a stochastic ensemble method based on an ensemble of directional derivatives. SEM only requires forward model runs and the simulator is then used as a black box and no adjoint code is needed. The developed HNS algorithm is successfully applied for Bayesian calibration and prior model selection of several nonlinear subsurface flow problems. © 2013 Elsevier Inc.
Using Bayesian Model Selection to Characterize Neonatal Eeg Recordings
Mitchell, Timothy J.
2009-12-01
The brains of premature infants must undergo significant maturation outside of the womb and are thus particularly susceptible to injury. Electroencephalographic (EEG) recordings are an important diagnostic tool in determining if a newborn's brain is functioning normally or if injury has occurred. However, interpreting the recordings is difficult and requires the skills of a trained electroencephelographer. Because these EEG specialists are rare, an automated interpretation of newborn EEG recordings would increase access to an important diagnostic tool for physicians. To automate this procedure, we employ Bayesian probability theory to compute the posterior probability for the EEG features of interest and use the results in a program designed to mimic EEG specialists. Specifically, we will be identifying waveforms of varying frequency and amplitude, as well as periods of flat recordings where brain activity is minimal.
Bayesian model selection validates a biokinetic model for zirconium processing in humans
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Schmidl Daniel
2012-08-01
Full Text Available Abstract Background In radiation protection, biokinetic models for zirconium processing are of crucial importance in dose estimation and further risk analysis for humans exposed to this radioactive substance. They provide limiting values of detrimental effects and build the basis for applications in internal dosimetry, the prediction for radioactive zirconium retention in various organs as well as retrospective dosimetry. Multi-compartmental models are the tool of choice for simulating the processing of zirconium. Although easily interpretable, determining the exact compartment structure and interaction mechanisms is generally daunting. In the context of observing the dynamics of multiple compartments, Bayesian methods provide efficient tools for model inference and selection. Results We are the first to apply a Markov chain Monte Carlo approach to compute Bayes factors for the evaluation of two competing models for zirconium processing in the human body after ingestion. Based on in vivo measurements of human plasma and urine levels we were able to show that a recently published model is superior to the standard model of the International Commission on Radiological Protection. The Bayes factors were estimated by means of the numerically stable thermodynamic integration in combination with a recently developed copula-based Metropolis-Hastings sampler. Conclusions In contrast to the standard model the novel model predicts lower accretion of zirconium in bones. This results in lower levels of noxious doses for exposed individuals. Moreover, the Bayesian approach allows for retrospective dose assessment, including credible intervals for the initially ingested zirconium, in a significantly more reliable fashion than previously possible. All methods presented here are readily applicable to many modeling tasks in systems biology.
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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...
Schöniger, Anneli; Illman, Walter A.; Wöhling, Thomas; Nowak, Wolfgang
2015-12-01
Groundwater modelers face the challenge of how to assign representative parameter values to the studied aquifer. Several approaches are available to parameterize spatial heterogeneity in aquifer parameters. They differ in their conceptualization and complexity, ranging from homogeneous models to heterogeneous random fields. While it is common practice to invest more effort into data collection for models with a finer resolution of heterogeneities, there is a lack of advice which amount of data is required to justify a certain level of model complexity. In this study, we propose to use concepts related to Bayesian model selection to identify this balance. We demonstrate our approach on the characterization of a heterogeneous aquifer via hydraulic tomography in a sandbox experiment (Illman et al., 2010). We consider four increasingly complex parameterizations of hydraulic conductivity: (1) Effective homogeneous medium, (2) geology-based zonation, (3) interpolation by pilot points, and (4) geostatistical random fields. First, we investigate the shift in justified complexity with increasing amount of available data by constructing a model confusion matrix. This matrix indicates the maximum level of complexity that can be justified given a specific experimental setup. Second, we determine which parameterization is most adequate given the observed drawdown data. Third, we test how the different parameterizations perform in a validation setup. The results of our test case indicate that aquifer characterization via hydraulic tomography does not necessarily require (or justify) a geostatistical description. Instead, a zonation-based model might be a more robust choice, but only if the zonation is geologically adequate.
Bayesian model selection without evidences: application to the dark energy equation-of-state
Hee, Sonke; Hobson, Mike P; Lasenby, Anthony N
2015-01-01
A method is presented for Bayesian model selection without explicitly computing evidences, by using a combined likelihood and introducing an integer model selection parameter $n$ so that Bayes factors, or more generally posterior odds ratios, may be read off directly from the posterior of $n$. If the total number of models under consideration is specified a priori, the full joint parameter space $(\\theta, n)$ of the models is of fixed dimensionality and can be explored using standard MCMC or nested sampling methods, without the need for reversible jump MCMC techniques. The posterior on $n$ is then obtained by straightforward marginalisation. We demonstrate the efficacy of our approach by application to several toy models. We then apply it to constraining the dark energy equation-of-state using a free-form reconstruction technique. We show that $\\Lambda$CDM is significantly favoured over all extensions, including the simple $w(z){=}{\\rm constant}$ model.
International Nuclear Information System (INIS)
A general adaptive modeling algorithm for selection and validation of coarse-grained models of atomistic systems is presented. A Bayesian framework is developed to address uncertainties in parameters, data, and model selection. Algorithms for computing output sensitivities to parameter variances, model evidence and posterior model plausibilities for given data, and for computing what are referred to as Occam Categories in reference to a rough measure of model simplicity, make up components of the overall approach. Computational results are provided for representative applications
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.
Comparison of Two Gas Selection Methodologies: An Application of Bayesian Model Averaging
Energy Technology Data Exchange (ETDEWEB)
Renholds, Andrea S.; Thompson, Sandra E.; Anderson, Kevin K.; Chilton, Lawrence K.
2006-03-31
One goal of hyperspectral imagery analysis is the detection and characterization of plumes. Characterization includes identifying the gases in the plumes, which is a model selection problem. Two gas selection methods compared in this report are Bayesian model averaging (BMA) and minimum Akaike information criterion (AIC) stepwise regression (SR). Simulated spectral data from a three-layer radiance transfer model were used to compare the two methods. Test gases were chosen to span the types of spectra observed, which exhibit peaks ranging from broad to sharp. The size and complexity of the search libraries were varied. Background materials were chosen to either replicate a remote area of eastern Washington or feature many common background materials. For many cases, BMA and SR performed the detection task comparably in terms of the receiver operating characteristic curves. For some gases, BMA performed better than SR when the size and complexity of the search library increased. This is encouraging because we expect improved BMA performance upon incorporation of prior information on background materials and gases.
A bayesian integrative model for genetical genomics with spatially informed variable selection.
Cassese, Alberto; Guindani, Michele; Vannucci, Marina
2014-01-01
We consider a Bayesian hierarchical model for the integration of gene expression levels with comparative genomic hybridization (CGH) array measurements collected on the same subjects. The approach defines a measurement error model that relates the gene expression levels to latent copy number states. In turn, the latent states are related to the observed surrogate CGH measurements via a hidden Markov model. The model further incorporates variable selection with a spatial prior based on a probit link that exploits dependencies across adjacent DNA segments. Posterior inference is carried out via Markov chain Monte Carlo stochastic search techniques. We study the performance of the model in simulations and show better results than those achieved with recently proposed alternative priors. We also show an application to data from a genomic study on lung squamous cell carcinoma, where we identify potential candidates of associations between copy number variants and the transcriptional activity of target genes. Gene ontology (GO) analyses of our findings reveal enrichments in genes that code for proteins involved in cancer. Our model also identifies a number of potential candidate biomarkers for further experimental validation. PMID:25288877
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...
Bayesian model selection for testing the no-hair theorem with black hole ringdowns
Gossan, S; Sathyaprakash, B S
2011-01-01
General relativity predicts that a black hole that results from the merger of two compact stars (either black holes or neutron stars) is initially highly deformed but soon settles down to a quiescent state by emitting a superposition of quasi-normal modes (QNMs). The QNMs are damped sinusoids with characteristic frequencies and decay times that depend only on the mass and spin of the black hole and no other parameter - a statement of the no-hair theorem. In this paper we have examined the extent to which QNMs could be used to test the no-hair theorem with future ground- and space-based gravitational-wave detectors. We model departures from general relativity (GR) by introducing extra parameters which change the mode frequencies or decay times from their general relativistic values. With the aid of numerical simulations and Bayesian model selection, we assess the extent to which the presence of such a parameter could be inferred, and its value estimated. We find that it is harder to decipher the departure of d...
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
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
Hug, Sabine Carolin
2015-01-01
In this thesis we use differential equations for mathematically representing biological processes. For this we have to infer the associated parameters for fitting the differential equations to measurement data. If the structure of the ODE itself is uncertain, model selection methods have to be applied. We refine several existing Bayesian methods, ranging from an adaptive scheme for the computation of high-dimensional integrals to multi-chain Metropolis-Hastings algorithms for high-dimensional...
Martínez, Isabel; Wiegand, Thorsten; Camarero, J Julio; Batllori, Enric; Gutiérrez, Emilia
2011-05-01
Alpine tree-line ecotones are characterized by marked changes at small spatial scales that may result in a variety of physiognomies. A set of alternative individual-based models was tested with data from four contrasting Pinus uncinata ecotones in the central Spanish Pyrenees to reveal the minimal subset of processes required for tree-line formation. A Bayesian approach combined with Markov chain Monte Carlo methods was employed to obtain the posterior distribution of model parameters, allowing the use of model selection procedures. The main features of real tree lines emerged only in models considering nonlinear responses in individual rates of growth or mortality with respect to the altitudinal gradient. Variation in tree-line physiognomy reflected mainly changes in the relative importance of these nonlinear responses, while other processes, such as dispersal limitation and facilitation, played a secondary role. Different nonlinear responses also determined the presence or absence of krummholz, in agreement with recent findings highlighting a different response of diffuse and abrupt or krummholz tree lines to climate change. The method presented here can be widely applied in individual-based simulation models and will turn model selection and evaluation in this type of models into a more transparent, effective, and efficient exercise. PMID:21508601
Wöhling, T.; Schöniger, A.; Geiges, A.; Nowak, W.; Gayler, S.
2013-12-01
The objective selection of appropriate models for realistic simulations of coupled soil-plant processes is a challenging task since the processes are complex, not fully understood at larger scales, and highly non-linear. Also, comprehensive data sets are scarce, and measurements are uncertain. In the past decades, a variety of different models have been developed that exhibit a wide range of complexity regarding their approximation of processes in the coupled model compartments. We present a method for evaluating experimental design for maximum confidence in the model selection task. The method considers uncertainty in parameters, measurements and model structures. Advancing the ideas behind Bayesian Model Averaging (BMA), we analyze the changes in posterior model weights and posterior model choice uncertainty when more data are made available. This allows assessing the power of different data types, data densities and data locations in identifying the best model structure from among a suite of plausible models. The models considered in this study are the crop models CERES, SUCROS, GECROS and SPASS, which are coupled to identical routines for simulating soil processes within the modelling framework Expert-N. The four models considerably differ in the degree of detail at which crop growth and root water uptake are represented. Monte-Carlo simulations were conducted for each of these models considering their uncertainty in soil hydraulic properties and selected crop model parameters. Using a Bootstrap Filter (BF), the models were then conditioned on field measurements of soil moisture, matric potential, leaf-area index, and evapotranspiration rates (from eddy-covariance measurements) during a vegetation period of winter wheat at a field site at the Swabian Alb in Southwestern Germany. Following our new method, we derived model weights when using all data or different subsets thereof. We discuss to which degree the posterior mean outperforms the prior mean and all
Bayesian model averaging to explore the worth of data for soil-plant model selection and prediction
Wöhling, Thomas; Schöniger, Anneli; Gayler, Sebastian; Nowak, Wolfgang
2015-04-01
A Bayesian model averaging (BMA) framework is presented to evaluate the worth of different observation types and experimental design options for (1) more confidence in model selection and (2) for increased predictive reliability. These two modeling tasks are handled separately because model selection aims at identifying the most appropriate model with respect to a given calibration data set, while predictive reliability aims at reducing uncertainty in model predictions through constraining the plausible range of both models and model parameters. For that purpose, we pursue an optimal design of measurement framework that is based on BMA and that considers uncertainty in parameters, measurements, and model structures. We apply this framework to select between four crop models (the vegetation components of CERES, SUCROS, GECROS, and SPASS), which are coupled to identical routines for simulating soil carbon and nitrogen turnover, soil heat and nitrogen transport, and soil water movement. An ensemble of parameter realizations was generated for each model using Monte-Carlo simulation. We assess each model's plausibility by determining its posterior weight, which signifies the probability to have generated a given experimental data set. Several BMA analyses were conducted for different data packages with measurements of soil moisture, evapotranspiration (ETa), and leaf area index (LAI). The posterior weights resulting from the different BMA runs were compared to the weight distribution of a reference run with all data types to investigate the utility of different data packages and monitoring design options in identifying the most appropriate model in the ensemble. We found that different (combinations of) data types support different models and none of the four crop models outperforms all others under all data scenarios. The best model discrimination was observed for those data where the competing models disagree the most. The data worth for reducing prediction
Multi-scale inference of interaction rules in animal groups using Bayesian model selection.
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Richard P Mann
Full Text Available Inference of interaction rules of animals moving in groups usually relies on an analysis of large scale system behaviour. Models are tuned through repeated simulation until they match the observed behaviour. More recent work has used the fine scale motions of animals to validate and fit the rules of interaction of animals in groups. Here, we use a Bayesian methodology to compare a variety of models to the collective motion of glass prawns (Paratya australiensis. We show that these exhibit a stereotypical 'phase transition', whereby an increase in density leads to the onset of collective motion in one direction. We fit models to this data, which range from: a mean-field model where all prawns interact globally; to a spatial Markovian model where prawns are self-propelled particles influenced only by the current positions and directions of their neighbours; up to non-Markovian models where prawns have 'memory' of previous interactions, integrating their experiences over time when deciding to change behaviour. We show that the mean-field model fits the large scale behaviour of the system, but does not capture the observed locality of interactions. Traditional self-propelled particle models fail to capture the fine scale dynamics of the system. The most sophisticated model, the non-Markovian model, provides a good match to the data at both the fine scale and in terms of reproducing global dynamics, while maintaining a biologically plausible perceptual range. We conclude that prawns' movements are influenced by not just the current direction of nearby conspecifics, but also those encountered in the recent past. Given the simplicity of prawns as a study system our research suggests that self-propelled particle models of collective motion should, if they are to be realistic at multiple biological scales, include memory of previous interactions and other non-Markovian effects.
Multi-scale inference of interaction rules in animal groups using Bayesian model selection.
Directory of Open Access Journals (Sweden)
Richard P Mann
2012-01-01
Full Text Available Inference of interaction rules of animals moving in groups usually relies on an analysis of large scale system behaviour. Models are tuned through repeated simulation until they match the observed behaviour. More recent work has used the fine scale motions of animals to validate and fit the rules of interaction of animals in groups. Here, we use a Bayesian methodology to compare a variety of models to the collective motion of glass prawns (Paratya australiensis. We show that these exhibit a stereotypical 'phase transition', whereby an increase in density leads to the onset of collective motion in one direction. We fit models to this data, which range from: a mean-field model where all prawns interact globally; to a spatial Markovian model where prawns are self-propelled particles influenced only by the current positions and directions of their neighbours; up to non-Markovian models where prawns have 'memory' of previous interactions, integrating their experiences over time when deciding to change behaviour. We show that the mean-field model fits the large scale behaviour of the system, but does not capture fine scale rules of interaction, which are primarily mediated by physical contact. Conversely, the Markovian self-propelled particle model captures the fine scale rules of interaction but fails to reproduce global dynamics. The most sophisticated model, the non-Markovian model, provides a good match to the data at both the fine scale and in terms of reproducing global dynamics. We conclude that prawns' movements are influenced by not just the current direction of nearby conspecifics, but also those encountered in the recent past. Given the simplicity of prawns as a study system our research suggests that self-propelled particle models of collective motion should, if they are to be realistic at multiple biological scales, include memory of previous interactions and other non-Markovian effects.
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
Directory of Open Access Journals (Sweden)
Pierre eBerthet
2012-10-01
Full Text Available Several studies have shown a strong involvement of the basal ganglia (BG in action selection and dopamine dependent learning. The dopaminergic signal to striatum, the input stage of the BG, has been commonly described as coding a reward prediction error (RPE, i.e. the difference between the predicted and actual reward. The RPE has been hypothesized to be critical in the modulation of the synaptic plasticity in cortico-striatal synapses in the direct and indirect pathway. We developed an abstract computational model of the BG, with a dual pathway structure functionally corresponding to the direct and indirect pathways, and compared its behaviour to biological data as well as other reinforcement learning models. The computations in our model are inspired by Bayesian inference, and the synaptic plasticity changes depend on a three factor Hebbian-Bayesian learning rule based on co-activation of pre- and post-synaptic units and on the value of the RPE. The model builds on a modified Actor-Critic architecture and implements the direct (Go and the indirect (NoGo pathway, as well as the reward prediction (RP system, acting in a complementary fashion. We investigated the performance of the model system when different configurations of the Go, NoGo and RP system were utilized, e.g. using only the Go, NoGo, or RP system, or combinations of those. Learning performance was investigated in several types of learning paradigms, such as learning-relearning, successive learning, stochastic learning, reversal learning and a two-choice task. The RPE and the activity of the model during learning were similar to monkey electrophysiological and behavioural data. Our results, however, show that there is not a unique best way to configure this BG model to handle well all the learning paradigms tested. We thus suggest that an agent might dynamically configure its action selection mode, possibly depending on task characteristics and also on how much time is available.
Berthet, Pierre; Hellgren-Kotaleski, Jeanette; Lansner, Anders
2012-01-01
Several studies have shown a strong involvement of the basal ganglia (BG) in action selection and dopamine dependent learning. The dopaminergic signal to striatum, the input stage of the BG, has been commonly described as coding a reward prediction error (RPE), i.e., the difference between the predicted and actual reward. The RPE has been hypothesized to be critical in the modulation of the synaptic plasticity in cortico-striatal synapses in the direct and indirect pathway. We developed an abstract computational model of the BG, with a dual pathway structure functionally corresponding to the direct and indirect pathways, and compared its behavior to biological data as well as other reinforcement learning models. The computations in our model are inspired by Bayesian inference, and the synaptic plasticity changes depend on a three factor Hebbian-Bayesian learning rule based on co-activation of pre- and post-synaptic units and on the value of the RPE. The model builds on a modified Actor-Critic architecture and implements the direct (Go) and the indirect (NoGo) pathway, as well as the reward prediction (RP) system, acting in a complementary fashion. We investigated the performance of the model system when different configurations of the Go, NoGo, and RP system were utilized, e.g., using only the Go, NoGo, or RP system, or combinations of those. Learning performance was investigated in several types of learning paradigms, such as learning-relearning, successive learning, stochastic learning, reversal learning and a two-choice task. The RPE and the activity of the model during learning were similar to monkey electrophysiological and behavioral data. Our results, however, show that there is not a unique best way to configure this BG model to handle well all the learning paradigms tested. We thus suggest that an agent might dynamically configure its action selection mode, possibly depending on task characteristics and also on how much time is available. PMID:23060764
Bayesian Variable Selection for Detecting Adaptive Genomic Differences Among Populations
Riebler, Andrea; Held, Leonhard; Stephan, Wolfgang
2008-01-01
We extend an Fst-based Bayesian hierarchical model, implemented via Markov chain Monte Carlo, for the detection of loci that might be subject to positive selection. This model divides the Fst-influencing factors into locus-specific effects, population-specific effects, and effects that are specific for the locus in combination with the population. We introduce a Bayesian auxiliary variable for each locus effect to automatically select nonneutral locus effects. As a by-product, the efficiency ...
Directory of Open Access Journals (Sweden)
Mark I Rowley
Full Text Available We present novel Bayesian methods for the analysis of exponential decay data that exploit the evidence carried by every detected decay event and enables robust extension to advanced processing. Our algorithms are presented in the context of fluorescence lifetime imaging microscopy (FLIM and particular attention has been paid to model the time-domain system (based on time-correlated single photon counting with unprecedented accuracy. We present estimates of decay parameters for mono- and bi-exponential systems, offering up to a factor of two improvement in accuracy compared to previous popular techniques. Results of the analysis of synthetic and experimental data are presented, and areas where the superior precision of our techniques can be exploited in Förster Resonance Energy Transfer (FRET experiments are described. Furthermore, we demonstrate two advanced processing methods: decay model selection to choose between differing models such as mono- and bi-exponential, and the simultaneous estimation of instrument and decay parameters.
Zhang, Linlin; Guindani, Michele; Versace, Francesco; Vannucci, Marina
2014-07-15
In this paper we present a novel wavelet-based Bayesian nonparametric regression model for the analysis of functional magnetic resonance imaging (fMRI) data. Our goal is to provide a joint analytical framework that allows to detect regions of the brain which exhibit neuronal activity in response to a stimulus and, simultaneously, infer the association, or clustering, of spatially remote voxels that exhibit fMRI time series with similar characteristics. We start by modeling the data with a hemodynamic response function (HRF) with a voxel-dependent shape parameter. We detect regions of the brain activated in response to a given stimulus by using mixture priors with a spike at zero on the coefficients of the regression model. We account for the complex spatial correlation structure of the brain by using a Markov random field (MRF) prior on the parameters guiding the selection of the activated voxels, therefore capturing correlation among nearby voxels. In order to infer association of the voxel time courses, we assume correlated errors, in particular long memory, and exploit the whitening properties of discrete wavelet transforms. Furthermore, we achieve clustering of the voxels by imposing a Dirichlet process (DP) prior on the parameters of the long memory process. For inference, we use Markov Chain Monte Carlo (MCMC) sampling techniques that combine Metropolis-Hastings schemes employed in Bayesian variable selection with sampling algorithms for nonparametric DP models. We explore the performance of the proposed model on simulated data, with both block- and event-related design, and on real fMRI data. PMID:24650600
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…
Sudre, Carole H; Cardoso, M Jorge; Bouvy, Willem H; Biessels, Geert Jan; Barnes, Josephine; Ourselin, Sebastien
2015-10-01
In neuroimaging studies, pathologies can present themselves as abnormal intensity patterns. Thus, solutions for detecting abnormal intensities are currently under investigation. As each patient is unique, an unbiased and biologically plausible model of pathological data would have to be able to adapt to the subject's individual presentation. Such a model would provide the means for a better understanding of the underlying biological processes and improve one's ability to define pathologically meaningful imaging biomarkers. With this aim in mind, this work proposes a hierarchical fully unsupervised model selection framework for neuroimaging data which enables the distinction between different types of abnormal image patterns without pathological a priori knowledge. Its application on simulated and clinical data demonstrated the ability to detect abnormal intensity clusters, resulting in a competitive to improved behavior in white matter lesion segmentation when compared to three other freely-available automated methods. PMID:25850086
Bayesian variable selection with spherically symmetric priors
De Kock, M B
2014-01-01
We propose that Bayesian variable selection for linear parametrisations with Gaussian iid likelihoods be based on the spherical symmetry of the diagonalised parameter space. This reduces the multidimensional parameter space problem to one dimension without the need for conjugate priors. Combining this likelihood with what we call the r-prior results in a framework in which we can derive closed forms for the evidence, posterior and characteristic function for four different r-priors, including the hyper-g prior and the Zellner-Siow prior, which are shown to be special cases of our r-prior. Two scenarios of a single variable dispersion parameter and of fixed dispersion are studied separately, and asymptotic forms comparable to the traditional information criteria are derived. In a simple simulation exercise, we find that model comparison based on our uniform r-prior appears to fare better than the current model comparison schemes.
Secondary eclipses in the CoRoT light curves: A homogeneous search based on Bayesian model selection
Parviainen, Hannu; Belmonte, Juan Antonio
2012-01-01
We aim to identify and characterize secondary eclipses in the original light curves of all published CoRoT planets using uniform detection and evaluation critetia. Our analysis is based on a Bayesian model selection between two competing models: one with and one without an eclipse signal. The search is carried out by mapping the Bayes factor in favor of the eclipse model as a function of the eclipse center time, after which the characterization of plausible eclipse candidates is done by estimating the posterior distributions of the eclipse model parameters using Markov Chain Monte Carlo. We discover statistically significant eclipse events for two planets, CoRoT-6b and CoRoT-11b, and for one brown dwarf, CoRoT-15b. We also find marginally significant eclipse events passing our plausibility criteria for CoRoT-3b, 13b, 18b, and 21b. The previously published CoRoT-1b and CoRoT-2b eclipses are also confirmed.
Bayesian model selection for electromagnetic kaon production in the Regge-plus-resonance framework
De Cruz, Lesley
2011-01-01
A long-standing goal of hadronic physics is to obtain a detailed map of the nucleon's resonance spectrum. This would help bridge the gap between hadrodynamical models on the one hand and constituent quark models on the other hand. Some quark models predict so-called "missing resonances" that have not been found in analyses of pion-nucleon scattering data. Input from non-pionic reactions such as open-strangeness photoproduction is key to resolve the status of these missing resonances, as some ...
Papastamoulis, Panagiotis; Rattray, Magnus
2014-01-01
Recent advances in molecular biology allow the quantification of the transcriptome and scoring transcripts as differentially or equally expressed between two biological conditions. Although these two tasks are closely linked, the available inference methods treat them separately: a primary model is used to estimate expression and its output is post-processed using a differential expression model. In this paper, both issues are simultaneously addressed by proposing the joint estimation of expr...
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 Variable Selection in Cost-Effectiveness Analysis
Directory of Open Access Journals (Sweden)
Miguel A. Negrín
2010-04-01
Full Text Available Linear regression models are often used to represent the cost and effectiveness of medical treatment. The covariates used may include sociodemographic variables, such as age, gender or race; clinical variables, such as initial health status, years of treatment or the existence of concomitant illnesses; and a binary variable indicating the treatment received. However, most studies estimate only one model, which usually includes all the covariates. This procedure ignores the question of uncertainty in model selection. In this paper, we examine four alternative Bayesian variable selection methods that have been proposed. In this analysis, we estimate the inclusion probability of each covariate in the real model conditional on the data. Variable selection can be useful for estimating incremental effectiveness and incremental cost, through Bayesian model averaging, as well as for subgroup analysis.
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 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 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...
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 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 item selection in constrained adaptive testing using shadow tests
Veldkamp, Bernard P.
2010-01-01
Application of Bayesian item selection criteria in computerized adaptive testing might result in improvement of bias and MSE of the ability estimates. The question remains how to apply Bayesian item selection criteria in the context of constrained adaptive testing, where large numbers of specificati
Bayesian Item Selection in Constrained Adaptive Testing Using Shadow Tests
Veldkamp, Bernard P.
2010-01-01
Application of Bayesian item selection criteria in computerized adaptive testing might result in improvement of bias and MSE of the ability estimates. The question remains how to apply Bayesian item selection criteria in the context of constrained adaptive testing, where large numbers of specifications have to be taken into account in the item…
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....
Cameron, Ewan
2013-01-01
In the second paper of this series we extend our Bayesian reanalysis of the evidence for a cosmic variation of the fine structure constant to the semi-parametric modelling regime. By adopting a mixture of Dirichlet processes prior for the unexplained errors in each instrumental subgroup of the benchmark quasar dataset we go some way towards freeing our model selection procedure from the apparent subjectivity of a fixed distributional form. Despite the infinite-dimensional domain of the error hierarchy so constructed we are able to demonstrate a recursive scheme for marginal likelihood estimation with prior-sensitivity analysis directly analogous to that presented in Paper I, thereby allowing the robustness of our posterior Bayes factors to hyper-parameter choice and model specification to be readily verified. In the course of this work we elucidate various similarities between unexplained error problems in the seemingly disparate fields of astronomy and clinical meta-analysis, and we highlight a number of sop...
Bayesian site selection for fast Gaussian process regression
Pourhabib, Arash
2014-02-05
Gaussian Process (GP) regression is a popular method in the field of machine learning and computer experiment designs; however, its ability to handle large data sets is hindered by the computational difficulty in inverting a large covariance matrix. Likelihood approximation methods were developed as a fast GP approximation, thereby reducing the computation cost of GP regression by utilizing a much smaller set of unobserved latent variables called pseudo points. This article reports a further improvement to the likelihood approximation methods by simultaneously deciding both the number and locations of the pseudo points. The proposed approach is a Bayesian site selection method where both the number and locations of the pseudo inputs are parameters in the model, and the Bayesian model is solved using a reversible jump Markov chain Monte Carlo technique. Through a number of simulated and real data sets, it is demonstrated that with appropriate priors chosen, the Bayesian site selection method can produce a good balance between computation time and prediction accuracy: it is fast enough to handle large data sets that a full GP is unable to handle, and it improves, quite often remarkably, the prediction accuracy, compared with the existing likelihood approximations. © 2014 Taylor and Francis Group, LLC.
Towards Distributed Bayesian Estimation A Short Note on Selected Aspects
Czech Academy of Sciences Publication Activity Database
Dedecius, Kamil; Sečkárová, Vladimíra
Prague: Institute of Information Theory and Automation, 2011, s. 67-72. ISBN 978-80-903834-6-3. [The 2nd International Workshop od Decision Making with Multiple Imperfect Decision Makers. Held in Conjunction with the 25th Annual Conference on Neural Information Processing Systems (NIPS 2011). Sierra Nevada (ES), 16.12.2011-16.12.2011] R&D Projects: GA ČR GA102/08/0567 Institutional research plan: CEZ:AV0Z10750506 Keywords : efficient estimation * a linear or nonlinear model * distributed estimation * Bayesian decision making Subject RIV: BB - Applied Statistics, Operational Research http://library.utia.cas.cz/separaty/2011/AS/dedecius-towards distributed bayesian estimation a short note on selected aspects.pdf
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...
Bayesian variable selection for detecting adaptive genomic differences among populations.
Riebler, Andrea; Held, Leonhard; Stephan, Wolfgang
2008-03-01
We extend an F(st)-based Bayesian hierarchical model, implemented via Markov chain Monte Carlo, for the detection of loci that might be subject to positive selection. This model divides the F(st)-influencing factors into locus-specific effects, population-specific effects, and effects that are specific for the locus in combination with the population. We introduce a Bayesian auxiliary variable for each locus effect to automatically select nonneutral locus effects. As a by-product, the efficiency of the original approach is improved by using a reparameterization of the model. The statistical power of the extended algorithm is assessed with simulated data sets from a Wright-Fisher model with migration. We find that the inclusion of model selection suggests a clear improvement in discrimination as measured by the area under the receiver operating characteristic (ROC) curve. Additionally, we illustrate and discuss the quality of the newly developed method on the basis of an allozyme data set of the fruit fly Drosophila melanogaster and a sequence data set of the wild tomato Solanum chilense. For data sets with small sample sizes, high mutation rates, and/or long sequences, however, methods based on nucleotide statistics should be preferred. PMID:18245358
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 item selection in constrained adaptive testing using shadow tests
Bernard P. Veldkamp
2010-01-01
Application of Bayesian item selection criteria in computerized adaptive testing might result in improvement of bias and MSE of the ability estimates. The question remains how to apply Bayesian item selection criteria in the context of constrained adaptive testing, where large numbers of specifications have to be taken into account in the item selection process. The Shadow Test Approach is a general purpose algorithm for administering constrained CAT. In this paper it is shown how the approac...
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 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...
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
Optimal predictive model selection
Barbieri, Maria Maddalena; Berger, James O.
2004-01-01
Often the goal of model selection is to choose a model for future prediction, and it is natural to measure the accuracy of a future prediction by squared error loss. Under the Bayesian approach, it is commonly perceived that the optimal predictive model is the model with highest posterior probability, but this is not necessarily the case. In this paper we show that, for selection among normal linear models, the optimal predictive model is often the median probability model, which is defined a...
Ross, Cody T; Strimling, Pontus; Ericksen, Karen Paige; Lindenfors, Patrik; Mulder, Monique Borgerhoff
2016-06-01
We present formal evolutionary models for the origins and persistence of the practice of Female Genital Modification (FGMo). We then test the implications of these models using normative cross-cultural data on FGMo in Africa and Bayesian phylogenetic methods that explicitly model adaptive evolution. Empirical evidence provides some support for the findings of our evolutionary models that the de novo origins of the FGMo practice should be associated with social stratification, and that social stratification should place selective pressures on the adoption of FGMo; these results, however, are tempered by the finding that FGMo has arisen in many cultures that have no social stratification, and that forces operating orthogonally to stratification appear to play a more important role in the cross-cultural distribution of FGMo. To explain these cases, one must consider cultural evolutionary explanations in conjunction with behavioral ecological ones. We conclude with a discussion of the implications of our study for policies designed to end the practice of FGMo. PMID:26846688
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 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’...
Kuiper, Rebecca M; Nederhoff, Tim; Klugkist, Irene
2015-05-01
In this paper, the performance of six types of techniques for comparisons of means is examined. These six emerge from the distinction between the method employed (hypothesis testing, model selection using information criteria, or Bayesian model selection) and the set of hypotheses that is investigated (a classical, exploration-based set of hypotheses containing equality constraints on the means, or a theory-based limited set of hypotheses with equality and/or order restrictions). A simulation study is conducted to examine the performance of these techniques. We demonstrate that, if one has specific, a priori specified hypotheses, confirmation (i.e., investigating theory-based hypotheses) has advantages over exploration (i.e., examining all possible equality-constrained hypotheses). Furthermore, examining reasonable order-restricted hypotheses has more power to detect the true effect/non-null hypothesis than evaluating only equality restrictions. Additionally, when investigating more than one theory-based hypothesis, model selection is preferred over hypothesis testing. Because of the first two results, we further examine the techniques that are able to evaluate order restrictions in a confirmatory fashion by examining their performance when the homogeneity of variance assumption is violated. Results show that the techniques are robust to heterogeneity when the sample sizes are equal. When the sample sizes are unequal, the performance is affected by heterogeneity. The size and direction of the deviations from the baseline, where there is no heterogeneity, depend on the effect size (of the means) and on the trend in the group variances with respect to the ordering of the group sizes. Importantly, the deviations are less pronounced when the group variances and sizes exhibit the same trend (e.g., are both increasing with group number). PMID:24975402
A Bayesian variable selection procedure for ranking overlapping gene sets
DEFF Research Database (Denmark)
Skarman, Axel; Mahdi Shariati, Mohammad; Janss, Luc;
2012-01-01
data to study how the variable selection method was affected by overlaps among the pathways. In addition, we compared our approach to another that ignores the overlaps, and studied the differences in the prioritization. The variable selection method was robust to a change in prior probability...... described. In many cases, these methods test one gene set at a time, and therefore do not consider overlaps among the pathways. Here, we present a Bayesian variable selection method to prioritize gene sets that overcomes this limitation by considering all gene sets simultaneously. We applied Bayesian...... variable selection to differential expression to prioritize the molecular and genetic pathways involved in the responses to Escherichia coli infection in Danish Holstein cows. Results We used a Bayesian variable selection method to prioritize Kyoto Encyclopedia of Genes and Genomes pathways. We used our...
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
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 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
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 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...
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...
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 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.
Dynamic sensor action selection with Bayesian decision analysis
Kristensen, Steen; Hansen, Volker; Kondak, Konstantin
1998-10-01
The aim of this work is to create a framework for the dynamic planning of sensor actions for an autonomous mobile robot. The framework uses Bayesian decision analysis, i.e., a decision-theoretic method, to evaluate possible sensor actions and selecting the most appropriate ones given the available sensors and what is currently known about the state of the world. Since sensing changes the knowledge of the system and since the current state of the robot (task, position, etc.) determines what knowledge is relevant, the evaluation and selection of sensing actions is an on-going process that effectively determines the behavior of the robot. The framework has been implemented on a real mobile robot and has been proven to be able to control in real-time the sensor actions of the system. In current work we are investigating methods to reduce or automatically generate the necessary model information needed by the decision- theoretic method to select the appropriate sensor actions.
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...
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.
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). ...
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 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 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.
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
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...
Feature Selection for Bayesian Evaluation of Trauma Death Risk
Jakaite, L
2008-01-01
In the last year more than 70,000 people have been brought to the UK hospitals with serious injuries. Each time a clinician has to urgently take a patient through a screening procedure to make a reliable decision on the trauma treatment. Typically, such procedure comprises around 20 tests; however the condition of a trauma patient remains very difficult to be tested properly. What happens if these tests are ambiguously interpreted, and information about the severity of the injury will come misleading? The mistake in a decision can be fatal: using a mild treatment can put a patient at risk of dying from posttraumatic shock, while using an overtreatment can also cause death. How can we reduce the risk of the death caused by unreliable decisions? It has been shown that probabilistic reasoning, based on the Bayesian methodology of averaging over decision models, allows clinicians to evaluate the uncertainty in decision making. Based on this methodology, in this paper we aim at selecting the most important screeni...
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.
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 variable selection and data integration for biological regulatory networks
Jensen, Shane T; Chen, Guang; Stoeckert, Jr, Christian J.
2007-01-01
A substantial focus of research in molecular biology are gene regulatory networks: the set of transcription factors and target genes which control the involvement of different biological processes in living cells. Previous statistical approaches for identifying gene regulatory networks have used gene expression data, ChIP binding data or promoter sequence data, but each of these resources provides only partial information. We present a Bayesian hierarchical model that integrates all three dat...
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...
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.
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.
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...
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...
Bayesian Factor Analysis as a Variable-Selection Problem: Alternative Priors and Consequences.
Lu, Zhao-Hua; Chow, Sy-Miin; Loken, Eric
2016-01-01
Factor analysis is a popular statistical technique for multivariate data analysis. Developments in the structural equation modeling framework have enabled the use of hybrid confirmatory/exploratory approaches in which factor-loading structures can be explored relatively flexibly within a confirmatory factor analysis (CFA) framework. Recently, Muthén & Asparouhov proposed a Bayesian structural equation modeling (BSEM) approach to explore the presence of cross loadings in CFA models. We show that the issue of determining factor-loading patterns may be formulated as a Bayesian variable selection problem in which Muthén and Asparouhov's approach can be regarded as a BSEM approach with ridge regression prior (BSEM-RP). We propose another Bayesian approach, denoted herein as the Bayesian structural equation modeling with spike-and-slab prior (BSEM-SSP), which serves as a one-stage alternative to the BSEM-RP. We review the theoretical advantages and disadvantages of both approaches and compare their empirical performance relative to two modification indices-based approaches and exploratory factor analysis with target rotation. A teacher stress scale data set is used to demonstrate our approach. PMID:27314566
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
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
Lu, Zhaohua; Zhu, Hongtu; Knickmeyer, Rebecca C.; Sullivan, Patrick F.; Stephanie, Williams N.; Zou, Fei
2015-01-01
The power of genome-wide association studies (GWAS) for mapping complex traits with single SNP analysis may be undermined by modest SNP effect sizes, unobserved causal SNPs, correlation among adjacent SNPs, and SNP-SNP interactions. Alternative approaches for testing the association between a single SNP-set and individual phenotypes have been shown to be promising for improving the power of GWAS. We propose a Bayesian latent variable selection (BLVS) method to simultaneously model the joint a...
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 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.
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...
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.
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...
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.
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...
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.
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.
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...
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.
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...
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 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 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}).
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...
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...
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...
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...
On the use of pseudo-likelihoods in Bayesian variable selection.
Racugno, Walter; Salvan, Alessandra; Ventura, Laura
2005-01-01
In the presence of nuisance parameters, we discuss a one-parameter Bayesian analysis based on a pseudo-likelihood assuming a default prior distribution for the parameter of interest only. Although this way to proceed cannot always be considered as orthodox in the Bayesian perspective, it is of interest to evaluate whether the use of suitable pseudo-likelihoods may be proposed for Bayesian inference. Attention is focused in the context of regression models, in particular on inference about a s...
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
Finding the Most Distant Quasars Using Bayesian Selection Methods
Mortlock, Daniel
2014-01-01
Quasars, the brightly glowing disks of material that can form around the super-massive black holes at the centres of large galaxies, are amongst the most luminous astronomical objects known and so can be seen at great distances. The most distant known quasars are seen as they were when the Universe was less than a billion years old (i.e., $\\sim\\!7%$ of its current age). Such distant quasars are, however, very rare, and so are difficult to distinguish from the billions of other comparably-bright sources in the night sky. In searching for the most distant quasars in a recent astronomical sky survey (the UKIRT Infrared Deep Sky Survey, UKIDSS), there were $\\sim\\!10^3$ apparently plausible candidates for each expected quasar, far too many to reobserve with other telescopes. The solution to this problem was to apply Bayesian model comparison, making models of the quasar population and the dominant contaminating population (Galactic stars) to utilise the information content in the survey measurements. The result wa...
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...
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
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...
Steady-state priors and Bayesian variable selection in VAR forecasting
Louzis, Dimitrios P.
2015-01-01
This study proposes methods for estimating Bayesian vector autoregressions (VARs) with an automatic variable selection and an informative prior on the unconditional mean or steady-state of the system. We show that extant Gibbs sampling methods for Bayesian variable selection can be efficiently extended to incorporate prior beliefs on the steady-state of the economy. Empirical analysis, based on three major US macroeconomic time series, indicates that the out-of-sample forecasting accuracy of ...
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.
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...
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.
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...
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.
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...
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 models and hyper-parameters for robust optic-flow estimation
Héas, Patrick; Herzet, Cédric; Memin, Etienne
2012-01-01
International audience Selecting optimal models and hyper-parameters is crucial for accurate optic-flow estimation. This paper provides a solution to the problem in a generic Bayesian framework. The method is based on a conditional model linking the image intensity function, the unknown velocity field, hyper-parameters and the prior and likelihood motion models. Inference is performed on each of the three-level of this so-defined hierarchical model by maximization of marginalized \\textit{a...
Gamma prior distribution selection for Bayesian analysis of failure rate and reliability
International Nuclear Information System (INIS)
It is assumed that the phenomenon under study is such that the time-to-failure may be modeled by an exponential distribution with failure rate lambda. For Bayesian analyses of the assumed model, the family of gamma distributions provides conjugate prior models for lambda. Thus, an experimenter needs to select a particular gamma model to conduct a Bayesian reliability analysis. The purpose of this report is to present a methodology that can be used to translate engineering information, experience, and judgment into a choice of a gamma prior distribution. The proposed methodology assumes that the practicing engineer can provide percentile data relating to either the failure rate or the reliability of the phenomenon being investigated. For example, the methodology will select the gamma prior distribution which conveys an engineer's belief that the failure rate lambda simultaneously satisfies the probability statements, P(lambda less than 1.0 x 10-3) equals 0.50 and P(lambda less than 1.0 x 10-5) equals 0.05. That is, two percentiles provided by an engineer are used to determine a gamma prior model which agrees with the specified percentiles. For those engineers who prefer to specify reliability percentiles rather than the failure rate percentiles illustrated above, it is possible to use the induced negative-log gamma prior distribution which satisfies the probability statements, P(R(t0) less than 0.99) equals 0.50 and P(R(t0) less than 0.99999) equals 0.95, for some operating time t0. The report also includes graphs for selected percentiles which assist an engineer in applying the procedure. 28 figures, 16 tables
Gamma prior distribution selection for Bayesian analysis of failure rate and reliability
Energy Technology Data Exchange (ETDEWEB)
Waller, R.A.; Johnson, M.M.; Waterman, M.S.; Martz, H.F. Jr.
1976-07-01
It is assumed that the phenomenon under study is such that the time-to-failure may be modeled by an exponential distribution with failure rate lambda. For Bayesian analyses of the assumed model, the family of gamma distributions provides conjugate prior models for lambda. Thus, an experimenter needs to select a particular gamma model to conduct a Bayesian reliability analysis. The purpose of this report is to present a methodology that can be used to translate engineering information, experience, and judgment into a choice of a gamma prior distribution. The proposed methodology assumes that the practicing engineer can provide percentile data relating to either the failure rate or the reliability of the phenomenon being investigated. For example, the methodology will select the gamma prior distribution which conveys an engineer's belief that the failure rate lambda simultaneously satisfies the probability statements, P(lambda less than 1.0 x 10/sup -3/) equals 0.50 and P(lambda less than 1.0 x 10/sup -5/) equals 0.05. That is, two percentiles provided by an engineer are used to determine a gamma prior model which agrees with the specified percentiles. For those engineers who prefer to specify reliability percentiles rather than the failure rate percentiles illustrated above, it is possible to use the induced negative-log gamma prior distribution which satisfies the probability statements, P(R(t/sub 0/) less than 0.99) equals 0.50 and P(R(t/sub 0/) less than 0.99999) equals 0.95, for some operating time t/sub 0/. The report also includes graphs for selected percentiles which assist an engineer in applying the procedure. 28 figures, 16 tables.
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.
Selection of Trusted Service Providers by Enforcing Bayesian Analysis in iVCE
Institute of Scientific and Technical Information of China (English)
GU Bao-jun; LI Xiao-yong; WANG Wei-nong
2008-01-01
The initiative of internet-based virtual computing environment (iVCE) aims to provide the end users and applications With a harmonious, trustworthy and transparent integrated computing environment which will facilitate sharing and collaborating of network resources between applications. Trust management is an elementary component for iVCE. The uncertain and dynamic characteristics of iVCE necessitate the requirement for the trust management to be subjective, historical evidence based and context dependent. This paper presents a Bayesian analysis-based trust model, which aims to secure the active agents for selecting appropriate trustod services in iVCE. Simulations are made to analyze the properties of the trust model which show that the subjective prior information influences trust evaluation a lot and the model stimulates positive interactions.
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 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 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,…
Brochu, Eric; de Freitas, Nando
2010-01-01
We present a tutorial on Bayesian optimization, a method of finding the maximum of expensive cost functions. Bayesian optimization employs the Bayesian technique of setting a prior over the objective function and combining it with evidence to get a posterior function. This permits a utility-based selection of the next observation to make on the objective function, which must take into account both exploration (sampling from areas of high uncertainty) and exploitation (sampling areas likely to offer improvement over the current best observation). We also present two detailed extensions of Bayesian optimization, with experiments---active user modelling with preferences, and hierarchical reinforcement learning---and a discussion of the pros and cons of Bayesian optimization based on our experiences.
Bayesian natural selection and the evolution of perceptual systems.
Geisler, Wilson S.; Diehl, Randy L.
2002-01-01
In recent years, there has been much interest in characterizing statistical properties of natural stimuli in order to better understand the design of perceptual systems. A fruitful approach has been to compare the processing of natural stimuli in real perceptual systems with that of ideal observers derived within the framework of Bayesian statistical decision theory. While this form of optimization theory has provided a deeper understanding of the information contained in natural stimuli as w...
Bayesian Biclustering on Discrete Data: Variable Selection Methods
Guo, Lei
2013-01-01
Biclustering is a technique for clustering rows and columns of a data matrix simultaneously. Over the past few years, we have seen its applications in biology-related fields, as well as in many data mining projects. As opposed to classical clustering methods, biclustering groups objects that are similar only on a subset of variables. Many biclustering algorithms on continuous data have emerged over the last decade. In this dissertation, we will focus on two Bayesian biclustering algorithms we...
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
Lin, Lin; Chan, Cliburn; West, Mike
2016-01-01
We discuss the evaluation of subsets of variables for the discriminative evidence they provide in multivariate mixture modeling for classification. The novel development of Bayesian classification analysis presented is partly motivated by problems of design and selection of variables in biomolecular studies, particularly involving widely used assays of large-scale single-cell data generated using flow cytometry technology. For such studies and for mixture modeling generally, we define discriminative analysis that overlays fitted mixture models using a natural measure of concordance between mixture component densities, and define an effective and computationally feasible method for assessing and prioritizing subsets of variables according to their roles in discrimination of one or more mixture components. We relate the new discriminative information measures to Bayesian classification probabilities and error rates, and exemplify their use in Bayesian analysis of Dirichlet process mixture models fitted via Markov chain Monte Carlo methods as well as using a novel Bayesian expectation-maximization algorithm. We present a series of theoretical and simulated data examples to fix concepts and exhibit the utility of the approach, and compare with prior approaches. We demonstrate application in the context of automatic classification and discriminative variable selection in high-throughput systems biology using large flow cytometry datasets. PMID:26040910
DEFF Research Database (Denmark)
Ødegård, Jørgen; Meuwissen, Theo HE; Heringstad, Bjørg;
2010-01-01
relationship matrix, but genetic (co)variance components are inferred from the sampled breeding values and relationships between "informative" individuals (usually parents) only. The latter is analogous to a sire-dam model (in cases with no individual records on the parents). Results When applied to simulated......, residual variance on the underlying scale is not identifiable. Hence, variance of fully confounded Mendelian sampling deviations cannot be identified either, but can be inferred from the between-family variation. In the new algorithm, breeding values are sampled as in a standard animal model using the full...
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
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...
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
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.
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.
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
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...
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...
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
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
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 ...
Locating disease genes using Bayesian variable selection with the Haseman-Elston method
Directory of Open Access Journals (Sweden)
He Qimei
2003-12-01
Full Text Available Abstract Background We applied stochastic search variable selection (SSVS, a Bayesian model selection method, to the simulated data of Genetic Analysis Workshop 13. We used SSVS with the revisited Haseman-Elston method to find the markers linked to the loci determining change in cholesterol over time. To study gene-gene interaction (epistasis and gene-environment interaction, we adopted prior structures, which incorporate the relationship among the predictors. This allows SSVS to search in the model space more efficiently and avoid the less likely models. Results In applying SSVS, instead of looking at the posterior distribution of each of the candidate models, which is sensitive to the setting of the prior, we ranked the candidate variables (markers according to their marginal posterior probability, which was shown to be more robust to the prior. Compared with traditional methods that consider one marker at a time, our method considers all markers simultaneously and obtains more favorable results. Conclusions We showed that SSVS is a powerful method for identifying linked markers using the Haseman-Elston method, even for weak effects. SSVS is very effective because it does a smart search over the entire model space.
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.
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
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 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 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...
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...
Selén, Yngve
2004-01-01
Before using a parametric model one has to be sure that it offers a reasonable description of the system to be modeled. If a bad model structure is employed, the obtained model will also be bad, no matter how good is the parameter estimation method. There exist many possible ways of validating candidate models. This thesis focuses on one of the most common ways, i.e., the use of information criteria. First, some common information criteria are presented, and in the later chapters, various ext...
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...
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
bspmma: An R Package for Bayesian Semiparametric Models for Meta-Analysis
Directory of Open Access Journals (Sweden)
Deborah Burr
2012-07-01
Full Text Available We introduce an R package, bspmma, which implements a Dirichlet-based random effects model specific to meta-analysis. In meta-analysis, when combining effect estimates from several heterogeneous studies, it is common to use a random-effects model. The usual frequentist or Bayesian models specify a normal distribution for the true effects. However, in many situations, the effect distribution is not normal, e.g., it can have thick tails, be skewed, or be multi-modal. A Bayesian nonparametric model based on mixtures of Dirichlet process priors has been proposed in the literature, for the purpose of accommodating the non-normality. We review this model and then describe a competitor, a semiparametric version which has the feature that it allows for a well-defined centrality parameter convenient for determining whether the overall effect is significant. This second Bayesian model is based on a different version of the Dirichlet process prior, and we call it the "conditional Dirichlet model". The package contains functions to carry out analyses based on either the ordinary or the conditional Dirichlet model, functions for calculating certain Bayes factors that provide a check on the appropriateness of the conditional Dirichlet model, and functions that enable an empirical Bayes selection of the precision parameter of the Dirichlet process. We illustrate the use of the package on two examples, and give an interpretation of the results in these two different scenarios.
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 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.
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
Model selection and comparison for independents sinusoids
DEFF Research Database (Denmark)
Nielsen, Jesper Kjær; Christensen, Mads Græsbøll; Jensen, Søren Holdt
method by considering the problem in a full Bayesian framework instead of the approximate formulation, on which the asymptotic MAP criterion is based. This leads to a new model selection and comparison method, the lp-BIC, whose computational complexity is of the same order as the asymptotic MAP criterion...
Bayesian rules and stochastic models for high accuracy prediction of solar radiation
International Nuclear Information System (INIS)
Highlights: • Global radiation prediction and PV energy integration. • Artificial intelligence and stochastic modeling in order to use the time series formalism. • Using Bayesian rules to select models. • MLP and ARMA forecasters are equivalent (nRMSE close to 40.5% for the both). • The hybridization of the three predictors (ARMA, MLP and persistence) induces very good results (nRMSE = 36.6%). - Abstract: It is essential to find solar predictive methods to massively insert renewable energies on the electrical distribution grid. The goal of this study is to find the best methodology allowing predicting with high accuracy the hourly global radiation. The knowledge of this quantity is essential for the grid manager or the private PV producer in order to anticipate fluctuations related to clouds occurrences and to stabilize the injected PV power. In this paper, we test both methodologies: single and hybrid predictors. In the first class, we include the multi-layer perceptron (MLP), auto-regressive and moving average (ARMA), and persistence models. In the second class, we mix these predictors with Bayesian rules to obtain ad hoc models selections, and Bayesian averages of outputs related to single models. If MLP and ARMA are equivalent (nRMSE close to 40.5% for the both), this hybridization allows a nRMSE gain upper than 14% points compared to the persistence estimation (nRMSE = 37% versus 51%)
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...
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...
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...
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 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...
Optimal speech motor control and token-to-token variability: a Bayesian modeling approach.
Patri, Jean-François; Diard, Julien; Perrier, Pascal
2015-12-01
The remarkable capacity of the speech motor system to adapt to various speech conditions is due to an excess of degrees of freedom, which enables producing similar acoustical properties with different sets of control strategies. To explain how the central nervous system selects one of the possible strategies, a common approach, in line with optimal motor control theories, is to model speech motor planning as the solution of an optimality problem based on cost functions. Despite the success of this approach, one of its drawbacks is the intrinsic contradiction between the concept of optimality and the observed experimental intra-speaker token-to-token variability. The present paper proposes an alternative approach by formulating feedforward optimal control in a probabilistic Bayesian modeling framework. This is illustrated by controlling a biomechanical model of the vocal tract for speech production and by comparing it with an existing optimal control model (GEPPETO). The essential elements of this optimal control model are presented first. From them the Bayesian model is constructed in a progressive way. Performance of the Bayesian model is evaluated based on computer simulations and compared to the optimal control model. This approach is shown to be appropriate for solving the speech planning problem while accounting for variability in a principled way. PMID:26497359
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.
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...
A Gene Selection Algorithm using Bayesian Classification Approach
Alok Sharma; Kuldip K. Paliwal
2012-01-01
In this study, we propose a new feature (or gene) selection algorithm using Bayes classification approach. The algorithm can find gene subset crucial for cancer classification problem. Problem statement: Gene identification plays important role in human cancer classification problem. Several feature selection algorithms have been proposed for analyzing and understanding influential genes using gene expression profiles. Approach: The feature selection algorithms aim to explore genes that are c...
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
Directory of Open Access Journals (Sweden)
Henry de-Graft Acquah
2013-03-01
Full Text Available Alternative formulations of the Bayesian Information Criteria provide a basis for choosing between competing methods for detecting price asymmetry. However, very little is understood about their performance in the asymmetric price transmission modelling framework. In addressing this issue, this paper introduces and applies parametric bootstrap techniques to evaluate the ability of Bayesian Information Criteria (BIC and Draper's Information Criteria (DIC in discriminating between alternative asymmetric price transmission models under various error and sample size conditions. The results of the bootstrap simulations indicate that model selection performance depends on bootstrap sample size and the amount of noise in the data generating process. The Bayesian criterion clearly identifies the true asymmetric model out of different competing models in the presence of bootstrap samples. Draper's Information Criteria (DIC; Draper, 1995 outperforms BIC at either larger bootstrap sample size or lower noise level.
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.
Kocherlakota, Narayana R.
2007-01-01
This paper uses an example to show that a model that fits the available data perfectly may provide worse answers to policy questions than an alternative, imperfectly fitting model. The author argues that, in the context of Bayesian estimation, this result can be interpreted as being due to the use of an inappropriate prior over the parameters of shock processes. He urges the use of priors that are obtained from explicit auxiliary information, not from the desire to obtain identification.
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...
Lessons Learned from a Past Series of Bayesian Model Averaging studies for Soil/Plant Models
Nowak, Wolfgang; Wöhling, Thomas; Schöniger, Anneli
2015-04-01
In this study we evaluate the lessons learned about modelling soil/plant systems from analyzing evapotranspiration data, soil moisture and leaf area index. The data were analyzed with advanced tools from the area of Bayesian Model Averaging, model ranking and Bayesian Model Selection. We have generated a large variety of model conceptualizations by sampling random parameter sets from the vegetation components of the CERES, SUCROS, GECROS, and SPASS models and a common model for soil water movement via Monte-Carlo simulations. We used data from a one vegetation period of winter wheat at a field site in Nellingen, Germany. The data set includes soil moisture, actual evapotranspiration (ETa) from an eddy covariance tower, and leaf-area index (LAI). The focus of data analysis was on how one can do model ranking and model selection. Further analysis steps included the predictive reliability of different soil/plant models calibrated on different subsets of the available data. Our main conclusion is that model selection between different competing soil-plant models remains a large challenge, because 1. different data types and their combinations favor different models, because competing models are more or less good in simulating the coupling processes between the various compartments and their states, 2. singular events (such as the evolution of LAI during plant senescence) can dominate an entire time series, and long time series can be represented well by the few data values where the models disagree most, 3. the different data types differ in their discriminating power for model selection, 4. the level of noise present in ETa and LAI data, and the level of systematic model bias through simplifications of the complex system (e.g., assuming a few internally homogeneous soil layers) substantially reduce the confidence in model ranking and model selection, 5. none of the models withstands a hypothesis test against the available data, 6. even the assumed level of measurement
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 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.
Furtado-Junior, I; Abrunhosa, F A; Holanda, F C A F; Tavares, M C S
2016-06-01
Fishing selectivity of the mangrove crab Ucides cordatus in the north coast of Brazil can be defined as the fisherman's ability to capture and select individuals from a certain size or sex (or a combination of these factors) which suggests an empirical selectivity. Considering this hypothesis, we calculated the selectivity curves for males and females crabs using the logit function of the logistic model in the formulation. The Bayesian inference consisted of obtaining the posterior distribution by applying the Markov chain Monte Carlo (MCMC) method to software R using the OpenBUGS, BRugs, and R2WinBUGS libraries. The estimated results of width average carapace selection for males and females compared with previous studies reporting the average width of the carapace of sexual maturity allow us to confirm the hypothesis that most mature individuals do not suffer from fishing pressure; thus, ensuring their sustainability. PMID:26934154
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
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.
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...
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
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
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
Barroso, L M A; Teodoro, P E; Nascimento, M; Torres, F E; Dos Santos, A; Corrêa, A M; Sagrilo, E; Corrêa, C C G; Silva, F A; Ceccon, G
2016-01-01
This study aimed to verify that a Bayesian approach could be used for the selection of upright cowpea genotypes with high adaptability and phenotypic stability, and the study also evaluated the efficiency of using informative and minimally informative a priori distributions. Six trials were conducted in randomized blocks, and the grain yield of 17 upright cowpea genotypes was assessed. To represent the minimally informative a priori distributions, a probability distribution with high variance was used, and a meta-analysis concept was adopted to represent the informative a priori distributions. Bayes factors were used to conduct comparisons between the a priori distributions. The Bayesian approach was effective for selection of upright cowpea genotypes with high adaptability and phenotypic stability using the Eberhart and Russell method. Bayes factors indicated that the use of informative a priori distributions provided more accurate results than minimally informative a priori distributions. PMID:26985961
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
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
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
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
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...
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.
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
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.
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
Directory of Open Access Journals (Sweden)
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
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
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
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.
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
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.
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...
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...
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
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.
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…
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
Modeling Land-Use Decision Behavior with Bayesian Belief Networks
Directory of Open Access Journals (Sweden)
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.
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.
GPU Computing in Bayesian Inference of Realized Stochastic Volatility Model
International Nuclear Information System (INIS)
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.
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
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.
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)
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
Directory of Open Access Journals (Sweden)
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
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.
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
Energy Technology Data Exchange (ETDEWEB)
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.
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
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.
Bhadra, Anindya
2013-04-22
We describe a Bayesian technique to (a) perform a sparse joint selection of significant predictor variables and significant inverse covariance matrix elements of the response variables in a high-dimensional linear Gaussian sparse seemingly unrelated regression (SSUR) setting and (b) perform an association analysis between the high-dimensional sets of predictors and responses in such a setting. To search the high-dimensional model space, where both the number of predictors and the number of possibly correlated responses can be larger than the sample size, we demonstrate that a marginalization-based collapsed Gibbs sampler, in combination with spike and slab type of priors, offers a computationally feasible and efficient solution. As an example, we apply our method to an expression quantitative trait loci (eQTL) analysis on publicly available single nucleotide polymorphism (SNP) and gene expression data for humans where the primary interest lies in finding the significant associations between the sets of SNPs and possibly correlated genetic transcripts. Our method also allows for inference on the sparse interaction network of the transcripts (response variables) after accounting for the effect of the SNPs (predictor variables). We exploit properties of Gaussian graphical models to make statements concerning conditional independence of the responses. Our method compares favorably to existing Bayesian approaches developed for this purpose. © 2013, The International Biometric Society.
Bhadra, Anindya; Mallick, Bani K
2013-06-01
We describe a Bayesian technique to (a) perform a sparse joint selection of significant predictor variables and significant inverse covariance matrix elements of the response variables in a high-dimensional linear Gaussian sparse seemingly unrelated regression (SSUR) setting and (b) perform an association analysis between the high-dimensional sets of predictors and responses in such a setting. To search the high-dimensional model space, where both the number of predictors and the number of possibly correlated responses can be larger than the sample size, we demonstrate that a marginalization-based collapsed Gibbs sampler, in combination with spike and slab type of priors, offers a computationally feasible and efficient solution. As an example, we apply our method to an expression quantitative trait loci (eQTL) analysis on publicly available single nucleotide polymorphism (SNP) and gene expression data for humans where the primary interest lies in finding the significant associations between the sets of SNPs and possibly correlated genetic transcripts. Our method also allows for inference on the sparse interaction network of the transcripts (response variables) after accounting for the effect of the SNPs (predictor variables). We exploit properties of Gaussian graphical models to make statements concerning conditional independence of the responses. Our method compares favorably to existing Bayesian approaches developed for this purpose. PMID:23607608
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
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.
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
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
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
Directory of Open Access Journals (Sweden)
Kuang Lin
2009-01-01
Full Text Available Understanding the mechanisms of gene transcriptional regulation through analysis of high-throughput postgenomic data is one of the central problems of computational systems biology. Various approaches have been proposed, but most of them fail to address at least one of the following objectives: (1 allow for the fact that transcription factors are potentially subject to posttranscriptional regulation; (2 allow for the fact that transcription factors cooperate as a functional complex in regulating gene expression, and (3 provide a model and a learning algorithm with manageable computational complexity. The objective of the present study is to propose and test a method that addresses these three issues. The model we employ is a mixture of factor analyzers, in which the latent variables correspond to different transcription factors, grouped into complexes or modules. We pursue inference in a Bayesian framework, using the Variational Bayesian Expectation Maximization (VBEM algorithm for approximate inference of the posterior distributions of the model parameters, and estimation of a lower bound on the marginal likelihood for model selection. We have evaluated the performance of the proposed method on three criteria: activity profile reconstruction, gene clustering, and network inference.
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...
Search for predictive generic model of aqueous solubility using Bayesian neural nets.
Bruneau, P
2001-01-01
Several predictive models of aqueous solubility have been published. They have good performances on the data sets which have been used for training the models, but usually these data sets do not contain many structures similar to the structures of interest to the drug research and their applicability in drug hunting is questionable. A very diverse data set has been gathered with compounds issued from literature reports and proprietary compounds. These compounds have been grouped in a so-called literature data set I, a proprietary data set II, and a mixed data set III formed by I and II. About 100 descriptors emphasizing surface properties were calculated for every compound. Bayesian learning of neural nets which cumulates the advantages of neural nets without having their weaknesses was used to select the most parsimonious models and train them, from I, II, and III. The models were established by either selecting the most efficient descriptors one by one using a modified Gram-Schmidt procedure (GS) or by simplifying a most complete model using automatic relevance procedure (ARD). The predictive ability of the models was accessed using validation data sets as much unrelated to the training sets as possible, using two new parameters: NDD(x,ref) the normalized smallest descriptor distance of a compound x to a reference data set and CD(x,mod) the combination of NDD(x,ref) with the dispersion of the Bayesian neural nets calculations. The results show that it is possible to obtain a generic predictive model from database I but that the diversity of database II is too restricted to give a model with good generalization ability and that the ARD method applied to the mixed database III gives the best predictive model. PMID:11749587
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.
Shih, Ann T.; Ancel, Ersin; Jones, Sharon M.
2012-01-01
The concern for reducing aviation safety risk is rising as the National Airspace System in the United States transforms to the Next Generation Air Transportation System (NextGen). The NASA Aviation Safety Program is committed to developing an effective aviation safety technology portfolio to meet the challenges of this transformation and to mitigate relevant safety risks. The paper focuses on the reasoning of selecting Object-Oriented Bayesian Networks (OOBN) as the technique and commercial software for the accident modeling and portfolio assessment. To illustrate the benefits of OOBN in a large and complex aviation accident model, the in-flight Loss-of-Control Accident Framework (LOCAF) constructed as an influence diagram is presented. An OOBN approach not only simplifies construction and maintenance of complex causal networks for the modelers, but also offers a well-organized hierarchical network that is easier for decision makers to exploit the model examining the effectiveness of risk mitigation strategies through technology insertions.
DEFF Research Database (Denmark)
Dashab, Golam Reza; Kadri, Naveen Kumar; Mahdi Shariati, Mohammad;
2012-01-01
) Mixed model analysis (MMA), 2) Random haplotype model (RHM), 3) Genealogy-based mixed model (GENMIX), and 4) Bayesian variable selection (BVS). The data consisted of phenotypes of 2000 animals from 20 sire families and were genotyped with 9990 SNPs on five chromosomes. Results: Out of the eight...
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 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.
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.
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.
Universal Darwinism as a process of Bayesian inference
Campbell, John O
2016-01-01
Many of the mathematical frameworks describing natural selection are equivalent to Bayes Theorem, also known as Bayesian updating. By definition, a process of Bayesian Inference is one which involves a Bayesian update, so we may conclude that these frameworks describe natural selection as a process of Bayesian inference. Thus natural selection serves as a counter example to a widely-held interpretation that restricts Bayesian Inference to human mental processes (including the endeavors of statisticians). As Bayesian inference can always be cast in terms of (variational) free energy minimization, natural selection can be viewed as comprising two components: a generative model of an "experiment" in the external world environment, and the results of that "experiment" or the "surprise" entailed by predicted and actual outcomes of the "experiment". Minimization of free energy implies that the implicit measure of "surprise" experienced serves to update the generative model in a Bayesian manner. This description clo...
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 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
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...
Yi Qian; Hui Xie
2011-01-01
In marketing applications, it is common that some key covariates in a regression model, such as marketing mix variables or consumer profiles, are subject to missingness. The convenient method that excludes the consumers with missingness in any covariate can result in a substantial loss of efficiency and may lead to strong selection bias in the estimation of consumer preferences and sensitivities. To solve these problems, we propose a new Bayesian distribution-free approach, which can ensure t...
DEFF Research Database (Denmark)
Widyas, Nuzul; Jensen, Just; Nielsen, Vivi Hunnicke
selected downwards and three lines were kept as controls. Bayesian statistical methods are used to estimate the genetic variance components. Mixed model analysis is modified including mutation effect following the methods by Wray (1990). DIC was used to compare the model. Models including mutation effect...... have better fit compared to the model with only additive effect. Mutation as direct effect contributes 3.18% of the total phenotypic variance. While in the model with interactions between additive and mutation, it contributes 1.43% as direct effect and 1.36% as interaction effect of the total variance...
Model structure selection in convolutive mixtures
DEFF Research Database (Denmark)
Dyrholm, Mads; Makeig, S.; Hansen, Lars Kai
2006-01-01
The CICAAR algorithm (convolutive independent component analysis with an auto-regressive inverse model) allows separation of white (i.i.d) source signals from convolutive mixtures. We introduce a source color model as a simple extension to the CICAAR which allows for a more parsimonious represent...... representation in many practical mixtures. The new filter-CICAAR allows Bayesian model selection and can help answer questions like: ’Are we actually dealing with a convolutive mixture?’. We try to answer this question for EEG data....
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 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
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
Hierarchical Bayesian spatial models for alcohol availability, drug "hot spots" and violent crime
Directory of Open Access Journals (Sweden)
Horel Scott
2006-12-01
Full Text Available Abstract Background Ecologic studies have shown a relationship between alcohol outlet densities, illicit drug use and violence. The present study examined this relationship in the City of Houston, Texas, using a sample of 439 census tracts. Neighborhood sociostructural covariates, alcohol outlet density, drug crime density and violent crime data were collected for the year 2000, and analyzed using hierarchical Bayesian models. Model selection was accomplished by applying the Deviance Information Criterion. Results The counts of violent crime in each census tract were modelled as having a conditional Poisson distribution. Four neighbourhood explanatory variables were identified using principal component analysis. The best fitted model was selected as the one considering both unstructured and spatial dependence random effects. The results showed that drug-law violation explained a greater amount of variance in violent crime rates than alcohol outlet densities. The relative risk for drug-law violation was 2.49 and that for alcohol outlet density was 1.16. Of the neighbourhood sociostructural covariates, males of age 15 to 24 showed an effect on violence, with a 16% decrease in relative risk for each increase the size of its standard deviation. Both unstructured heterogeneity random effect and spatial dependence need to be included in the model. Conclusion The analysis presented suggests that activity around illicit drug markets is more strongly associated with violent crime than is alcohol outlet density. Unique among the ecological studies in this field, the present study not only shows the direction and magnitude of impact of neighbourhood sociostructural covariates as well as alcohol and illicit drug activities in a neighbourhood, it also reveals the importance of applying hierarchical Bayesian models in this research field as both spatial dependence and heterogeneity random effects need to be considered simultaneously.
Elsheikh, Ahmed H.
2014-02-01
An efficient Bayesian calibration method based on the nested sampling (NS) algorithm and non-intrusive polynomial chaos method is presented. Nested sampling is a Bayesian sampling algorithm that builds a discrete representation of the posterior distributions by iteratively re-focusing a set of samples to high likelihood regions. NS allows representing the posterior probability density function (PDF) with a smaller number of samples and reduces the curse of dimensionality effects. The main difficulty of the NS algorithm is in the constrained sampling step which is commonly performed using a random walk Markov Chain Monte-Carlo (MCMC) algorithm. In this work, we perform a two-stage sampling using a polynomial chaos response surface to filter out rejected samples in the Markov Chain Monte-Carlo method. The combined use of nested sampling and the two-stage MCMC based on approximate response surfaces provides significant computational gains in terms of the number of simulation runs. The proposed algorithm is applied for calibration and model selection of subsurface flow models. © 2013.
Gas turbine engine prognostics using Bayesian hierarchical models: A variational approach
Zaidan, Martha A.; Mills, Andrew R.; Harrison, Robert F.; Fleming, Peter J.
2016-03-01
Prognostics is an emerging requirement of modern health monitoring that aims to increase the fidelity of failure-time predictions by the appropriate use of sensory and reliability information. In the aerospace industry it is a key technology to reduce life-cycle costs, improve reliability and asset availability for a diverse fleet of gas turbine engines. In this work, a Bayesian hierarchical model is selected to utilise fleet data from multiple assets to perform probabilistic estimation of remaining useful life (RUL) for civil aerospace gas turbine engines. The hierarchical formulation allows Bayesian updates of an individual predictive model to be made, based upon data received asynchronously from a fleet of assets with different in-service lives and for the entry of new assets into the fleet. In this paper, variational inference is applied to the hierarchical formulation to overcome the computational and convergence concerns that are raised by the numerical sampling techniques needed for inference in the original formulation. The algorithm is tested on synthetic data, where the quality of approximation is shown to be satisfactory with respect to prediction performance, computational speed, and ease of use. A case study of in-service gas turbine engine data demonstrates the value of integrating fleet data for accurately predicting degradation trajectories of assets.
Ferragina, A; de los Campos, G; Vazquez, A I; Cecchinato, A; Bittante, G
2015-11-01
The aim of this study was to assess the performance of Bayesian models commonly used for genomic selection to predict "difficult-to-predict" dairy traits, such as milk fatty acid (FA) expressed as percentage of total fatty acids, and technological properties, such as fresh cheese yield and protein recovery, using Fourier-transform infrared (FTIR) spectral data. Our main hypothesis was that Bayesian models that can estimate shrinkage and perform variable selection may improve our ability to predict FA traits and technological traits above and beyond what can be achieved using the current calibration models (e.g., partial least squares, PLS). To this end, we assessed a series of Bayesian methods and compared their prediction performance with that of PLS. The comparison between models was done using the same sets of data (i.e., same samples, same variability, same spectral treatment) for each trait. Data consisted of 1,264 individual milk samples collected from Brown Swiss cows for which gas chromatographic FA composition, milk coagulation properties, and cheese-yield traits were available. For each sample, 2 spectra in the infrared region from 5,011 to 925 cm(-1) were available and averaged before data analysis. Three Bayesian models: Bayesian ridge regression (Bayes RR), Bayes A, and Bayes B, and 2 reference models: PLS and modified PLS (MPLS) procedures, were used to calibrate equations for each of the traits. The Bayesian models used were implemented in the R package BGLR (http://cran.r-project.org/web/packages/BGLR/index.html), whereas the PLS and MPLS were those implemented in the WinISI II software (Infrasoft International LLC, State College, PA). Prediction accuracy was estimated for each trait and model using 25 replicates of a training-testing validation procedure. Compared with PLS, which is currently the most widely used calibration method, MPLS and the 3 Bayesian methods showed significantly greater prediction accuracy. Accuracy increased in moving from
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
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
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...
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 ...
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...
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...
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...
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
Directory of Open Access Journals (Sweden)
Kok-Chin Khor
2009-01-01
Full Text Available Problem statement: Implementing a single or multiple classifiers that involve a Bayesian Network (BN is a rising research interest in network intrusion detection domain. Approach: However, little attention has been given to evaluate the performance of BN classifiers before they could be implemented in a real system. In this research, we proposed a novel approach to select important features by utilizing two selected feature selection algorithms utilizing filter approach. Results: The selected features were further validated by domain experts where extra features were added into the final proposed feature set. We then constructed three types of BN namely, Naive Bayes Classifiers (NBC, Learned BN and Expert-elicited BN by utilizing a standard network intrusion dataset. The performance of each classifier was recorded. We found that there was no difference in overall performance of the BNs and therefore, concluded that the BNs performed equivalently well in detecting network attacks. Conclusion/Recommendations: The results of the study indicated that the BN built using the proposed feature set has less features but the performance was comparable to BNs built using other feature sets generated by the two algorithms.
Application of hierarchical Bayesian unmixing models in river sediment source apportionment
Blake, Will; Smith, Hugh; Navas, Ana; Bodé, Samuel; Goddard, Rupert; Zou Kuzyk, Zou; Lennard, Amy; Lobb, David; Owens, Phil; Palazon, Leticia; Petticrew, Ellen; Gaspar, Leticia; Stock, Brian; Boeckx, Pacsal; Semmens, Brice
2016-04-01
Fingerprinting and unmixing concepts are used widely across environmental disciplines for forensic evaluation of pollutant sources. In aquatic and marine systems, this includes tracking the source of organic and inorganic pollutants in water and linking problem sediment to soil erosion and land use sources. It is, however, the particular complexity of ecological systems that has driven creation of the most sophisticated mixing models, primarily to (i) evaluate diet composition in complex ecological food webs, (ii) inform population structure and (iii) explore animal movement. In the context of the new hierarchical Bayesian unmixing model, MIXSIAR, developed to characterise intra-population niche variation in ecological systems, we evaluate the linkage between ecological 'prey' and 'consumer' concepts and river basin sediment 'source' and sediment 'mixtures' to exemplify the value of ecological modelling tools to river basin science. Recent studies have outlined advantages presented by Bayesian unmixing approaches in handling complex source and mixture datasets while dealing appropriately with uncertainty in parameter probability distributions. MixSIAR is unique in that it allows individual fixed and random effects associated with mixture hierarchy, i.e. factors that might exert an influence on model outcome for mixture groups, to be explored within the source-receptor framework. This offers new and powerful ways of interpreting river basin apportionment data. In this contribution, key components of the model are evaluated in the context of common experimental designs for sediment fingerprinting studies namely simple, nested and distributed catchment sampling programmes. Illustrative examples using geochemical and compound specific stable isotope datasets are presented and used to discuss best practice with specific attention to (1) the tracer selection process, (2) incorporation of fixed effects relating to sample timeframe and sediment type in the modelling
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.
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...
Mortezapouraghdam, Zeinab; Wilson, Robert C; Schwabe, Lars; Strauss, Daniel J
2016-01-01
We study the effect of long-term habituation signatures of auditory selective attention reflected in the instantaneous phase information of the auditory event-related potentials (ERPs) at four distinct stimuli levels of 60, 70, 80, and 90 dB SPL. The analysis is based on the single-trial level. The effect of habituation can be observed in terms of the changes (jitter) in the instantaneous phase information of ERPs. In particular, the absence of habituation is correlated with a consistently high phase synchronization over ERP trials. We estimate the changes in phase concentration over trials using a Bayesian approach, in which the phase is modeled as being drawn from a von Mises distribution with a concentration parameter which varies smoothly over trials. The smoothness assumption reflects the fact that habituation is a gradual process. We differentiate between different stimuli based on the relative changes and absolute values of the estimated concentration parameter using the proposed Bayesian model. PMID:26858631
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...
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
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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.
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.
Bayesian model-based approach for developing a river water quality index
Ali, Zalina Mohd; Ibrahim, Noor Akma; Mengersen, Kerrie; Shitan, Mahendran; Juahir, Hafizan
2014-09-01
Six main pollutants have been previously identified by expert opinion to determine river condition in Malaysia. The pollutants were Dissolved Oxygen (DO), Biochemical Oxygen Demand (BOD), Chemical Oxygen Demand (COD), Suspended Solid (SS), potential of Hydrogen (pH) and Ammonia (AN). The selected variables together with the respective weights have been applied to calculate the water quality index of all rivers in Malaysia. However, the relative weights established in DOE-WQI formula are subjective in nature and not unanimously agreed upon, as indicated by different weight being proposed for the same variables by various panels of experts. Focusing on the Langat River, a Bayesian model-based approach was introduced for the first time in this study to obtain new objective relative weights. The new weights used in WQI calculation are shown to be capable of capturing similar distributions in water quality compared with the existing DOE-WQI.
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 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.
Brochu, Eric; Cora, Vlad M.; De Freitas, Nando
2010-01-01
We present a tutorial on Bayesian optimization, a method of finding the maximum of expensive cost functions. Bayesian optimization employs the Bayesian technique of setting a prior over the objective function and combining it with evidence to get a posterior function. This permits a utility-based selection of the next observation to make on the objective function, which must take into account both exploration (sampling from areas of high uncertainty) and exploitation (sampling areas likely to...
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...
B2Z: R Package for Bayesian Two-Zone Models
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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.
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.
A Bayesian Approach to Service Selection for Secondary Users in Cognitive Radio Networks
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Elaheh Homayounvala
2015-10-01
Full Text Available In cognitive radio networks where secondary users (SUs use the time-frequency gaps of primary users' (PUs licensed spectrum opportunistically, the experienced throughput of SUs depend not only on the traffic load of the PUs but also on the PUs' service type. Each service has its own pattern of channel usage, and if the SUs know the dominant pattern of primary channel usage, then they can make a better decision on choosing which service is better to be used at a specific time to get the best advantage of the primary channel, in terms of higher achievable throughput. However, it is difficult to inform directly SUs of PUs' dominant used services in each area, for practical reasons. This paper proposes a learning mechanism embedded in SUs to sense the primary channel for a specific length of time. This algorithm recommends the SUs upon sensing a free primary channel, to choose the best service in order to get the best performance, in terms of maximum achieved throughput and the minimum experienced delay. The proposed learning mechanism is based on a Bayesian approach that can predict the performance of a requested service for a given SU. Simulation results show that this service selection method outperforms the blind opportunistic SU service selection, significantly.
Bayesian Analysis of a Doubly Truncated ARMA-GARCH Model
Goldman Elena; Tsurumi Hiroki
2005-01-01
We develop a new Markov Chain Monte Carlo procedure for a time series regression model truncated by upper and lower bounds. The regression error term is assumed to follow an ARMA--GARCH process. We use a convergence diagnostics with a simultaneous test of mean and covariance stationarity and discuss model selection criteria. Using MCMC procedure we test the purchasing power parity theory for the Japanese yen controlled to fluctuate in a narrow band and find that the theory is supported if dou...
Unified phenology model with Bayesian calibration for several European species in Belgium
Fu, Y. S. H.; Demarée, G.; Hamdi, R.; Deckmyn, A.; Deckmyn, G.; Janssens, I. A.
2009-04-01
Plant phenology is a good bio-indicator for climate change, and this has brought a significant increase of interest. Many kinds of phenology models have been developed to analyze and predict the phenological response to climate change, and those models have been summarized into one kind of unified model, which could be applied to different species and environments. In our study, we selected seven European woody plant species (Betula verrucosa, Quercus robur pedunculata, Fagus sylvatica, Fraxinus excelsior, Symphoricarpus racemosus, Aesculus hippocastanum, Robinia pseudoacacia) occurring in five sites distributed across Belgium. For those sites and tree species, phenological observations such as bud burst were available for the period 1956 - 2002. We also obtained regional downscaled climatic data for each of these sites, and combined both data sets to test the unified model. We used a Bayesian approach to generate distributions of model parameters from the observation data. In this poster presentation, we compare parameter distributions between different species and between different sites for individual species. The results of the unified model show a good agreement with the observations, except for Fagus sylvatica. The failure to reproduce the bud burst data for Fagus sylvatica suggest that the other factors not included in the unified model affect the phenology of this species. The parameter series show differences among species as we expected. However, they also differed strongly for the same species among sites.Further work should elucidate the mechanism that explains why model parameters differ among species and sites.
Bayesian network modeling method based on case reasoning for emergency decision-making
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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.
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.
Directory of Open Access Journals (Sweden)
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)
Moritz eBoos
2016-05-01
Full Text Available Cognitive determinants of probabilistic inference were examined using hierarchical Bayesian modelling techniques. A classic urn-ball paradigm served as experimental strategy, involving a factorial two (prior probabilities by two (likelihoods design. Five computational models of cognitive processes were compared with the observed behaviour. Parameter-free Bayesian posterior probabilities and parameter-free base rate neglect provided inadequate models of probabilistic inference. The introduction of distorted subjective probabilities yielded more robust and generalizable results. A general class of (inverted S-shaped probability weighting functions had been proposed; however, the possibility of large differences in probability distortions not only across experimental conditions, but also across individuals, seems critical for the model’s success. It also seems advantageous to consider individual differences in parameters of probability weighting as being sampled from weakly informative prior distributions of individual parameter values. Thus, the results from hierarchical Bayesian modelling converge with previous results in revealing that probability weighting parameters show considerable task dependency and individual differences. Methodologically, this work exemplifies the usefulness of hierarchical Bayesian modelling techniques for cognitive psychology. Theoretically, human probabilistic inference might be best described as the application of individualized strategic policies for Bayesian belief revision.
Bayesian 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...
DEFF Research Database (Denmark)
Do, Duy Ngoc; Janss, L. L. G.; Strathe, Anders Bjerring;
Improvement of feed efficiency is essential in pig breeding and selection for reduced residual feed intake (RFI) is an option. The study applied Bayesian Power LASSO (BPL) models with different power parameter to investigate genetic architecture, to predict genomic breeding values, and to partition...... genomic variance for RFI and daily feed intake (DFI). A total of 1272 Duroc pigs had both genotypic and phenotypic records for these traits. Significant SNPs were detected on chromosome 1 (SSC 1) and SSC 14 for RFI and on SSC 1 for DFI. BPL models had similar accuracy and bias as GBLUP method but use of...
An evolutionary algorithm for model selection
International Nuclear Information System (INIS)
When performing partial-wave analyses of multi-body final states, the choice of the fit model, i.e. the set of waves to be used in the fit, can significantly alter the results of the partial wave fit. Traditionally, the models were chosen based on physical arguments and by observing the changes in log-likelihood of the fits. To reduce possible bias in the model selection process, an evolutionary algorithm was developed based on a Bayesian goodness-of-fit criterion which takes into account the model complexity. Starting from systematically constructed pools of waves which contain significantly more waves than the typical fit model, the algorithm yields a model with an optimal log-likelihood and with a number of partial waves which is appropriate for the number of events in the data. Partial waves with small contributions to the total intensity are penalized and likely to be dropped during the selection process, as are models were excessive correlations between single waves occur. Due to the automated nature of the model selection, a much larger part of the model space can be explored than would be possible in a manual selection. In addition the method allows to assess the dependence of the fit result on the fit model which is an important contribution to the systematic uncertainty.
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).
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.
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.
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
Nomogram of Naive Bayesian Model for Recurrence Prediction of Breast Cancer
Kim, Woojae; Kim, Ku Sang
2016-01-01
Objectives Breast cancer has a high rate of recurrence, resulting in the need for aggressive treatment and close follow-up. However, previously established classification guidelines, based on expert panels or regression models, are controversial. Prediction models based on machine learning show excellent performance, but they are not widely used because they cannot explain their decisions and cannot be presented on paper in the way that knowledge is customarily represented in the clinical world. The principal objective of this study was to develop a nomogram based on a naïve Bayesian model for the prediction of breast cancer recurrence within 5 years after breast cancer surgery. Methods The nomogram can provide a visual explanation of the predicted probabilities on a sheet of paper. We used a data set from a Korean tertiary teaching hospital of 679 patients who had undergone breast cancer surgery between 1994 and 2002. Seven prognostic factors were selected as independent variables for the model. Results The accuracy was 80%, and the area under the receiver operating characteristics curve (AUC) of the model was 0.81. Conclusions The nomogram can be easily used in daily practice to aid physicians and patients in making appropriate treatment decisions after breast cancer surgery. PMID:27200218
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.
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...
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…
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
Inflation Model Selection meets Dark Radiation
Tram, Thomas; Vennin, Vincent
2016-01-01
We investigate how inflation model selection is affected by the presence of additional free-streaming relativistic degrees of freedom, i.e. dark radiation. We perform a full Bayesian analysis of both inflation parameters and cosmological parameters taking reheating into account self-consistently. We compute the Bayesian evidence for a few representative inflation scenarios in both the standard $\\Lambda\\mathrm{CDM}$ model and an extension including dark radiation parametrised by its effective number of relativistic species $N_\\mathrm{eff}$. We find that the observational status of most inflationary models is unchanged, with the exception of potentials such as power-law inflation that predict a value for the scalar spectral index that is too large in $\\Lambda\\mathrm{CDM}$ but which can be accommodated when $N_\\mathrm{eff}$ is allowed to vary. In this case, cosmic microwave background data indicate that power-law inflation is one of the best models together with plateau potentials. However, contrary to plateau p...
Ershadi, Ali
2013-05-01
The influence of uncertainty in land surface temperature, air temperature, and wind speed on the estimation of sensible heat flux is analyzed using a Bayesian inference technique applied to the Surface Energy Balance System (SEBS) model. The Bayesian approach allows for an explicit quantification of the uncertainties in input variables: a source of error generally ignored in surface heat flux estimation. An application using field measurements from the Soil Moisture Experiment 2002 is presented. The spatial variability of selected input meteorological variables in a multitower site is used to formulate the prior estimates for the sampling uncertainties, and the likelihood function is formulated assuming Gaussian errors in the SEBS model. Land surface temperature, air temperature, and wind speed were estimated by sampling their posterior distribution using a Markov chain Monte Carlo algorithm. Results verify that Bayesian-inferred air temperature and wind speed were generally consistent with those observed at the towers, suggesting that local observations of these variables were spatially representative. Uncertainties in the land surface temperature appear to have the strongest effect on the estimated sensible heat flux, with Bayesian-inferred values differing by up to ±5°C from the observed data. These differences suggest that the footprint of the in situ measured land surface temperature is not representative of the larger-scale variability. As such, these measurements should be used with caution in the calculation of surface heat fluxes and highlight the importance of capturing the spatial variability in the land surface temperature: particularly, for remote sensing retrieval algorithms that use this variable for flux estimation.
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
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.
Directory of Open Access Journals (Sweden)
Entin Hidayah
2011-02-01
Full Text Available Disaggregation of hourly rainfall data is very important to fulfil the input of continual rainfall-runoff model, when the availability of automatic rainfall records are limited. Continual rainfall-runoff modeling requires rainfall data in form of series of hourly. Such specification can be obtained by temporal disaggregation in single site. The paper attempts to generate single-site rainfall model based upon time series (AR1 model by adjusting and establishing dummy procedure. Estimated with Bayesian Markov Chain Monte Carlo (MCMC the objective variable is hourly rainfall depth. Performance of model has been evaluated by comparison of history data and model prediction. The result shows that the model has a good performance for dry interval periods. The performance of the model good represented by smaller number of MAE by 0.21 respectively.
Bayesian Credit Ratings (new version)
Paola Cerchiello; Paolo Giudici
2013-01-01
In this contribution we aim at improving ordinal variable selection in the context of causal models. In this regard, we propose an approach that provides a formal inferential tool to compare the explanatory power of each covariate, and, therefore, to select an effective model for classification purposes. Our proposed model is Bayesian nonparametric, and, thus, keeps the amount of model specification to a minimum. We consider the case in which information from the covariates is at the ordinal ...
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...
Institute of Scientific and Technical Information of China (English)
李茂柏; 王慧; 张建明; 李丁鲁; 杨润清; 周宇琼; 朴钟泽
2009-01-01
Main QTL and epistasis interaction effects for phytic acid concentration in rice grain were investigated by using a F_2 population consisted of 172 lines derived from the cross between an indica rice LPA(the grain phytic acid concentration was 7.11 mg/g) and a japonica rice Zhonghua 11(the phytic acid concentration was 11.92 mg/g) with the Bayesian model selection. A genetic linkage map including 126 SSR and 4 STS markers was constructed with the F_2 population. Three main QTLs related to phytic acid concentration in rice grain were detected. They were located on chromosomes 3, 5, and 6, explaining 5.38%, 8.02%, and 4.62% of phenotypic variation, respectively. The three alleles for reducing the phytic aid concentration were from the parent LPA. Ten pairs of epistatic interaction were detected on chromosomes 1, 3, 5, 6, and 11, with the interaction effects from 1.69 to 5.18 and the percentages of phenotypic variance ranged from 8.67% to 24.73%.%利用水稻植酸含量差异较大的品种中花11(粳型)和LPA(籼型)为亲本杂交获得F_2群体的172个单株,构建了含126个SSR和4个STS标记的遗传连锁图谱,利用贝叶斯(Bayesian)法对水稻籽粒植酸含量性状进行了主效应QTL定位和上位性互作分析.共检测到 3 个与水稻籽粒植酸含量性状有关的主效QTL,分布在第3、5和6 染色体的相应区间内,表型贡献率分别为5.38%、8.02%和4.62%,降低籽粒植酸含量的等位基因均来自亲本LPA.检测到10对上位性互作影响籽粒植酸含量, 分布于水稻第1、3、5、6、11染色体上,互作效应值为1.69～5.18,其表型变异的解释率为8.67%～24.73%.
Improving Local and Regional Flood Quantile Estimates Using a Hierarchical Bayesian GEV Model
Ribeiro Lima, C. H.; Lall, U.; Devineni, N.; Troy, T.
2013-12-01
Flood risk management usually relies on local and regional flood frequency analysis, which tends to suffer from lack of data and parameter uncertainties. Here we estimate local and regional Generalized Extreme Value (GEV) distribution parameters in a hierarchical Bayesian framework, which helps reduce uncertainties by pooling more information in the estimation process and provides a simple topology to propagate model and parameter uncertainties to flood quantile estimates. As prior information for the Bayesian model, it is assumed for each site that the GEV location and scale parameters come from independent log-normal distributions, whose mean parameter follows the well known log-log scaling law with the drainage area. The shape parameter for each site is shrunk towards a common mean. Non-informative prior distributions are assumed for the hyperparameters and the MCMC method is used to sample from the posterior distributions. The model is tested using annual maximum series from 20 streamflow gauges located in an 83.000 km2 basin in southeastern Brazil. The results show a significant improvement of flood quantile estimates over the traditional GEV model, particularly for sites with few data. For return periods within the range of the data (around 50 years), the Bayesian credible intervals for the flood quantiles are narrower than the classical confidence limits based on the delta method. As the return period increases beyond the range of the data, the confidence limits from the delta method become unreliable and the Bayesian credible intervals provide a way to estimate satisfactory confidence bands for the flood quantiles considering the parameter uncertainties. In order to evaluate the applicability of the proposed hierarchical Bayesian model for flood frequency regional analysis, we estimate flood quantiles for three randomly chosen out-of-sample sites and compare with classical estimates using the index flood method. The posterior distributions of the scaling
DEFF Research Database (Denmark)
Do, Duy Ngoc; Janss, Luc L G; Strathe, Anders B;
Improvement of feed efficiency is essential in pig breeding and selection for reduced residual feed intake (RFI) is an option. The study applied Bayesian Power LASSO (BPL) models with different power parameter to investigate genetic architecture, to predict genomic breeding values, and to partition...... genomic variance for RFI and daily feed intake (DFI). A total of 1272 Duroc pigs had both genotypic and phenotypic records for these traits. Significant SNPs were detected on chromosome 1 (SSC 1) and SSC 14 for RFI and on SSC 1 for DFI. BPL had similar accuracy and bias as GBLUP but power parameters had...
Balfer, Jenny; Bajorath, Jürgen
2014-09-22
Supervised machine learning models are widely used in chemoinformatics, especially for the prediction of new active compounds or targets of known actives. Bayesian classification methods are among the most popular machine learning approaches for the prediction of activity from chemical structure. Much work has focused on predicting structure-activity relationships (SARs) on the basis of experimental training data. By contrast, only a few efforts have thus far been made to rationalize the performance of Bayesian or other supervised machine learning models and better understand why they might succeed or fail. In this study, we introduce an intuitive approach for the visualization and graphical interpretation of naïve Bayesian classification models. Parameters derived during supervised learning are visualized and interactively analyzed to gain insights into model performance and identify features that determine predictions. The methodology is introduced in detail and applied to assess Bayesian modeling efforts and predictions on compound data sets of varying structural complexity. Different classification models and features determining their performance are characterized in detail. A prototypic implementation of the approach is provided. PMID:25137527
Plackett-Luce regression: A new Bayesian model for polychotomous data
Archambeau, Cedric; Caron, Francois
2012-01-01
Multinomial logistic regression is one of the most popular models for modelling the effect of explanatory variables on a subject choice between a set of specified options. This model has found numerous applications in machine learning, psychology or economy. Bayesian inference in this model is non trivial and requires, either to resort to a MetropolisHastings algorithm, or rejection sampling within a Gibbs sampler. In this paper, we propose an alternative model to multinomial logistic regress...
Non-parametric Bayesian graph models reveal community structure in resting state fMRI
DEFF Research Database (Denmark)
Andersen, Kasper Winther; Madsen, Kristoffer H.; Siebner, Hartwig Roman;
2014-01-01
Modeling of resting state functional magnetic resonance imaging (rs-fMRI) data using network models is of increasing interest. It is often desirable to group nodes into clusters to interpret the communication patterns between nodes. In this study we consider three different nonparametric Bayesian...... models for node clustering in complex networks. In particular, we test their ability to predict unseen data and their ability to reproduce clustering across datasets. The three generative models considered are the Infinite Relational Model (IRM), Bayesian Community Detection (BCD), and the Infinite...... Diagonal Model (IDM). The models define probabilities of generating links within and between clusters and the difference between the models lies in the restrictions they impose upon the between-cluster link probabilities. IRM is the most flexible model with no restrictions on the probabilities of links...
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
Henry de-Graft Acquah; Joseph Acquah
2013-01-01
Alternative formulations of the Bayesian Information Criteria provide a basis for choosing between competing methods for detecting price asymmetry. However, very little is understood about their performance in the asymmetric price transmission modelling framework. In addressing this issue, this paper introduces and applies parametric bootstrap techniques to evaluate the ability of Bayesian Information Criteria (BIC) and Draper's Information Criteria (DIC) in discriminating between alternative...
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 Nonparametric Graph Clustering
Banerjee, Sayantan; Akbani, Rehan; Baladandayuthapani, Veerabhadran
2015-01-01
We present clustering methods for multivariate data exploiting the underlying geometry of the graphical structure between variables. As opposed to standard approaches that assume known graph structures, we first estimate the edge structure of the unknown graph using Bayesian neighborhood selection approaches, wherein we account for the uncertainty of graphical structure learning through model-averaged estimates of the suitable parameters. Subsequently, we develop a nonparametric graph cluster...
A Software Risk Analysis Model Using Bayesian Belief Network
Institute of Scientific and Technical Information of China (English)
Yong Hu; Juhua Chen; Mei Liu; Yang Yun; Junbiao Tang
2006-01-01
The uncertainty during the period of software project development often brings huge risks to contractors and clients. Ifwe can find an effective method to predict the cost and quality of software projects based on facts like the project character and two-side cooperating capability at the beginning of the project, we can reduce the risk.Bayesian Belief Network(BBN) is a good tool for analyzing uncertain consequences, but it is difficult to produce precise network structure and conditional probability table. In this paper, we built up network structure by Delphi method for conditional probability table learning, and learn update probability table and nodes' confidence levels continuously according to the application cases, which made the evaluation network have learning abilities, and evaluate the software development risk of organization more accurately. This paper also introduces EM algorithm, which will enhance the ability to produce hidden nodes caused by variant software projects.
Bayesian state space models for dynamic genetic network construction across multiple tissues.
Liang, Yulan; Kelemen, Arpad
2016-08-01
Construction of gene-gene interaction networks and potential pathways is a challenging and important problem in genomic research for complex diseases while estimating the dynamic changes of the temporal correlations and non-stationarity are the keys in this process. In this paper, we develop dynamic state space models with hierarchical Bayesian settings to tackle this challenge for inferring the dynamic profiles and genetic networks associated with disease treatments. We treat both the stochastic transition matrix and the observation matrix time-variant and include temporal correlation structures in the covariance matrix estimations in the multivariate Bayesian state space models. The unevenly spaced short time courses with unseen time points are treated as hidden state variables. Hierarchical Bayesian approaches with various prior and hyper-prior models with Monte Carlo Markov Chain and Gibbs sampling algorithms are used to estimate the model parameters and the hidden state variables. We apply the proposed Hierarchical Bayesian state space models to multiple tissues (liver, skeletal muscle, and kidney) Affymetrix time course data sets following corticosteroid (CS) drug administration. Both simulation and real data analysis results show that the genomic changes over time and gene-gene interaction in response to CS treatment can be well captured by the proposed models. The proposed dynamic Hierarchical Bayesian state space modeling approaches could be expanded and applied to other large scale genomic data, such as next generation sequence (NGS) combined with real time and time varying electronic health record (EHR) for more comprehensive and robust systematic and network based analysis in order to transform big biomedical data into predictions and diagnostics for precision medicine and personalized healthcare with better decision making and patient outcomes. PMID:27343475
Chen, X.; Hao, Z; N. Devineni; U. Lall
2014-01-01
A Hierarchal Bayesian model is presented for one season-ahead forecasts of summer rainfall and streamflow using exogenous climate variables for east central China. The model provides estimates of the posterior forecasted probability distribution for 12 rainfall and 2 streamflow stations considering parameter uncertainty, and cross-site correlation. The model has a multi-level structure with regression coefficients modeled from a common multi-variate normal distribution resul...
Chen, X.; Hao, Z; N. Devineni; U. Lall
2013-01-01
A Hierarchal Bayesian model for forecasting regional summer rainfall and streamflow season-ahead using exogenous climate variables for East Central China is presented. The model provides estimates of the posterior forecasted probability distribution for 12 rainfall and 2 streamflow stations considering parameter uncertainty, and cross-site correlation. The model has a multilevel structure with regression coefficients modeled from a common multivariate normal distribution results in partial-po...
Bayesian Forecasting of US Growth using Basic Time Varying Parameter Models and Expectations Data
Basturk, Nalan; Ceyhan, Pinar; Dijk, Herman
2014-01-01
markdownabstract__Abstract__ Time varying patterns in US growth are analyzed using various univariate model structures, starting from a naive model structure where all features change every period to a model where the slow variation in the conditional mean and changes in the conditional variance are specified together with their interaction, including survey data on expected growth in order to strengthen the information in the model. Use is made of a simulation based Bayesian inferential meth...
Modeling and Analysis of Call Center Arrival Data: A Bayesian Approach
Refik Soyer; M. Murat Tarimcilar
2008-01-01
In this paper, we present a modulated Poisson process model to describe and analyze arrival data to a call center. The attractive feature of this model is that it takes into account both covariate and time effects on the call volume intensity, and in so doing, enables us to assess the effectiveness of different advertising strategies along with predicting the arrival patterns. A Bayesian analysis of the model is developed and an extension of the model is presented to describe potential hetero...
A General and Flexible Approach to Estimating the Social Relations Model Using Bayesian Methods
Ludtke, Oliver; Robitzsch, Alexander; Kenny, David A.; Trautwein, Ulrich
2013-01-01
The social relations model (SRM) is a conceptual, methodological, and analytical approach that is widely used to examine dyadic behaviors and interpersonal perception within groups. This article introduces a general and flexible approach to estimating the parameters of the SRM that is based on Bayesian methods using Markov chain Monte Carlo…
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
A Bayesian model for predicting face recognition performance using image quality
Dutta, Abhishek; Veldhuis, Raymond; Spreeuwers, Luuk
2014-01-01
Quality of a pair of facial images is a strong indicator of the uncertainty in decision about identity based on that image pair. In this paper, we describe a Bayesian approach to model the relation between image quality (like pose, illumination, noise, sharpness, etc) and corresponding face recognit
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.
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
Khoshravesh, Mojtaba; Sefidkouhi, Mohammad Ali Gholami; Valipour, Mohammad
2015-12-01
The proper evaluation of evapotranspiration is essential in food security investigation, farm management, pollution detection, irrigation scheduling, nutrient flows, carbon balance as well as hydrologic modeling, especially in arid environments. To achieve sustainable development and to ensure water supply, especially in arid environments, irrigation experts need tools to estimate reference evapotranspiration on a large scale. In this study, the monthly reference evapotranspiration was estimated by three different regression models including the multivariate fractional polynomial (MFP), robust regression, and Bayesian regression in Ardestan, Esfahan, and Kashan. The results were compared with Food and Agriculture Organization (FAO)-Penman-Monteith (FAO-PM) to select the best model. The results show that at a monthly scale, all models provided a closer agreement with the calculated values for FAO-PM (R 2 > 0.95 and RMSE < 12.07 mm month-1). However, the MFP model gives better estimates than the other two models for estimating reference evapotranspiration at all stations.
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
Directory of Open Access Journals (Sweden)
X. Chen
2013-09-01
Full Text Available A Hierarchal Bayesian model for forecasting regional summer rainfall and streamflow season-ahead using exogenous climate variables for East Central China is presented. The model provides estimates of the posterior forecasted probability distribution for 12 rainfall and 2 streamflow stations considering parameter uncertainty, and cross-site correlation. The model has a multilevel structure with regression coefficients modeled from a common multivariate normal distribution results in partial-pooling of information across multiple stations and better representation of parameter and posterior distribution uncertainty. Covariance structure of the residuals across stations is explicitly modeled. Model performance is tested under leave-10-out cross-validation. Frequentist and Bayesian performance metrics used include Receiver Operating Characteristic, Reduction of Error, Coefficient of Efficiency, Rank Probability Skill Scores, and coverage by posterior credible intervals. The ability of the model to reliably forecast regional summer rainfall and streamflow season-ahead offers potential for developing adaptive water risk management strategies.
An Application of Bayesian Approach in Modeling Risk of Death in an Intensive Care Unit
Wong, Rowena Syn Yin; Ismail, Noor Azina
2016-01-01
Background and Objectives There are not many studies that attempt to model intensive care unit (ICU) risk of death in developing countries, especially in South East Asia. The aim of this study was to propose and describe application of a Bayesian approach in modeling in-ICU deaths in a Malaysian ICU. Methods This was a prospective study in a mixed medical-surgery ICU in a multidisciplinary tertiary referral hospital in Malaysia. Data collection included variables that were defined in Acute Physiology and Chronic Health Evaluation IV (APACHE IV) model. Bayesian Markov Chain Monte Carlo (MCMC) simulation approach was applied in the development of four multivariate logistic regression predictive models for the ICU, where the main outcome measure was in-ICU mortality risk. The performance of the models were assessed through overall model fit, discrimination and calibration measures. Results from the Bayesian models were also compared against results obtained using frequentist maximum likelihood method. Results The study involved 1,286 consecutive ICU admissions between January 1, 2009 and June 30, 2010, of which 1,111 met the inclusion criteria. Patients who were admitted to the ICU were generally younger, predominantly male, with low co-morbidity load and mostly under mechanical ventilation. The overall in-ICU mortality rate was 18.5% and the overall mean Acute Physiology Score (APS) was 68.5. All four models exhibited good discrimination, with area under receiver operating characteristic curve (AUC) values approximately 0.8. Calibration was acceptable (Hosmer-Lemeshow p-values > 0.05) for all models, except for model M3. Model M1 was identified as the model with the best overall performance in this study. Conclusion Four prediction models were proposed, where the best model was chosen based on its overall performance in this study. This study has also demonstrated the promising potential of the Bayesian MCMC approach as an alternative in the analysis and modeling of
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.
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.
Robertson, D. E.; Wang, Q. J.; Malano, H.; Etchells, T.
2009-02-01
For models to be useful, they need to adequately describe the systems they represent. The probabilistic nature of Bayesian network models has traditionally meant that model validation is difficult. In this paper we present a process to validate Inteca-Farm, a Bayesian network model of farm irrigation that we described in the first paper of this series. We assessed three aspects of the quality of model predictions, namely, bias, accuracy, and skill, for the two variables for which validation data are available directly or indirectly. We also examined model predictions for any systematic errors. The validation results show that the bias and accuracy of the two validated variables are within acceptable tolerances and that systematic errors are minimal. This suggests that Inteca-Farm is a plausible representation of farm irrigation system in the Shepparton Irrigation Region of northern Victoria, Australia.
Bayesian spatio-temporal modeling of particulate matter concentrations in Peninsular Malaysia
Manga, Edna; Awang, Norhashidah
2016-06-01
This article presents an application of a Bayesian spatio-temporal Gaussian process (GP) model on particulate matter concentrations from Peninsular Malaysia. We analyze daily PM10 concentration levels from 35 monitoring sites in June and July 2011. The spatiotemporal model set in a Bayesian hierarchical framework allows for inclusion of informative covariates, meteorological variables and spatiotemporal interactions. Posterior density estimates of the model parameters are obtained by Markov chain Monte Carlo methods. Preliminary data analysis indicate information on PM10 levels at sites classified as industrial locations could explain part of the space time variations. We include the site-type indicator in our modeling efforts. Results of the parameter estimates for the fitted GP model show significant spatio-temporal structure and positive effect of the location-type explanatory variable. We also compute some validation criteria for the out of sample sites that show the adequacy of the model for predicting PM10 at unmonitored sites.
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 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...
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...
Comparing measures of model selection for penalized splines in Cox models
Malloy, Elizabeth J.; Spiegelman, Donna; Eisen, Ellen A
2009-01-01
This article presents an application and a simulation study of model fit criteria for selecting the optimal degree of smoothness for penalized splines in Cox models. The criteria considered were the Akaike information criterion, the corrected AIC, two formulations of the Bayesian information criterion, and a generalized cross-validation method. The estimated curves selected by the five methods were compared to each other in a study of rectal cancer mortality in autoworkers. In the stimulation...
Lu, Dan; Ye, Ming; Curtis, Gary P.
2015-10-01
While Bayesian model averaging (BMA) has been widely used in groundwater modeling, it is infrequently applied to groundwater reactive transport modeling because of multiple sources of uncertainty in the coupled hydrogeochemical processes and because of the long execution time of each model run. To resolve these problems, this study analyzed different levels of uncertainty in a hierarchical way, and used the maximum likelihood version of BMA, i.e., MLBMA, to improve the computational efficiency. This study demonstrates the applicability of MLBMA to groundwater reactive transport modeling in a synthetic case in which twenty-seven reactive transport models were designed to predict the reactive transport of hexavalent uranium (U(VI)) based on observations at a former uranium mill site near Naturita, CO. These reactive transport models contain three uncertain model components, i.e., parameterization of hydraulic conductivity, configuration of model boundary, and surface complexation reactions that simulate U(VI) adsorption. These uncertain model components were aggregated into the alternative models by integrating a hierarchical structure into MLBMA. The modeling results of the individual models and MLBMA were analyzed to investigate their predictive performance. The predictive logscore results show that MLBMA generally outperforms the best model, suggesting that using MLBMA is a sound strategy to achieve more robust model predictions relative to a single model. MLBMA works best when the alternative models are structurally distinct and have diverse model predictions. When correlation in model structure exists, two strategies were used to improve predictive performance by retaining structurally distinct models or assigning smaller prior model probabilities to correlated models. Since the synthetic models were designed using data from the Naturita site, the results of this study are expected to provide guidance for real-world modeling. Limitations of applying MLBMA to the
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
International Nuclear Information System (INIS)
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-modelingclose 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
Inglis, Andrew; Ireland, Jack; Dominique, Marie
2015-04-01
Recent work has shown that power-law-like Fourier power spectra are an intrinsic property of solar and stellar flare signals, similarly to other astrophysical objects such as gamma-ray bursts and magnetars. It is therefore critical to account for this in order to understand the nature and significance of short-timescale fluctuations in flares.We present the results of a Bayesian model comparison method for investigating flare time series, fully considering these Fourier power-law properties. Using data from the PROBA2/Large Yield Radiometer, Fermi/Gamma-ray Burst Monitor, Nobeyama Radioheliograph, and Yohkoh/HXT instruments, we study a selection of flares from the literature identified as 'quasi-periodic puslation (QPP)' events. While emphasising that the observed fluctuations are real and of solar origin, we find that, for all but one event tested, an explicit oscillation is not required to explain the observations. Instead, the observed flare signals are adequately described as a manifestation of a power law in the Fourier power spectrum. This evaluation of the QPP phenomenon is markedly different from much of the prior literature.We conclude that the prevalence of oscillatory signatures in solar and stellar flares may be less than previously believed. Furthermore, studying the slope of the observed Fourier power spectrum as a function of energy may provide us with a diagnostic window into the fundamental nature of solar flares.
Bayesian nonparametric data analysis
Müller, Peter; Jara, Alejandro; Hanson, Tim
2015-01-01
This book reviews nonparametric Bayesian methods and models that have proven useful in the context of data analysis. Rather than providing an encyclopedic review of probability models, the book’s structure follows a data analysis perspective. As such, the chapters are organized by traditional data analysis problems. In selecting specific nonparametric models, simpler and more traditional models are favored over specialized ones. The discussed methods are illustrated with a wealth of examples, including applications ranging from stylized examples to case studies from recent literature. The book also includes an extensive discussion of computational methods and details on their implementation. R code for many examples is included in on-line software pages.
Prediction and assimilation of surf-zone processes using a Bayesian network: Part I: Forward models
Plant, Nathaniel G.; Holland, K. Todd
2011-01-01
Prediction of coastal processes, including waves, currents, and sediment transport, can be obtained from a variety of detailed geophysical-process models with many simulations showing significant skill. This capability supports a wide range of research and applied efforts that can benefit from accurate numerical predictions. However, the predictions are only as accurate as the data used to drive the models and, given the large temporal and spatial variability of the surf zone, inaccuracies in data are unavoidable such that useful predictions require corresponding estimates of uncertainty. We demonstrate how a Bayesian-network model can be used to provide accurate predictions of wave-height evolution in the surf zone given very sparse and/or inaccurate boundary-condition data. The approach is based on a formal treatment of a data-assimilation problem that takes advantage of significant reduction of the dimensionality of the model system. We demonstrate that predictions of a detailed geophysical model of the wave evolution are reproduced accurately using a Bayesian approach. In this surf-zone application, forward prediction skill was 83%, and uncertainties in the model inputs were accurately transferred to uncertainty in output variables. We also demonstrate that if modeling uncertainties were not conveyed to the Bayesian network (i.e., perfect data or model were assumed), then overly optimistic prediction uncertainties were computed. More consistent predictions and uncertainties were obtained by including model-parameter errors as a source of input uncertainty. Improved predictions (skill of 90%) were achieved because the Bayesian network simultaneously estimated optimal parameters while predicting wave heights.
Prediction and assimilation of surf-zone processes using a Bayesian network: Part II: Inverse models
Plant, Nathaniel G.; Holland, K. Todd
2011-01-01
A Bayesian network model has been developed to simulate a relatively simple problem of wave propagation in the surf zone (detailed in Part I). Here, we demonstrate that this Bayesian model can provide both inverse modeling and data-assimilation solutions for predicting offshore wave heights and depth estimates given limited wave-height and depth information from an onshore location. The inverse method is extended to allow data assimilation using observational inputs that are not compatible with deterministic solutions of the problem. These inputs include sand bar positions (instead of bathymetry) and estimates of the intensity of wave breaking (instead of wave-height observations). Our results indicate that wave breaking information is essential to reduce prediction errors. In many practical situations, this information could be provided from a shore-based observer or from remote-sensing systems. We show that various combinations of the assimilated inputs significantly reduce the uncertainty in the estimates of water depths and wave heights in the model domain. Application of the Bayesian network model to new field data demonstrated significant predictive skill (R2 = 0.7) for the inverse estimate of a month-long time series of offshore wave heights. The Bayesian inverse results include uncertainty estimates that were shown to be most accurate when given uncertainty in the inputs (e.g., depth and tuning parameters). Furthermore, the inverse modeling was extended to directly estimate tuning parameters associated with the underlying wave-process model. The inverse estimates of the model parameters not only showed an offshore wave height dependence consistent with results of previous studies but the uncertainty estimates of the tuning parameters also explain previously reported variations in the model parameters.
Bayesian inference for a wavefront model of the Neolithisation of Europe
Baggaley, Andrew W; Shukurov, Anvar; Boys, Richard J; Golightly, Andrew
2012-01-01
We consider a wavefront model for the spread of Neolithic culture across Europe, and use Bayesian inference techniques to provide estimates for the parameters within this model, as constrained by radiocarbon data from Southern and Western Europe. Our wavefront model allows for both an isotropic background spread (incorporating the effects of local geography), and a localized anisotropic spread associated with major waterways. We introduce an innovative numerical scheme to track the wavefront, allowing us to simulate the times of the first arrival at any site orders of magnitude more efficiently than traditional PDE approaches. We adopt a Bayesian approach to inference and use Gaussian process emulators to facilitate further increases in efficiency in the inference scheme, thereby making Markov chain Monte Carlo methods practical. We allow for uncertainty in the fit of our model, and also infer a parameter specifying the magnitude of this uncertainty. We obtain a magnitude for the background spread of order 1 ...
Directory of Open Access Journals (Sweden)
Pengpeng Jiao
2014-01-01
Full Text Available Time-dependent turning movement flows are very important input data for intelligent transportation systems but are impossible to be detected directly through current traffic surveillance systems. Existing estimation models have proved to be not accurate and reliable enough during all intervals. An improved way to address this problem is to develop a combined model framework that can integrate multiple submodels running simultaneously. This paper first presents a back propagation neural network model to estimate dynamic turning movements, as well as the self-adaptive learning rate approach and the gradient descent with momentum method for solving. Second, this paper develops an efficient Kalman filtering model and designs a revised sequential Kalman filtering algorithm. Based on the Bayesian method using both historical data and currently estimated results for error calibration, this paper further integrates above two submodels into a Bayesian combined model framework and proposes a corresponding algorithm. A field survey is implemented at an intersection in Beijing city to collect both time series of link counts and actual time-dependent turning movement flows, including historical and present data. The reported estimation results show that the Bayesian combined model is much more accurate and stable than other models.
A Hierarchical Bayesian Model to Predict Self-Thinning Line for Chinese Fir in Southern China.
Directory of Open Access Journals (Sweden)
Xiongqing Zhang
Full Text Available Self-thinning is a dynamic equilibrium between forest growth and mortality at full site occupancy. Parameters of the self-thinning lines are often confounded by differences across various stand and site conditions. For overcoming the problem of hierarchical and repeated measures, we used hierarchical Bayesian method to estimate the self-thinning line. The results showed that the self-thinning line for Chinese fir (Cunninghamia lanceolata (Lamb.Hook. plantations was not sensitive to the initial planting density. The uncertainty of model predictions was mostly due to within-subject variability. The simulation precision of hierarchical Bayesian method was better than that of stochastic frontier function (SFF. Hierarchical Bayesian method provided a reasonable explanation of the impact of other variables (site quality, soil type, aspect, etc. on self-thinning line, which gave us the posterior distribution of parameters of self-thinning line. The research of self-thinning relationship could be benefit from the use of hierarchical Bayesian method.
Bayesian model for strategic level risk assessment in continuing airthworthiness of air transport
Jayakody-Arachchige, Dhanapala
2010-01-01
Continuing airworthiness (CAW) of aircraft is an essential pre-requisite for the safe operation of air transport. Human errors that occur in CAW organizations and processes could undermine the airworthiness and constitute a risk to flight safety. This thesis reports on a generic Bayesian model that has been designed to assess and quantify this risk. The model removes the vagueness inherent in the subjective methods of assessment of risk and its qualitative expression. Instead, relying on a...
A Bayesian Based Functional Mixed-Effects Model for Analysis of LC-MS Data
Befekadu, Getachew K.; Tadesse, Mahlet G.; Ressom, Habtom W
2009-01-01
A Bayesian multilevel functional mixed-effects model with group specific random-effects is presented for analysis of liquid chromatography-mass spectrometry (LC-MS) data. The proposed framework allows alignment of LC-MS spectra with respect to both retention time (RT) and mass-to-charge ratio (m/z). Affine transformations are incorporated within the model to account for any variability along the RT and m/z dimensions. Simultaneous posterior inference of all unknown parameters is accomplished ...
A Bayesian model for predicting face recognition performance using image quality
Dutta, Abhishek; Veldhuis, Raymond; Spreeuwers, Luuk
2014-01-01
Quality of a pair of facial images is a strong indicator of the uncertainty in decision about identity based on that image pair. In this paper, we describe a Bayesian approach to model the relation between image quality (like pose, illumination, noise, sharpness, etc) and corresponding face recognition performance. Experiment results based on the MultiPIE data set show that our model can accurately aggregate verification samples into groups for which the verification performance varies fairly...
Determinants of Low Birth Weight in Malawi: Bayesian Geo-Additive Modelling
Ngwira, Alfred; Stanley, Christopher C.
2015-01-01
Studies on factors of low birth weight in Malawi have neglected the flexible approach of using smooth functions for some covariates in models. Such flexible approach reveals detailed relationship of covariates with the response. The study aimed at investigating risk factors of low birth weight in Malawi by assuming a flexible approach for continuous covariates and geographical random effect. A Bayesian geo-additive model for birth weight in kilograms and size of the child at birth (less than ...
Murray, Thomas A.; Hobbs, Brian P.; Sargent, Daniel J; Carlin, Bradley P.
2016-01-01
Presently, there are few options with available software to perform a fully Bayesian analysis of time-to-event data wherein the hazard is estimated semi- or non-parametrically. One option is the piecewise exponential model, which requires an often unrealistic assumption that the hazard is piecewise constant over time. The primary aim of this paper is to construct a tractable semiparametric alternative to the piecewise exponential model that assumes the hazard is continuous, and to provide mod...
Caiado, C. C. S.; Goldstein, M.
2015-09-01
In this paper we present and illustrate basic Bayesian techniques for the uncertainty analysis of complex physical systems modelled by computer simulators. We focus on emulation and history matching and also discuss the treatment of observational errors and structural discrepancies in time series. We exemplify such methods using a four-box model for the termohaline circulation. We show how these methods may be applied to systems containing tipping points and how to treat possible discontinuities using multiple emulators.
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 ...
A Note on Bayesian Estimation for the Negative-Binomial Model
L. Lio, Y.
2009-01-01
2000 Mathematics Subject Classification: 62F15. The Negative Binomial model, which is generated by a simple mixture model, has been widely applied in the social, health and economic market prediction. The most commonly used methods were the maximum likelihood estimate (MLE) and the moment method estimate (MME). Bradlow et al. (2002) proposed a Bayesian inference with beta-prime and Pearson Type VI as priors for the negative binomial distribution. It is due to the complicated posterior dens...
A Bayesian Estimation of Real Business-Cycle Models for the Turkish Economy
Hüseyin Taştan; Bekir Aşık
2014-01-01
We estimate a canonical small open economy real business-cycle model and its several extensions using a Bayesian approach to explore the effects of different structural shocks on macroeconomic fluctuations in Turkey. Alternative models include several theoretical exogenous shocks, such as those to temporary and permanent productivity, world interest rates, preferences, and domestic spending, as driving forces together with financial frictions. Results indicate that output is mostly driven by ...
Universal Darwinism As a Process of Bayesian Inference.
Campbell, John O
2016-01-01
Many of the mathematical frameworks describing natural selection are equivalent to Bayes' Theorem, also known as Bayesian updating. By definition, a process of Bayesian Inference is one which involves a Bayesian update, so we may conclude that these frameworks describe natural selection as a process of Bayesian inference. Thus, natural selection serves as a counter example to a widely-held interpretation that restricts Bayesian Inference to human mental processes (including the endeavors of statisticians). As Bayesian inference can always be cast in terms of (variational) free energy minimization, natural selection can be viewed as comprising two components: a generative model of an "experiment" in the external world environment, and the results of that "experiment" or the "surprise" entailed by predicted and actual outcomes of the "experiment." Minimization of free energy implies that the implicit measure of "surprise" experienced serves to update the generative model in a Bayesian manner. This description closely accords with the mechanisms of generalized Darwinian process proposed both by Dawkins, in terms of replicators and vehicles, and Campbell, in terms of inferential systems. Bayesian inference is an algorithm for the accumulation of evidence-based knowledge. This algorithm is now seen to operate over a wide range of evolutionary processes, including natural selection, the evolution of mental models and cultural evolutionary processes, notably including science itself. The variational principle of free energy minimization may thus serve as a unifying mathematical framework for universal Darwinism, the study of evolutionary processes operating throughout nature. PMID:27375438
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.
Fijani, E.; Chitsazan, N.; Nadiri, A.; Tsai, F. T.; Asghari Moghaddam, A.
2012-12-01
Artificial Neural Networks (ANNs) have been widely used to estimate concentration of chemicals in groundwater systems. However, estimation uncertainty is rarely discussed in the literature. Uncertainty in ANN output stems from three sources: ANN inputs, ANN parameters (weights and biases), and ANN structures. Uncertainty in ANN inputs may come from input data selection and/or input data error. ANN parameters are naturally uncertain because they are maximum-likelihood estimated. ANN structure is also uncertain because there is no unique ANN model given a specific case. Therefore, multiple plausible AI models are generally resulted for a study. One might ask why good models have to be ignored in favor of the best model in traditional estimation. What is the ANN estimation variance? How do the variances from different ANN models accumulate to the total estimation variance? To answer these questions we propose a Hierarchical Bayesian Model Averaging (HBMA) framework. Instead of choosing one ANN model (the best ANN model) for estimation, HBMA averages outputs of all plausible ANN models. The model weights are based on the evidence of data. Therefore, the HBMA avoids overconfidence on the single best ANN model. In addition, HBMA is able to analyze uncertainty propagation through aggregation of ANN models in a hierarchy framework. This method is applied for estimation of fluoride concentration in the Poldasht plain and the Bazargan plain in Iran. Unusually high fluoride concentration in the Poldasht and Bazargan plains has caused negative effects on the public health. Management of this anomaly requires estimation of fluoride concentration distribution in the area. The results show that the HBMA provides a knowledge-decision-based framework that facilitates analyzing and quantifying ANN estimation uncertainties from different sources. In addition HBMA allows comparative evaluation of the realizations for each source of uncertainty by segregating the uncertainty sources in
Impact of Frequentist and Bayesian Methods on Survey Sampling Practice: A Selective Appraisal
Rao, J. N. K.
2011-01-01
According to Hansen, Madow and Tepping [J. Amer. Statist. Assoc. 78 (1983) 776--793], "Probability sampling designs and randomization inference are widely accepted as the standard approach in sample surveys." In this article, reasons are advanced for the wide use of this design-based approach, particularly by federal agencies and other survey organizations conducting complex large scale surveys on topics related to public policy. Impact of Bayesian methods in survey sampling is also discussed...
An introduction to Bayesian model selection for evaluating informative hypotheses
van de Schoot, Rens; Mulder, Joris; Hoijtink, Herbert; van Aken, Marcel A. G.; Dubas, Judith Semon; de Castro, Bram Orobio; Meeus, Wim; Romeijn, Jan-Willem
2011-01-01
Most researchers have specific expectations concerning their research questions. These may be derived from theory, empirical evidence, or both. Yet despite these expectations, most investigators still use null hypothesis testing to evaluate their data, that is, when analysing their data they ignore
Bayesian selection of scaling laws for motion modeling in images
Héas, P.; Mémin, E.; Heitz, D; Mininni, P.D.
2009-01-01
Based on scaling laws describing the statistical structure of turbulent motion across scales, we propose a multiscale and non-parametric regularizer for optic-ﬂow estimation. Regularization is achieved by constraining motion increments to behave through scales as the most likely self-similar process given some image data. In a ﬁrst level of inference, the hard constrained minimization problem is optimally solved by taking advantage of lagrangian duality. It results in a collecti...
DEFF Research Database (Denmark)
Møller, Jesper; Rasmussen, Jakob Gulddahl
We introduce a flexible spatial point process model for spatial point patterns exhibiting linear structures, without incorporating a latent line process. The model is given by an underlying sequential point process model, i.e. each new point is generated given the previous points. Under this model...... previous points is such that the dependent cluster point is likely to occur closely to a previous cluster point. We demonstrate the flexibility of the model for producing point patterns with linear structures, and propose to use the model as the likelihood in a Bayesian setting when analyzing a spatial...
Consistency in Estimation and Model Selection of Dynamic Panel Data Models with Fixed Effects
Directory of Open Access Journals (Sweden)
Guangjie Li
2015-07-01
Full Text Available We examine the relationship between consistent parameter estimation and model selection for autoregressive panel data models with fixed effects. We find that the transformation of fixed effects proposed by Lancaster (2002 does not necessarily lead to consistent estimation of common parameters when some true exogenous regressors are excluded. We propose a data dependent way to specify the prior of the autoregressive coefficient and argue for comparing different model specifications before parameter estimation. Model selection properties of Bayes factors and Bayesian information criterion (BIC are investigated. When model uncertainty is substantial, we recommend the use of Bayesian Model Averaging to obtain point estimators with lower root mean squared errors (RMSE. We also study the implications of different levels of inclusion probabilities by simulations.
Noise in Genotype Selection Model
Institute of Scientific and Technical Information of China (English)
AI Bao-Quan; CHEN Wei; WANG Xian-Ju; LIU Guo-Tao; WEN De-Hua; LIU Liang-Gang
2003-01-01
We study the steady state properties ofa genotype selection model in presence of correlated Gaussian whitenoise. The effect of the noise on the genotype selection model is discussed. It is found that correlated noise can breakthe balance of gene selection and induce the phase transition which can makes us select one type gene haploid from agene group.
Marshall, L. A.; Weber, K.; Smith, T. J.; Greenwood, M. C.; Sharma, A.
2012-12-01
In an effort to improve hydrologic analysis in areas with limited data, hydrologists often seek to link catchments where little to no data collection occurs to catchments that are gauged. Various metrics and methods have been proposed to identify such relationships, in the hope that "surrogate" catchments might provide information for those catchments that are hydrologically similar. In this study we present a statistical analysis of over 150 catchments located in southeast Australia to examine the relationship between a hydrological model and certain catchment metrics. A conceptual rainfall-runoff model is optimized for each of the catchments and hierarchical clustering is performed to link catchments based on their calibrated model parameters. Clustering has been used in recent hydrologic studies but catchments are often clustered based on physical characteristics alone. Usually there is little evidence to suggest that such "surrogate" data approaches provide sufficiently similar model predictions. Beginning with model parameters and working backwards, we hope to establish if there is a relationship between the model parameters and physical characteristics for improved model predictions in the ungauged catchment. To analyze relationships, permutational multivariate analysis of variance tests are used that suggest which hydrologic metrics are most appropriate for discriminating between calibrated catchment clusters. Additional analysis is performed to determine which cluster pairs show significant differences for various metrics. We further examine the extent to which these results may be insightful for a hierarchical Bayesian modeling approach that is aimed at generating model predictions at an ungauged site. The method, known as Bayes Empirical Bayes (BEB) works to pool information from similar catchments to generate informed probability distributions for each model parameter at a data-limited catchment of interest. We demonstrate the effect of selecting
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
A Bayesian Hierarchical Model for Reconstructing Sea Levels: From Raw Data to Rates of Change
Cahill, Niamh; Horton, Benjamin P; Parnell, Andrew 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 ({\\delta}13C) 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, which is flexible enough to formally accommodate additional proxies (in this case bulk-sediment {\\delta}13C values); (2) A chronology developed from an existing Bchron age-depth model, and (3) An existing errors-in-variables integrated Gaussian process (EIV-IGP) model for estimating rates of sea-level change. We illustrate our approach using a case study of Common Era sea-level variability from New Jersey, U.S.A. We develop a new Bayesian transfer function (B-TF), with and without the {\\delta}13C proxy and compare our results to those from a widely...
From least squares to multilevel modeling: A graphical introduction to Bayesian inference
Loredo, Thomas J.
2016-01-01
This tutorial presentation will introduce some of the key ideas and techniques involved in applying Bayesian methods to problems in astrostatistics. The focus will be on the big picture: understanding the foundations (interpreting probability, Bayes's theorem, the law of total probability and marginalization), making connections to traditional methods (propagation of errors, least squares, chi-squared, maximum likelihood, Monte Carlo simulation), and highlighting problems where a Bayesian approach can be particularly powerful (Poisson processes, density estimation and curve fitting with measurement error). The "graphical" component of the title reflects an emphasis on pictorial representations of some of the math, but also on the use of graphical models (multilevel or hierarchical models) for analyzing complex data. Code for some examples from the talk will be available to participants, in Python and in the Stan probabilistic programming language.
PARALLEL ADAPTIVE MULTILEVEL SAMPLING ALGORITHMS FOR THE BAYESIAN ANALYSIS OF MATHEMATICAL MODELS
Prudencio, Ernesto
2012-01-01
In recent years, Bayesian model updating techniques based on measured data have been applied to many engineering and applied science problems. At the same time, parallel computational platforms are becoming increasingly more powerful and are being used more frequently by the engineering and scientific communities. Bayesian techniques usually require the evaluation of multi-dimensional integrals related to the posterior probability density function (PDF) of uncertain model parameters. The fact that such integrals cannot be computed analytically motivates the research of stochastic simulation methods for sampling posterior PDFs. One such algorithm is the adaptive multilevel stochastic simulation algorithm (AMSSA). In this paper we discuss the parallelization of AMSSA, formulating the necessary load balancing step as a binary integer programming problem. We present a variety of results showing the effectiveness of load balancing on the overall performance of AMSSA in a parallel computational environment.
A BAYESIAN ABDUCTION MODEL FOR EXTRACTING THE MOST PROBABLE EVIDENCE TO SUPPORT SENSEMAKING
Directory of Open Access Journals (Sweden)
Paul Munya
2015-01-01
Full Text Available In this paper, we discuss the development of a Bayesian Abduction Model of Sensemaking Support (BAMSS as a tool for information fusion to support prospective sensemaking. Currently, BAMSS can identify the Most Probable Explanation from a Bayesian Belief Network (BBN and extract the prevalent conditional probability values to help the sensemaking analysts to understand the cause-effect of the adversary information. Actual vignettes from databases of modern insurgencies and asymmetry warfare are used to validate the performance of BAMSS. BAMSS computes the posterior probability of the network edges and performs information fusion using a clustering algorithm. In the model, the friendly force commander uses the adversary information to prospectively make sense of the enemy’s intent. Sensitivity analyses were used to confirm the robustness of BAMSS in generating the Most Probable Explanations from a BBN through abductive inference. The simulation results demonstrate the utility of BAMSS as a computational tool to support sense making.
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.
Bayesian Option Pricing Using Mixed Normal Heteroskedasticity Models
DEFF Research Database (Denmark)
Rombouts, Jeroen V.K.; Stentoft, Lars Peter
While stochastic volatility models improve on the option pricing error when compared to the Black-Scholes-Merton model, mispricings remain. This paper uses mixed normal heteroskedasticity models to price options. Our model allows for significant negative skewness and time varying higher order...
Directory of Open Access Journals (Sweden)
Zeinab eMortezapouraghdam
2016-01-01
Full Text Available We study the effect of long-term habituation signatures of auditory selective attention reflected in the instantaneous phase information of the auditory event-related potentials (ERPs at four distinct stimuli levels of 60dB SPL, 70dB SPL, 80dB SPL and 90dB SPL. The analysis is based on the single-trial level. The effect of habituation can be observed in terms of the changes (jitter in the instantaneous phase information of ERPs. In particular, the absence of habituation is correlated with a consistently high phase synchronization over ERP trials.We estimate the changes in phase concentration over trials using a Bayesian approach, in which the phase is modeled as being drawn from a von Mises distribution with a concentration parameter which varies smoothly over trials. The smoothness assumption reflects the fact that habituation is a gradual process.We differentiate between different stimuli based on the relative changes and absolute values of the estimated concentration parameter using the proposed Bayesian model.
Cuevas Rivera, Dario; Bitzer, Sebastian; Kiebel, Stefan J
2015-10-01
The olfactory information that is received by the insect brain is encoded in the form of spatiotemporal patterns in the projection neurons of the antennal lobe. These dense and overlapping patterns are transformed into a sparse code in Kenyon cells in the mushroom body. Although it is clear that this sparse code is the basis for rapid categorization of odors, it is yet unclear how the sparse code in Kenyon cells is computed and what information it represents. Here we show that this computation can be modeled by sequential firing rate patterns using Lotka-Volterra equations and Bayesian online inference. This new model can be understood as an 'intelligent coincidence detector', which robustly and dynamically encodes the presence of specific odor features. We found that the model is able to qualitatively reproduce experimentally observed activity in both the projection neurons and the Kenyon cells. In particular, the model explains mechanistically how sparse activity in the Kenyon cells arises from the dense code in the projection neurons. The odor classification performance of the model proved to be robust against noise and time jitter in the observed input sequences. As in recent experimental results, we found that recognition of an odor happened very early during stimulus presentation in the model. Critically, by using the model, we found surprising but simple computational explanations for several experimental phenomena. PMID:26451888
Directory of Open Access Journals (Sweden)
Dario Cuevas Rivera
2015-10-01
Full Text Available The olfactory information that is received by the insect brain is encoded in the form of spatiotemporal patterns in the projection neurons of the antennal lobe. These dense and overlapping patterns are transformed into a sparse code in Kenyon cells in the mushroom body. Although it is clear that this sparse code is the basis for rapid categorization of odors, it is yet unclear how the sparse code in Kenyon cells is computed and what information it represents. Here we show that this computation can be modeled by sequential firing rate patterns using Lotka-Volterra equations and Bayesian online inference. This new model can be understood as an 'intelligent coincidence detector', which robustly and dynamically encodes the presence of specific odor features. We found that the model is able to qualitatively reproduce experimentally observed activity in both the projection neurons and the Kenyon cells. In particular, the model explains mechanistically how sparse activity in the Kenyon cells arises from the dense code in the projection neurons. The odor classification performance of the model proved to be robust against noise and time jitter in the observed input sequences. As in recent experimental results, we found that recognition of an odor happened very early during stimulus presentation in the model. Critically, by using the model, we found surprising but simple computational explanations for several experimental phenomena.
Bayesian estimation of small-scale DSGE model of the Ukrainian economy
Semko, Roman
2011-01-01
In this article we try to introduce Bayesian methodology for the estimation of dynamic stochastic general equilibrium model of the Ukrainian economy. The resulting impulse response functions can be used for increasing the efficiency of monetary and fiscal policy interventions. In addition, we showed that technology is one of the most important factors contributing to the stable long-term growth path of the economic system of Ukraine.
An Improved Approximate-Bayesian Model-choice Method for Estimating Shared Evolutionary History
Oaks, Jamie R.
2014-01-01
Background To understand biological diversification, it is important to account for large-scale processes that affect the evolutionary history of groups of co-distributed populations of organisms. Such events predict temporally clustered divergences times, a pattern that can be estimated using genetic data from co-distributed species. I introduce a new approximate-Bayesian method for comparative phylogeographical model-choice that estimates the temporal distribution of divergences across taxa...
Bhattacharjee, Arnab; Bhattacharjee, Madhuchhanda
2007-01-01
We propose Bayesian inference in hazard regression models where the baseline hazard is unknown, covariate effects are possibly age-varying (non-proportional), and there is multiplicative frailty with arbitrary distribution. Our framework incorporates a wide variety of order restrictions on covariate dependence and duration dependence (ageing). We propose estimation and evaluation of age-varying covariate effects when covariate dependence is monotone rather than proportional. In particular, we...
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.
A space-time multivariate Bayesian model to analyse road traffic accidents by severity
Boulieri, A; Liverani, S; Hoogh, K. de; Blangiardo, M.
2016-01-01
The paper investigates the dependences between levels of severity of road traffic accidents, accounting at the same time for spatial and temporal correlations. The study analyses road traffic accidents data at ward level in England over the period 2005–2013. We include in our model multivariate spatially structured and unstructured effects to capture the dependences between severities, within a Bayesian hierarchical formulation. We also include a temporal component to capture the time effects...
A BAYESIAN NETWORKS APPROACH TO MODELING FINANCIAL RISKS OF E-LOGISTICS INVESTMENTS
CHIEN-WEN SHEN
2009-01-01
To evaluate whether the investments of e-logistics systems may increase financial risks, models of Bayesian networks are constructed in this study with the mechanism of structural learning and parameter learning. Empirical findings from the transport and logistics sectors suggest that the e-logistics investments generally do not increase the financial risks of companies except the implementation of computer aided picking systems and radio frequency identification. Meanwhile, only the investme...
Bayesian Estimation of the GARCH(1,1) Model with Student-t Innovations
David, David; Hoogerheide, Lennart
2010-01-01
textabstractThis note presents the R package bayesGARCH (Ardia, 2007) which provides functions for the Bayesian estimation of the parsimonious and effective GARCH(1,1) model with Student-t innovations. The estimation procedure is fully automatic and thus avoids the tedious task of tuning a MCMC sampling algorithm. The usage of the package is shown in an empirical application to exchange rate logreturns.
Bayesian Estimation of the GARCH(1,1) Model with Student-t Innovations in R
Ardia, David
2009-01-01
This paper presents the R package bayesGARCH which provides functions for the Bayesian estimation of the parsimonious but effective GARCH(1,1) model with Student-t innovations. The estimation procedure is fully automatic and thus avoids the time-consuming and difficult task of tuning a sampling algorithm. The usage of the package is shown in an empirical application to exchange rate log-returns.
Low bitrate object coding of musical audio using bayesian harmonic models
Vincent, Emmanuel; PLUMBLEY, Mark
2007-01-01
This article deals with the decomposition of music signals into pitched sound objects made of harmonic sinusoidal partials for very low bitrate coding purposes. After a brief review of existing methods, we recast this problem in the Bayesian framework. We propose a family of probabilistic signal models combining learnt object priors and various perceptually motivated distortion measures. We design efficient algorithms to infer object parameters and build a coder based on the interpolation of ...
Data-driven and Model-based Verification:a Bayesian Identification Approach
Haesaert, S Sofie; Hof, van den, S.; Abate, A.
2015-01-01
This work develops a measurement-driven and model-based formal verification approach, applicable to systems with partly unknown dynamics. We provide a principled method, grounded on reachability analysis and on Bayesian inference, to compute the confidence that a physical system driven by external inputs and accessed under noisy measurements, verifies a temporal logic property. A case study is discussed, where we investigate the bounded- and unbounded-time safety of a partly unknown linear ti...
Mixture-based extension of the AR model and its recursive Bayesian identification
Czech Academy of Sciences Publication Activity Database
Šmídl, Václav; Quinn, A.
2005-01-01
Roč. 53, č. 9 (2005), s. 3530-3542. ISSN 1053-587X R&D Projects: GA AV ČR IBS1075102; GA ČR GA102/03/0049; GA MŠk 1M0572 Institutional research plan: CEZ:AV0Z10750506 Keywords : AR model * Bayesian identification * Variational Bayes Subject RIV: BC - Control Systems Theory Impact factor: 1.820, year: 2005
An examination of disparities in cancer incidence in Texas using Bayesian random coefficient models
Sparks, Corey
2015-01-01
Disparities in cancer risk exist between ethnic groups in the United States. These disparities often result from differential access to healthcare, differences in socioeconomic status and differential exposure to carcinogens. This study uses cancer incidence data from the population based Texas Cancer Registry to investigate the disparities in digestive and respiratory cancers from 2000 to 2008. A Bayesian hierarchical regression approach is used. All models are fit using the INLA method of B...
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...
Evaluation of Image Registration Spatial Accuracy Using a Bayesian Hierarchical Model
Liu, Suyu; Yuan, Ying; Castillo, Richard; Guerrero, Thomas; Johnson, Valen E.
2014-01-01
To evaluate the utility of automated deformable image registration (DIR) algorithms, it is necessary to evaluate both the registration accuracy of the DIR algorithm itself, as well as the registration accuracy of the human readers from whom the ”gold standard” is obtained. We propose a Bayesian hierarchical model to evaluate the spatial accuracy of human readers and automatic DIR methods based on multiple image registration data generated by human readers and automatic DIR methods. To fully a...
Bayesian network as a modelling tool for risk management in agriculture
Svend Rasmussen; Madsen, Anders L.; Mogens Lund
2013-01-01
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 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 e...
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.
2010-01-01
BACKGROUND: Culture remains the diagnostic gold standard for many bacterial infections, and the method against which other tests are often evaluated. Specificity of culture is 100% if the pathogenic organism is not found in healthy subjects, but the sensitivity of culture is more difficult to determine and may be low. Here, we apply Bayesian latent class models (LCMs) to data from patients with a single Gram-negative bacterial infection and define the true sensitivity of culture together with...
Complexity regularized hydrological model selection
Pande, S.; Arkesteijn, L.; Bastidas, L.A.
2014-01-01
This paper uses a recently proposed measure of hydrological model complexity in a model selection exercise. It demonstrates that a robust hydrological model is selected by penalizing model complexity while maximizing a model performance measure. This especially holds when limited data is available.
Individual Influence on Model Selection
Sterba, Sonya K.; Pek, Jolynn
2012-01-01
Researchers in psychology are increasingly using model selection strategies to decide among competing models, rather than evaluating the fit of a given model in isolation. However, such interest in model selection outpaces an awareness that one or a few cases can have disproportionate impact on the model ranking. Though case influence on the fit…
Braess, Dietrich; Dette, Holger
2004-01-01
We consider maximin and Bayesian D -optimal designs for nonlinear regression models. The maximin criterion requires the specification of a region for the nonlinear parameters in the model, while the Bayesian optimality criterion assumes that a prior distribution for these parameters is available. It was observed empirically by many authors that an increase of uncertainty in the prior information (i.e. a larger range for the parameter space in the maximin criterion or a larger variance of the ...
A surrogate model enables a Bayesian approach to the inverse problem of scatterometry
International Nuclear Information System (INIS)
Scatterometry is an indirect optical method for the determination of photomask geometry parameters from scattered light intensities by solving an inverse problem. The Bayesian approach is a powerful method to solve the inverse problem. In the Bayesian framework estimates of parameters and associated uncertainties are obtained from posterior distributions. The determination the probability distribution is typically based on Markov chain Monte Carlo (MCMC) methods. However, in scatterometry the evaluation of MCMC steps require solutions of partial differential equations that are computationally expensive and application of MCMC methods is thus impractical. In this article we introduce a surrogate model for scatterometry based on polynomial chaos that can be treated by Bayesian inference. We compare the results of the surrogate model with rigorous finite element simulations and demonstrate its convergence. The accuracy reaches a value of lower than one percent for a sufficient fine mesh and the speed up amounts more than two order of magnitudes. Furthermore, we apply the surrogate model to MCMC calculations and we reconstruct geometry parameters of a photomask
Gene function classification using Bayesian models with hierarchy-based priors
Directory of Open Access Journals (Sweden)
Neal Radford M
2006-10-01
Full Text Available Abstract Background We investigate whether annotation of gene function can be improved using a classification scheme that is aware that functional classes are organized in a hierarchy. The classifiers look at phylogenic descriptors, sequence based attributes, and predicted secondary structure. We discuss three Bayesian models and compare their performance in terms of predictive accuracy. These models are the ordinary multinomial logit (MNL model, a hierarchical model based on a set of nested MNL models, and an MNL model with a prior that introduces correlations between the parameters for classes that are nearby in the hierarchy. We also provide a new scheme for combining different sources of information. We use these models to predict the functional class of Open Reading Frames (ORFs from the E. coli genome. Results The results from all three models show substantial improvement over previous methods, which were based on the C5 decision tree algorithm. The MNL model using a prior based on the hierarchy outperforms both the non-hierarchical MNL model and the nested MNL model. In contrast to previous attempts at combining the three sources of information in this dataset, our new approach to combining data sources produces a higher accuracy rate than applying our models to each data source alone. Conclusion Together, these results show that gene function can be predicted with higher accuracy than previously achieved, using Bayesian models that incorporate suitable prior information.
Bayesian model comparison in nonlinear BOLD fMRI hemodynamics
DEFF Research Database (Denmark)
Jacobsen, Danjal Jakup; Hansen, Lars Kai; Madsen, Kristoffer Hougaard
2008-01-01
Nonlinear hemodynamic models express the BOLD (blood oxygenation level dependent) signal as a nonlinear, parametric functional of the temporal sequence of local neural activity. Several models have been proposed for both the neural activity and the hemodynamics. We compare two such combined models...
Directory of Open Access Journals (Sweden)
Tsuda Koji
2007-11-01
Full Text Available Abstract Background Identifying large gene regulatory networks is an important task, while the acquisition of data through perturbation experiments (e.g., gene switches, RNAi, heterozygotes is expensive. It is thus desirable to use an identification method that effectively incorporates available prior knowledge – such as sparse connectivity – and that allows to design experiments such that maximal information is gained from each one. Results Our main contributions are twofold: a method for consistent inference of network structure is provided, incorporating prior knowledge about sparse connectivity. The algorithm is time efficient and robust to violations of model assumptions. Moreover, we show how to use it for optimal experimental design, reducing the number of required experiments substantially. We employ sparse linear models, and show how to perform full Bayesian inference for these. We not only estimate a single maximum likelihood network, but compute a posterior distribution over networks, using a novel variant of the expectation propagation method. The representation of uncertainty enables us to do effective experimental design in a standard statistical setting: experiments are selected such that the experiments are maximally informative. Conclusion Few methods have addressed the design issue so far. Compared to the most well-known one, our method is more transparent, and is shown to perform qualitatively superior. In the former, hard and unrealistic constraints have to be placed on the network structure for mere computational tractability, while such are not required in our method. We demonstrate reconstruction and optimal experimental design capabilities on tasks generated from realistic non-linear network simulators. The methods described in the paper are available as a Matlab package at http://www.kyb.tuebingen.mpg.de/sparselinearmodel.
A fully Bayesian method for jointly fitting instrumental calibration and X-ray spectral models
Energy Technology Data Exchange (ETDEWEB)
Xu, Jin; Yu, Yaming [Department of Statistics, University of California, Irvine, Irvine, CA 92697-1250 (United States); Van Dyk, David A. [Statistics Section, Imperial College London, Huxley Building, South Kensington Campus, London SW7 2AZ (United Kingdom); Kashyap, Vinay L.; Siemiginowska, Aneta; Drake, Jeremy; Ratzlaff, Pete [Smithsonian Astrophysical Observatory, 60 Garden Street, Cambridge, MA 02138 (United States); Connors, Alanna; Meng, Xiao-Li, E-mail: jinx@uci.edu, E-mail: yamingy@ics.uci.edu, E-mail: dvandyk@imperial.ac.uk, E-mail: vkashyap@cfa.harvard.edu, E-mail: asiemiginowska@cfa.harvard.edu, E-mail: jdrake@cfa.harvard.edu, E-mail: pratzlaff@cfa.harvard.edu, E-mail: meng@stat.harvard.edu [Department of Statistics, Harvard University, 1 Oxford Street, Cambridge, MA 02138 (United States)
2014-10-20
Owing to a lack of robust principled methods, systematic instrumental uncertainties have generally been ignored in astrophysical data analysis despite wide recognition of the importance of including them. Ignoring calibration uncertainty can cause bias in the estimation of source model parameters and can lead to underestimation of the variance of these estimates. We previously introduced a pragmatic Bayesian method to address this problem. The method is 'pragmatic' in that it introduced an ad hoc technique that simplified computation by neglecting the potential information in the data for narrowing the uncertainty for the calibration product. Following that work, we use a principal component analysis to efficiently represent the uncertainty of the effective area of an X-ray (or γ-ray) telescope. Here, however, we leverage this representation to enable a principled, fully Bayesian method that coherently accounts for the calibration uncertainty in high-energy spectral analysis. In this setting, the method is compared with standard analysis techniques and the pragmatic Bayesian method. The advantage of the fully Bayesian method is that it allows the data to provide information not only for estimation of the source parameters but also for the calibration product—here the effective area, conditional on the adopted spectral model. In this way, it can yield more accurate and efficient estimates of the source parameters along with valid estimates of their uncertainty. Provided that the source spectrum can be accurately described by a parameterized model, this method allows rigorous inference about the effective area by quantifying which possible curves are most consistent with the data.
A fully Bayesian method for jointly fitting instrumental calibration and X-ray spectral models
International Nuclear Information System (INIS)
Owing to a lack of robust principled methods, systematic instrumental uncertainties have generally been ignored in astrophysical data analysis despite wide recognition of the importance of including them. Ignoring calibration uncertainty can cause bias in the estimation of source model parameters and can lead to underestimation of the variance of these estimates. We previously introduced a pragmatic Bayesian method to address this problem. The method is 'pragmatic' in that it introduced an ad hoc technique that simplified computation by neglecting the potential information in the data for narrowing the uncertainty for the calibration product. Following that work, we use a principal component analysis to efficiently represent the uncertainty of the effective area of an X-ray (or γ-ray) telescope. Here, however, we leverage this representation to enable a principled, fully Bayesian method that coherently accounts for the calibration uncertainty in high-energy spectral analysis. In this setting, the method is compared with standard analysis techniques and the pragmatic Bayesian method. The advantage of the fully Bayesian method is that it allows the data to provide information not only for estimation of the source parameters but also for the calibration product—here the effective area, conditional on the adopted spectral model. In this way, it can yield more accurate and efficient estimates of the source parameters along with valid estimates of their uncertainty. Provided that the source spectrum can be accurately described by a parameterized model, this method allows rigorous inference about the effective area by quantifying which possible curves are most consistent with the data.
Zhao, Ningning; Basarab, Adrian; Kouame, Denis; Tourneret, Jean-Yves
2016-08-01
This paper proposes a joint segmentation and deconvolution Bayesian method for medical ultrasound (US) images. Contrary to piecewise homogeneous images, US images exhibit heavy characteristic speckle patterns correlated with the tissue structures. The generalized Gaussian distribution (GGD) has been shown to be one of the most relevant distributions for characterizing the speckle in US images. Thus, we propose a GGD-Potts model defined by a label map coupling US image segmentation and deconvolution. The Bayesian estimators of the unknown model parameters, including the US image, the label map, and all the hyperparameters are difficult to be expressed in a closed form. Thus, we investigate a Gibbs sampler to generate samples distributed according to the posterior of interest. These generated samples are finally used to compute the Bayesian estimators of the unknown parameters. The performance of the proposed Bayesian model is compared with the existing approaches via several experiments conducted on realistic synthetic data and in vivo US images. PMID:27187959
Energy Technology Data Exchange (ETDEWEB)
Ajami, N K; Duan, Q; Sorooshian, S
2006-05-05
This paper presents a new technique--Integrated Bayesian Uncertainty Estimator (IBUNE) to account for the major uncertainties of hydrologic rainfall-runoff predictions explicitly. The uncertainties from the input (forcing) data--mainly the precipitation observations and from the model parameters are reduced through a Monte Carlo Markov Chain (MCMC) scheme named Shuffled Complex Evolution Metropolis (SCEM) algorithm which has been extended to include a precipitation error model. Afterwards, the Bayesian Model Averaging (BMA) scheme is employed to further improve the prediction skill and uncertainty estimation using multiple model output. A series of case studies using three rainfall-runoff models to predict the streamflow in the Leaf River basin, Mississippi are used to examine the necessity and usefulness of this technique. The results suggests that ignoring either input forcings error or model structural uncertainty will lead to unrealistic model simulations and their associated uncertainty bounds which does not consistently capture and represent the real-world behavior of the watershed.
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
Combining Bayesian Networks and Agent Based Modeling to develop a decision-support model in Vietnam
Nong, Bao Anh; Ertsen, Maurits; Schoups, Gerrit
2016-04-01
Complexity and uncertainty in natural resources management have been focus themes in recent years. Within these debates, with the aim to define an approach feasible for water management practice, we are developing an integrated conceptual modeling framework for simulating decision-making processes of citizens, in our case in the Day river area, Vietnam. The model combines Bayesian Networks (BNs) and Agent-Based Modeling (ABM). BNs are able to combine both qualitative data from consultants / experts / stakeholders, and quantitative data from observations on different phenomena or outcomes from other models. Further strengths of BNs are that the relationship between variables in the system is presented in a graphical interface, and that components of uncertainty are explicitly related to their probabilistic dependencies. A disadvantage is that BNs cannot easily identify the feedback of agents in the system once changes appear. Hence, ABM was adopted to represent the reaction among stakeholders under changes. The modeling framework is developed as an attempt to gain better understanding about citizen's behavior and factors influencing their decisions in order to reduce uncertainty in the implementation of water management policy.
A Bayesian framework for parameter estimation in dynamical models.
Directory of Open Access Journals (Sweden)
Flávio Codeço Coelho
Full Text Available Mathematical models in biology are powerful tools for the study and exploration of complex dynamics. Nevertheless, bringing theoretical results to an agreement with experimental observations involves acknowledging a great deal of uncertainty intrinsic to our theoretical representation of a real system. Proper handling of such uncertainties is key to the successful usage of models to predict experimental or field observations. This problem has been addressed over the years by many tools for model calibration and parameter estimation. In this article we present a general framework for uncertainty analysis and parameter estimation that is designed to handle uncertainties associated with the modeling of dynamic biological systems while remaining agnostic as to the type of model used. We apply the framework to fit an SIR-like influenza transmission model to 7 years of incidence data in three European countries: Belgium, the Netherlands and Portugal.
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...
Bayesian Inference in the Time Varying Cointegration Model
Gary Koop; Roberto Leon-Gonzalez; Rodney Strachan
2008-01-01
There are both theoretical and empirical reasons for believing that the pa- rameters of macroeconomic models may vary over time. However, work with time-varying parameter models has largely involved Vector autoregressions (VARs), ignoring cointegration. This is despite the fact that cointegration plays an important role in informing macroeconomists on a range of issues. In this paper we develop time varying parameter models which permit coin- tegration. Time-varying parameter VARs (TVP-VARs) ...
Bayesian Nonstationary Gaussian Process Models via Treed Process Convolutions
Liang, Waley Wei Jie
2012-01-01
Spatial modeling with stationary Gaussian processes (GPs) has been widely used, but the assumption that the correlation structure is independent of spatial location is invalid in many applications. Various nonstationary GP models have been developed to solve this problem, however, many of them become impractical when the sample size is large. To tackle this problem, a more computationally efficient GP model is developed by convolving a smoothing kernel with a latent process. Nonstationarit...
Integrating Anticipatory Competence into a Bayesian Driver Model
Möbus, Claus; Eilers, Mark
2011-01-01
We present a probabilistic model architecture combining a layered model of human driver expertise with a cognitive map and beliefs about the driver-vehicle state to describe the effect of anticipations on driver actions. It implements the sensory-motor system of human drivers with autonomous, goal-based attention allocation and anticipation processes. The model has emergent properties and combines reactive with prospective behavior based on anticipated or imagined percepts obtained from a Bay...
A Pseudo-Bayesian Model for Stock Returns In Financial Crises
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Eric S. Fung
2011-12-01
Full Text Available Recently, there has been a considerable interest in the Bayesian approach for explaining investors' behaviorial biases by incorporating conservative and representative heuristics when making financial decisions, (see, for example, Barberis, Shleifer and Vishny (1998. To establish a quantitative link between some important market anomalies and investors' behaviorial biases, Lam, Liu, and Wong (2010 introduced a pseudo-Bayesian approach for developing properties of stock returns, where weights induced by investors' conservative and representative heuristics are assigned to observations of the earning shocks and stock prices. In response to the recent global financial crisis, we introduce a new pseudo-Bayesian model to incorporate the impact of a financial crisis. Properties of stock returns during the financial crisis and recovery from the crisis are established. The proposed model can be applied to investigate some important market anomalies including short-term underreaction, long-term overreaction, and excess volatility during financial crisis. We also explain in some detail the linkage between these market anomalies and investors' behavioral biases during financial crisis.
A Bayesian Semiparametric Item Response Model with Dirichlet Process Priors
Miyazaki, Kei; Hoshino, Takahiro
2009-01-01
In Item Response Theory (IRT), item characteristic curves (ICCs) are illustrated through logistic models or normal ogive models, and the probability that examinees give the correct answer is usually a monotonically increasing function of their ability parameters. However, since only limited patterns of shapes can be obtained from logistic models…
Han, Feng; Zheng, Yi
2016-02-01
While watershed water quality (WWQ) models have been widely used to support water quality management, their profound modeling uncertainty remains an unaddressed issue. Data assimilation via Bayesian calibration is a promising solution to the uncertainty, but has been rarely practiced for WWQ modeling. This study applied multiple-response Bayesian calibration (MRBC) to SWAT, a classic WWQ model, using the nitrate pollution in the Newport Bay Watershed (southern California, USA) as the study case. How typical input and model structure errors would impact modeling uncertainty, parameter identification and management decision-making was systematically investigated through both synthetic and real-situation modeling cases. The main study findings include: (1) with an efficient sampling scheme, MRBC is applicable to WWQ modeling in characterizing its parametric and predictive uncertainties; (2) incorporating hydrology responses, which are less susceptible to input and model structure errors than water quality responses, can improve the Bayesian calibration results and benefit potential modeling-based management decisions; and (3) the value of MRBC to modeling-based decision-making essentially depends on pollution severity, management objective and decision maker's risk tolerance.
A Bayesian state-space formulation of dynamic occupancy models.
Royle, J Andrew; Kéry, Marc
2007-07-01
Species occurrence and its dynamic components, extinction and colonization probabilities, are focal quantities in biogeography and metapopulation biology, and for species conservation assessments. It has been increasingly appreciated that these parameters must be estimated separately from detection probability to avoid the biases induced by non-detection error. Hence, there is now considerable theoretical and practical interest in dynamic occupancy models that contain explicit representations of metapopulation dynamics such as extinction, colonization, and turnover as well as growth rates. We describe a hierarchical parameterization of these models that is analogous to the state-space formulation of models in time series, where the model is represented by two components, one for the partially observable occupancy process and another for the observations conditional on that process. This parameterization naturally allows estimation of all parameters of the conventional approach to occupancy models, but in addition, yields great flexibility and extensibility, e.g., to modeling heterogeneity or latent structure in model parameters. We also highlight the important distinction between population and finite sample inference; the latter yields much more precise estimates for the particular sample at hand. Finite sample estimates can easily be obtained using the state-space representation of the model but are difficult to obtain under the conventional approach of likelihood-based estimation. We use R and WinBUGS to apply the model to two examples. In a standard analysis for the European Crossbill in a large Swiss monitoring program, we fit a model with year-specific parameters. Estimates of the dynamic parameters varied greatly among years, highlighting the irruptive population dynamics of that species. In the second example, we analyze route occupancy of Cerulean Warblers in the North American Breeding Bird Survey (BBS) using a model allowing for site