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Marc Kery - One of the best experts on this subject based on the ideXlab platform.
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Chapter 11 – General Linear Model (ANCOVA)
Introduction to WinBUGS for Ecologists, 2020Co-Authors: Marc KeryAbstract:Publisher Summary The “model of the mean,” t-test, simple linear regression, and analysis of variance (ANOVA) are all just special cases of a very general and powerful statistical model, the general linear model. This model expresses a continuous response as a linear combination of the effects of discrete and/or continuous explanatory variables plus a single random contribution from a normal distribution, whose variance is estimated along with the coefficients of all discrete and continuous covariates and possible interactions. Models that contained both types of explanatory variables were usually treated as ANOVAs with typically a single continuous covariate to correct for preexisting variation among experimental units. These models were called analysis of covariance (ANCOVA) models. In WinBUGS, it is much easier to fit the means parameterization of the model, i.e., to specify three separate linear regressions for each mountain range. The effects are trivially easy to recover as derived parameters by just adding a few WinBUGS code lines. This allows for better comparison between input and output values.
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Chapter 19 – Binomial Mixed-Effects Model (Binomial GLMM)
Introduction to WinBUGS for Ecologists, 2020Co-Authors: Marc KeryAbstract:Publisher Summary As in a Poisson generalized linear mixed model (GLMM), one can also add into a binomial generalized linear model (GLM) random variation beyond what is stipulated by the binomial distribution. The chapter examines the relationship between precipitation during the breeding season and reproductive success; wet springs are likely to depress the proportion of successful nests. One can assume that all shrike populations have the same relation- ship between breeding success and standardized spring precipitation, but at different levels, corresponding to a random-intercepts model. This means assuming that every shrike population has a specific response to precipitation but that both intercept and slope are “similar” among populations. As for the Poisson case, the introduction of random effects into a binomial GLM in WinBUGS is particularly straightforward and transparent. Fitting the resulting binomial GLMM in WinBUGS is very helpful for the general understanding of this class of models.
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Chapter 22 – Conclusions
Introduction to WinBUGS for Ecologists, 2020Co-Authors: Marc KeryAbstract:Publisher Summary This chapter provides practical understanding for how Bayesian inference with vague priors works and why Bayesian inference is simply so useful. WinBUGS is the most widely used general-purpose Bayesian software. WinBUGS allows the average, somewhat numerate ecologist to conduct his or her own creative statistical modeling. WinBUGS has the potential to free the statistical modeler in anyone. Even without the benefits of the Bayesian paradigm of statistical inference, this would be enough to recommend WinBUGS to any ambitious quantitative ecologist. Implementation in WinBUGS is much more straightforward and arguably easier to understand for an ecologist. The reason for this is that in the BUGS language, a complex model is naturally broken apart into hierarchically linked submodels. Nonlinear models may be more realistic representations of a study system and may yield better predictions, especially outside of the observed range of covariates.
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Chapter 8 – Normal Linear Regression
Introduction to WinBUGS for Ecologists, 2020Co-Authors: Marc KeryAbstract:Publisher Summary WinBUGS is used to fit a linear regression, the algebraic model and the WinBUGS code for which is essentially identical to that for the t-test. We have also introduced posterior predictive distributions along with the Bayesian p-value as a very general and flexible way of assessing goodness-of-fit of a model analyzed using MCMC. In the WinBUGS code, there are two components included to assess the goodness-of-fit of our model. First, there are two lines that compute residuals and predicted values under the model. And second, there is code to compute a Bayesian p-value, i.e., a posterior predictive check. As an instructive example, it assesses the adequacy of the model using a traditional residual check and then using posterior predictive distributions, including a Bayesian p-value, as an overall measure of fit for a chosen fit criterion. One commonly produced graphical check of the residuals of a linear model is a plot of the residuals against the predicted values. Under the normal linear regression model, residuals are assumed to be a random sample from one single normal distribution. The use of posterior predictive distributions is a very general way of assessing the fit of a model when using MCMC model fitting techniques. The idea of a posterior predictive check is to compare the lack of fit of the model for the actual data set with the lack of fit of the model when fitted to replicated, “ideal” data sets. One of the best ways to assess model adequacy based on posterior predictive distributions is graphically, in a plot of the lack of fit for the ideal data vs. the lack of fit for the actual data.
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Chapter 7 – t-Test: Equal and Unequal Variances
Introduction to WinBUGS for Ecologists, 2020Co-Authors: Marc KeryAbstract:Publisher Summary One of the most commonly used linear models is that underlying the simple t-test. The t-test comes in two flavors: one for the case with equal variances and another for unequal variances. WinBUGS is used to conduct the most widely used statistical test, the t-test. This chapter shows that not only the mean but also the variance may be modeled. In classical statistics, variance modeling may be rather hard and fairly obscure in its application to an ecologist. In contrast in WinBUGS, the modeling of variances, e.g., as a function of some covariate, could be simply undertaken by use of a log link function. Variance modeling, either for the residuals or for random effects, may be required to adequately characterize the stochastic system components when inference is focusing on the mean structure. Alternatively, one may focus on a relation between an explanatory variable and a variance, for instance, to test a hypothesis that some conditions increase the variance in some trait.
Mark Smith - One of the best experts on this subject based on the ideXlab platform.
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complex bayesian modeling workflows encoding and execution made easy with a novel WinBUGS plugin of the drug disease model resources interoperability framework
CPT: pharmacometrics & systems pharmacology, 2018Co-Authors: Cristiana Larizza, Mark Smith, Elisa Borella, Lorenzo Pasotti, Palma Tartaglione, Stuart L Moodie, Paolo MagniAbstract:: The Drug Disease Model Resources (DDMoRe) Interoperability Framework (IOF) enables pharmacometric model encoding and execution via Model Description Language (MDL) and R language, through the ddmore package. Through its components and converter plugins, the IOF can execute pharmacometric tasks using different target tools, starting from a single MDL-encoded model. In this article, we present the WinBUGS plugin and show how its integration in the IOF enables an easy implementation of complex Bayesian workflows. We selected a published diabetes-linked study as a real-world example, in which two inter-related models are used to estimate insulin secretion rate in response to a glucose stimulus from intravenous glucose tolerance test (IVGTT) data. This model was implemented following different approaches to propagate uncertainty, via diverse IOF target tools (NONMEM, WinBUGS, PsN, and Xpose). The developed software supports a plethora of pharmacokinetic/pharmacodynamic (PK/PD) modeling features. It provides solutions to reproducibility and interoperability issues in Bayesian modeling, and facilitates the difficult encoding of complex PK/PD models in WinBUGS.
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WinBUGSio a sas macro for the remote execution of WinBUGS
Journal of Statistical Software, 2007Co-Authors: Mark SmithAbstract:This is a macro which facilitates remote execution of WinBUGS from within SAS. The macro pre-processes data for WinBUGS, writes the WinBUGS batch-script, executes this script and reads in output statistics from the WinBUGS log-file back into SAS native format. The user specifies the input and output file names and directory path as well as the statistics to be monitored in WinBUGS. The code works best for a model that has already been set up and checked for convergence diagnostics within WinBUGS. An obvious extension of the use of this macro is for running simulations where the input and output files all have the same name but all that differs between simulation iterations is the input dataset. The functionality and syntax of the macro call are described in this paper and illustrated using a simple linear regression model.
Mark F J Steel - One of the best experts on this subject based on the ideXlab platform.
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bayesian stochastic frontier analysis using WinBUGS
Journal of Productivity Analysis, 2007Co-Authors: Jim E Griffin, Mark F J SteelAbstract:Markov chain Monte Carlo (MCMC) methods have become a ubiquitous tool in Bayesian analysis. This paper implements MCMC methods for Bayesian analysis of stochastic frontier models using the WinBUGS package, a freely available software. General code for cross-sectional and panel data are presented and various ways of summarizing posterior inference are discussed. Several examples illustrate that analyses with models of genuine practical interest can be performed straightforwardly and model changes are easily implemented. Although WinBUGS may not be that efficient for more complicated models, it does make Bayesian inference with stochastic frontier models easily accessible for applied researchers and its generic structure allows for a lot of flexibility in model specification.
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bayesian stochastic frontier analysis using WinBUGS
Econometrics, 2005Co-Authors: Jim E Griffin, Mark F J SteelAbstract:Markov chain Monte Carlo (MCMC) methods have become a ubiquitous tool in Bayesian analysis. This paper implements MCMC methods for Bayesian analysis of stochastic frontier models using the WinBUGS package, a freely available software. General code for cross-sectional and panel data are presented and various ways of summarizing posterior inference are discussed. Several examples illustrate that analyses with models of genuine practical interest can be performed straightforwardly and model changes are easily implemented.
Jim E Griffin - One of the best experts on this subject based on the ideXlab platform.
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bayesian stochastic frontier analysis using WinBUGS
Journal of Productivity Analysis, 2007Co-Authors: Jim E Griffin, Mark F J SteelAbstract:Markov chain Monte Carlo (MCMC) methods have become a ubiquitous tool in Bayesian analysis. This paper implements MCMC methods for Bayesian analysis of stochastic frontier models using the WinBUGS package, a freely available software. General code for cross-sectional and panel data are presented and various ways of summarizing posterior inference are discussed. Several examples illustrate that analyses with models of genuine practical interest can be performed straightforwardly and model changes are easily implemented. Although WinBUGS may not be that efficient for more complicated models, it does make Bayesian inference with stochastic frontier models easily accessible for applied researchers and its generic structure allows for a lot of flexibility in model specification.
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bayesian stochastic frontier analysis using WinBUGS
Econometrics, 2005Co-Authors: Jim E Griffin, Mark F J SteelAbstract:Markov chain Monte Carlo (MCMC) methods have become a ubiquitous tool in Bayesian analysis. This paper implements MCMC methods for Bayesian analysis of stochastic frontier models using the WinBUGS package, a freely available software. General code for cross-sectional and panel data are presented and various ways of summarizing posterior inference are discussed. Several examples illustrate that analyses with models of genuine practical interest can be performed straightforwardly and model changes are easily implemented.
Ioannis Ntzoufras - One of the best experts on this subject based on the ideXlab platform.
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WinBUGS a tutorial
Wiley Interdisciplinary Reviews: Computational Statistics, 2011Co-Authors: Anastasia Lykou, Ioannis NtzoufrasAbstract:The reinvention of Markov chain Monte Carlo (MCMC) methods and their implementation within the Bayesian framework in the early 1990s has established the Bayesian approach as one of the standard methods within the applied quantitative sciences. Their extensive use in complex real life problems has lead to the increased demand for a friendly and easily accessible software, which implements Bayesian models by exploiting the possibilities provided by MCMC algorithms. WinBUGS is the software that covers this increased need. It is the Windows version of BUGS (Bayesian inference using Gibbs sampling) package appeared in the mid-1990s. It is a free and a relatively easy tool that estimates the posterior distribution of any parameter of interest in complicated Bayesian models. In this article, we present an overview of the basic features of WinBUGS, including information for the model and prior specification, the code and its compilation, and the analysis and the interpretation of the MCMC output. Some simple examples and the Bayesian implementation of the Lasso are illustrated in detail. 2011 John
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bayesian modeling using WinBUGS
2009Co-Authors: Christian P Robert, Ioannis NtzoufrasAbstract:Preface. Acknowledgments. Acronyms. 1. Introduction to Bayesian inference. 1.1 Introduction: Bayesian modeling in the 21st century. 1.2 Definition of statistical models. 1.3 Bayes theorem. 1.4 Model-based Bayesian Inference. 1.5 Inference using conjugate prior distributions. 1.6 Nonconjugate Analysis. Problems. 2. Markov Chain Monte Carlo Algorithms in Bayesian Inference. 2.1 Simulation, Monte Carlo integration, and their implementation in Bayesian inference. 2.2 Markov chain Monte Carlo methods. 2.3 Popular MCMC algorithms. 2.4 Summary and closing remarks. Problems. 3. WinBUGS Software: Introduction, Setup and Basic Analysis. 3.1 Introduction and historical background. 3.2 The WinBUGS environment. 3.3 Preliminaries on using WinBUGS. 3.4 Building Bayesian models in WinBUGS. 3.5 Compiling the model and simulating values. 3.6 Basic output analysis using the sample monitor tool. 3.7 Summarizing the procedure. 3.8 Chapter summary and concluding comments. Problems. 4. WinBUGS Software: Illustration, Results, and Further Analysis. 4.1 A complete example of running MCMC in WinBUGS for a simple model. 4.2 Further output analysis using the inference menu. 4.3 Multiple chains. 4.4 Changing the properties of a figure. 4.5 Other tools and menus. 4.6 Summary and concluding remarks. Problems. 5. Introduction to Bayesian Models: Normal models. 5.1 General modeling principles. 5.2 Model specification in normal regression models. 5.3 Using vectors and multivariate priors in normal regression models. 5.4 Analysis of variance models. Problems. 6. Incorporating Categorical Variables in Normal Models and Further Modeling Issues. 6.1 Analysis of variance models using dummy variables. 6.2 Analysis of covariance models. 6.3 A Bioassay example. 6.4 Further modeling issues. 6.5 Closing remarks. Problems. 7. Introduction to Generalized Linear Models: Binomial and Poisson Data. 7.1 Introduction. 7.2 Prior distributions. 7.3 Posterior inference. 7.4 Poisson regression models. 7.5 Binomial response models. 7.6 Models for contingency tables. Problems. 8. Models for Positive Continuous Data, Count Data, and Other GLM-Based Extensions. 8.1 Models with nonstandard distributions. 8.2 Models for positive continuous response variables. 8.3 Additional models for count data. 8.4 Further GLM-based models and extensions. Problems. 9. Bayesian Hierarchical Models. 9.1 Introduction. 9.2 Some simple examples. 9.3 The generalized linear mixed model formulation. 9.4 Discussion, closing remarks, and further reading. Problems. 10. The Predictive Distribution and Model Checking. 10.1 Introduction. 10.2 Estimating the predictive distribution for future or missing observations using MCMC. 10.3 Using the predictive distribution for model checking. 10.4 Using cross-validation predictive densities for model checking, evaluation, and comparison. 10.5 Illustration of a complete predictive analysis: Normal regression models. 10.6 Discussion. Problems. 11. Bayesian Model and Variable Evaluation. 11.1 Prior predictive distributions as measures of model comparison: Posterior model odds and Bayes factors. 11.2 Sensitivity of the posterior model probabilities: The Lindley-Bartlett paradox. 11.3 Computation of the marginal likelihood. 11.4 Computation of the marginal likelihood using WinBUGS. 11.5 Bayesian variable selection using Gibbs-based methods. 11.6 Posterior inference using the output of Bayesian variable selection samplers. 11.7 Implementation of Gibbs variable selection in WinBUGS using an illustrative example. 11.8 The Carlin Chib's method. 11.9 Reversible jump MCMC (RJMCMC). 11.10 Using posterior predictive densities for model evaluation. 11.11 Information criteria. 11.12 Discussion and further reading. Problems. Appendix A: Model Specification via Directed Acyclic Graphs: The Doodle Menu. A.1 Introduction: Starting with DOODLE. A.2 Nodes. A.3 Edges. A.4 Panels. A.5 A simple example. Appendix B: The Batch Mode: Running a Model in the Background Using Scripts. B.1 Introduction. B.2 Basic commands: Compiling and running the model. Appendix C: Checking Convergence Using CODA/BOA. C.1 Introduction. C.2 A short historical review. C.3 Diagnostics implemented by CODA/BOA. C.4 A first look of CODA/BOA. C.5 A simple example. Appendix D: Notation Summary. D.1 MCMC. D.2 Subscripts and indices. D.3 Parameters. D.4 Random variables and data. D.5 Sample estimates. D.6 Special functions, vectors and matrices. D.7 Distributions. D.8 Distribution-related notation. D.9 Notation used in ANOVA and ANCOVA. D.10 Variable and model specification. D.11 Deviance information criterion (DIC). D.12 Predictive measures. References. Index.
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Bayesian Modeling Using WinBUGS
Bayesian Modeling Using WinBUGS, 2008Co-Authors: Ioannis NtzoufrasAbstract:A hands-on introduction to the principles of Bayesian modeling using WinBUGSBayesian 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 inferenceGeneralized linear modelsBayesian hierarchical modelsPredictive distribution and model checkingBayesian model and variable evaluationComputational 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 data sets and code are available on the book's related Web site.Requiring only a working knowledge of probability theory and statistics, Bayesian Modeling Using WinBUGS serves as an excellent book for courses on Bayesian statistics at the upper-undergraduate and graduate levels. It is also a valuable reference for researchers and practitioners in the fields of statistics, actuarial science, medicine, and the social sciences who use WinBUGS in their everyday work.
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Bayesian hypothesis testing for the distribution of insurance claim counts using the Gibbs sampler
Journal of Computational Methods in Sciences and Engineering, 2005Co-Authors: Athanassios Katsis, Ioannis NtzoufrasAbstract:We construct and present a Markov Chain Monte Carlo {(MCMC)} algorithm\nfor the estimation of posterior odds and probabilities of alternative\nmodels used to evaluate competing hypotheses regarding three common\ndiscrete distributions involved in the modeling of the outstanding\nclaim counts in actuarial science. The proposed methodology involves\nadvanced statistical techniques of Bayesian modeling which make use\nof the Gibbs sampling variable selection algorithm. One of the main\nadvantages of this approach over the popular reversible jump algorithm\n[12] is its straightforward implementation using the {MCMC} language\ntool of {WinBUGS} software [17]. The methodology is applied to a\nreal data set. Directions regarding the implementation in {WinBUGS}\nare provided at the Appendix. It is worth noting that although the\ncontext of the problem is actuarial, the methodology can be applied\nto any field of science where the aim is the comparison or selection\nof discrete distributions of counts.
