Download or read book Bayesian Variable Selection and Computation for Generalized Linear Models with Conjugate Priors written by Ming-Hui Chen and published by . This book was released on 2007 with total page 54 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Handbook of Bayesian Variable Selection written by Mahlet G. Tadesse and published by CRC Press. This book was released on 2021-12-24 with total page 762 pages. Available in PDF, EPUB and Kindle. Book excerpt: Bayesian variable selection has experienced substantial developments over the past 30 years with the proliferation of large data sets. Identifying relevant variables to include in a model allows simpler interpretation, avoids overfitting and multicollinearity, and can provide insights into the mechanisms underlying an observed phenomenon. Variable selection is especially important when the number of potential predictors is substantially larger than the sample size and sparsity can reasonably be assumed. The Handbook of Bayesian Variable Selection provides a comprehensive review of theoretical, methodological and computational aspects of Bayesian methods for variable selection. The topics covered include spike-and-slab priors, continuous shrinkage priors, Bayes factors, Bayesian model averaging, partitioning methods, as well as variable selection in decision trees and edge selection in graphical models. The handbook targets graduate students and established researchers who seek to understand the latest developments in the field. It also provides a valuable reference for all interested in applying existing methods and/or pursuing methodological extensions. Features: Provides a comprehensive review of methods and applications of Bayesian variable selection. Divided into four parts: Spike-and-Slab Priors; Continuous Shrinkage Priors; Extensions to various Modeling; Other Approaches to Bayesian Variable Selection. Covers theoretical and methodological aspects, as well as worked out examples with R code provided in the online supplement. Includes contributions by experts in the field. Supported by a website with code, data, and other supplementary material
Download or read book Nonlocal Priors for Bayesian Variable Selection in Generalized Linear Models and Generalized Linear Mixed Models and Their Applications in Biology Data written by Ho-Hsiang Wu and published by . This book was released on 2016 with total page 111 pages. Available in PDF, EPUB and Kindle. Book excerpt: A crucial problem in building a generalized linear model (GLM) or a generalized linear mixed model (GLMM) is to identify which subset of predictors should be included into the model. Hence, the main thrust of this dissertation is aimed to discuss and showcase our promising Bayesian methods that circumvent this problem in both GLMs and GLMMs. In the first part of the dissertation, we study the hyper-g prior based Bayesian variable selection procedure for generalized linear models. In the second part of the dissertation, we propose two novel scale mixtures of nonlocal priors (SMNP) for variable selection in GLMs. In the last part of the dissertation, we develop novel nonlocal prior for variable selection in generalized linear mixed models (GLMM) and apply the proposed nonlocal prior and its inference procedure for the whole genome allelic imbalance detection.
Download or read book Bayesian Modeling Using WinBUGS written by Ioannis Ntzoufras and published by John Wiley & Sons. This book was released on 2011-09-20 with total page 477 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 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.
Download or read book Bayesian Analysis of Linear Models written by Broemeling and published by CRC Press. This book was released on 1984-12-06 with total page 480 pages. Available in PDF, EPUB and Kindle. Book excerpt: With Bayesian statistics rapidly becoming accepted as a way to solve applied statisticalproblems, the need for a comprehensive, up-to-date source on the latest advances in thisfield has arisen.Presenting the basic theory of a large variety of linear models from a Bayesian viewpoint,Bayesian Analysis of Linear Models fills this need. Plus, this definitive volume containssomething traditional-a review of Bayesian techniques and methods of estimation, hypothesis,testing, and forecasting as applied to the standard populations ... somethinginnovative-a new approach to mixed models and models not generally studied by statisticianssuch as linear dynamic systems and changing parameter models ... and somethingpractical-clear graphs, eary-to-understand examples, end-of-chapter problems, numerousreferences, and a distribution appendix.Comprehensible, unique, and in-depth, Bayesian Analysis of Linear Models is the definitivemonograph for statisticians, econometricians, and engineers. In addition, this text isideal for students in graduate-level courses such as linear models, econometrics, andBayesian inference.
Download or read book Model Selection written by Parhasarathi Lahiri and published by IMS. This book was released on 2001 with total page 262 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Bayesian Analysis of Linear Models written by Lyle D. Broemeling and published by . This book was released on 1985 with total page 480 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Bayes Rules written by Alicia A. Johnson and published by CRC Press. This book was released on 2022-03-03 with total page 606 pages. Available in PDF, EPUB and Kindle. Book excerpt: Praise for Bayes Rules!: An Introduction to Applied Bayesian Modeling “A thoughtful and entertaining book, and a great way to get started with Bayesian analysis.” Andrew Gelman, Columbia University “The examples are modern, and even many frequentist intro books ignore important topics (like the great p-value debate) that the authors address. The focus on simulation for understanding is excellent.” Amy Herring, Duke University “I sincerely believe that a generation of students will cite this book as inspiration for their use of – and love for – Bayesian statistics. The narrative holds the reader’s attention and flows naturally – almost conversationally. Put simply, this is perhaps the most engaging introductory statistics textbook I have ever read. [It] is a natural choice for an introductory undergraduate course in applied Bayesian statistics." Yue Jiang, Duke University “This is by far the best book I’ve seen on how to (and how to teach students to) do Bayesian modeling and understand the underlying mathematics and computation. The authors build intuition and scaffold ideas expertly, using interesting real case studies, insightful graphics, and clear explanations. The scope of this book is vast – from basic building blocks to hierarchical modeling, but the authors’ thoughtful organization allows the reader to navigate this journey smoothly. And impressively, by the end of the book, one can run sophisticated Bayesian models and actually understand the whys, whats, and hows.” Paul Roback, St. Olaf College “The authors provide a compelling, integrated, accessible, and non-religious introduction to statistical modeling using a Bayesian approach. They outline a principled approach that features computational implementations and model assessment with ethical implications interwoven throughout. Students and instructors will find the conceptual and computational exercises to be fresh and engaging.” Nicholas Horton, Amherst College An engaging, sophisticated, and fun introduction to the field of Bayesian statistics, Bayes Rules!: An Introduction to Applied Bayesian Modeling brings the power of modern Bayesian thinking, modeling, and computing to a broad audience. In particular, the book is an ideal resource for advanced undergraduate statistics students and practitioners with comparable experience. Bayes Rules! empowers readers to weave Bayesian approaches into their everyday practice. Discussions and applications are data driven. A natural progression from fundamental to multivariable, hierarchical models emphasizes a practical and generalizable model building process. The evaluation of these Bayesian models reflects the fact that a data analysis does not exist in a vacuum. Features • Utilizes data-driven examples and exercises. • Emphasizes the iterative model building and evaluation process. • Surveys an interconnected range of multivariable regression and classification models. • Presents fundamental Markov chain Monte Carlo simulation. • Integrates R code, including RStan modeling tools and the bayesrules package. • Encourages readers to tap into their intuition and learn by doing. • Provides a friendly and inclusive introduction to technical Bayesian concepts. • Supports Bayesian applications with foundational Bayesian theory.
Download or read book Prior Elicitation and Variable Selection for Bayesian Quantile Regression written by Rahim Jabbar Thaher Al-Hamzawi and published by . This book was released on 2013 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: Bayesian subset selection suffers from three important difficulties: assigning priors over model space, assigning priors to all components of the regression coefficients vector given a specific model and Bayesian computational efficiency (Chen et al., 1999). These difficulties become more challenging in Bayesian quantile regression framework when one is interested in assigning priors that depend on different quantile levels. The objective of Bayesian quantile regression (BQR), which is a newly proposed tool, is to deal with unknown parameters and model uncertainty in quantile regression (QR). However, Bayesian subset selection in quantile regression models is usually a difficult issue due to the computational challenges and nonavailability of conjugate prior distributions that are dependent on the quantile level. These challenges are rarely addressed via either penalised likelihood function or stochastic search variable selection (SSVS). These methods typically use symmetric prior distributions for regression coefficients, such as the Gaussian and Laplace, which may be suitable for median regression. However, an extreme quantile regression should have different regression coefficients from the median regression, and thus the priors for quantile regression coefficients should depend on quantiles. This thesis focuses on three challenges: assigning standard quantile dependent prior distributions for the regression coefficients, assigning suitable quantile dependent priors over model space and achieving computational efficiency. The first of these challenges is studied in Chapter 2 in which a quantile dependent prior elicitation scheme is developed. In particular, an extension of the Zellners prior which allows for a conditional conjugate prior and quantile dependent prior on Bayesian quantile regression is proposed. The prior is generalised in Chapter 3 by introducing a ridge parameter to address important challenges that may arise in some applications, such as multicollinearity and overfitting problems. The proposed prior is also used in Chapter 4 for subset selection of the fixed and random coefficients in a linear mixedeffects QR model. In Chapter 5 we specify normal-exponential prior distributions for the regression coefficients which can provide adaptive shrinkage and represent an alternative model to the Bayesian Lasso quantile regression model. For the second challenge, we assign a quantile dependent prior over model space in Chapter 2. The prior is based on the percentage bend correlation which depends on the quantile level. This prior is novel and is used in Bayesian regression for the first time. For the third challenge of computational efficiency, Gibbs samplers are derived and setup to facilitate the computation of the proposed methods. In addition to the three major aforementioned challenges this thesis also addresses other important issues such as the regularisation in quantile regression and selecting both random and fixed effects in mixed quantile regression models.
Download or read book Probability and Bayesian Modeling written by Jim Albert and published by CRC Press. This book was released on 2019-12-06 with total page 553 pages. Available in PDF, EPUB and Kindle. Book excerpt: Probability and Bayesian Modeling is an introduction to probability and Bayesian thinking for undergraduate students with a calculus background. The first part of the book provides a broad view of probability including foundations, conditional probability, discrete and continuous distributions, and joint distributions. Statistical inference is presented completely from a Bayesian perspective. The text introduces inference and prediction for a single proportion and a single mean from Normal sampling. After fundamentals of Markov Chain Monte Carlo algorithms are introduced, Bayesian inference is described for hierarchical and regression models including logistic regression. The book presents several case studies motivated by some historical Bayesian studies and the authors’ research. This text reflects modern Bayesian statistical practice. Simulation is introduced in all the probability chapters and extensively used in the Bayesian material to simulate from the posterior and predictive distributions. One chapter describes the basic tenets of Metropolis and Gibbs sampling algorithms; however several chapters introduce the fundamentals of Bayesian inference for conjugate priors to deepen understanding. Strategies for constructing prior distributions are described in situations when one has substantial prior information and for cases where one has weak prior knowledge. One chapter introduces hierarchical Bayesian modeling as a practical way of combining data from different groups. There is an extensive discussion of Bayesian regression models including the construction of informative priors, inference about functions of the parameters of interest, prediction, and model selection. The text uses JAGS (Just Another Gibbs Sampler) as a general-purpose computational method for simulating from posterior distributions for a variety of Bayesian models. An R package ProbBayes is available containing all of the book datasets and special functions for illustrating concepts from the book. A complete solutions manual is available for instructors who adopt the book in the Additional Resources section.
Download or read book Bayesian Data Analysis Third Edition written by Andrew Gelman and published by CRC Press. This book was released on 2013-11-01 with total page 677 pages. Available in PDF, EPUB and Kindle. Book excerpt: Now in its third edition, this classic book is widely considered the leading text on Bayesian methods, lauded for its accessible, practical approach to analyzing data and solving research problems. Bayesian Data Analysis, Third Edition continues to take an applied approach to analysis using up-to-date Bayesian methods. The authors—all leaders in the statistics community—introduce basic concepts from a data-analytic perspective before presenting advanced methods. Throughout the text, numerous worked examples drawn from real applications and research emphasize the use of Bayesian inference in practice. New to the Third Edition Four new chapters on nonparametric modeling Coverage of weakly informative priors and boundary-avoiding priors Updated discussion of cross-validation and predictive information criteria Improved convergence monitoring and effective sample size calculations for iterative simulation Presentations of Hamiltonian Monte Carlo, variational Bayes, and expectation propagation New and revised software code The book can be used in three different ways. For undergraduate students, it introduces Bayesian inference starting from first principles. For graduate students, the text presents effective current approaches to Bayesian modeling and computation in statistics and related fields. For researchers, it provides an assortment of Bayesian methods in applied statistics. Additional materials, including data sets used in the examples, solutions to selected exercises, and software instructions, are available on the book’s web page.
Download or read book Variable Selection and Model Averaging in Semiparametric Overdispersed Generalized Linear Models written by Remy Cottet and published by . This book was released on 2008 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: We express the mean and variance terms in a double exponential regression model as additive functions of the predictors and use Bayesian variable selection to determine which predictors enter the model, and whether they enter linearly or flexibly. When the variance term is null we obtain a generalized additive model, which becomes a generalized linear model if the predictors enter the mean linearly. The model is estimated using Markov chain Monte Carlo simulation and the methodology is illustrated using real and simulated data sets.
Download or read book Bayesian Core A Practical Approach to Computational Bayesian Statistics written by Jean-Michel Marin and published by Springer Science & Business Media. This book was released on 2007-05-26 with total page 265 pages. Available in PDF, EPUB and Kindle. Book excerpt: This Bayesian modeling book is intended for practitioners and applied statisticians looking for a self-contained entry to computational Bayesian statistics. Focusing on standard statistical models and backed up by discussed real datasets available from the book website, it provides an operational methodology for conducting Bayesian inference, rather than focusing on its theoretical justifications. Special attention is paid to the derivation of prior distributions in each case and specific reference solutions are given for each of the models. Similarly, computational details are worked out to lead the reader towards an effective programming of the methods given in the book.
Download or read book Handbook of Bayesian Variable Selection written by Mahlet G. Tadesse and published by CRC Press. This book was released on 2021-12-24 with total page 491 pages. Available in PDF, EPUB and Kindle. Book excerpt: Bayesian variable selection has experienced substantial developments over the past 30 years with the proliferation of large data sets. Identifying relevant variables to include in a model allows simpler interpretation, avoids overfitting and multicollinearity, and can provide insights into the mechanisms underlying an observed phenomenon. Variable selection is especially important when the number of potential predictors is substantially larger than the sample size and sparsity can reasonably be assumed. The Handbook of Bayesian Variable Selection provides a comprehensive review of theoretical, methodological and computational aspects of Bayesian methods for variable selection. The topics covered include spike-and-slab priors, continuous shrinkage priors, Bayes factors, Bayesian model averaging, partitioning methods, as well as variable selection in decision trees and edge selection in graphical models. The handbook targets graduate students and established researchers who seek to understand the latest developments in the field. It also provides a valuable reference for all interested in applying existing methods and/or pursuing methodological extensions. Features: Provides a comprehensive review of methods and applications of Bayesian variable selection. Divided into four parts: Spike-and-Slab Priors; Continuous Shrinkage Priors; Extensions to various Modeling; Other Approaches to Bayesian Variable Selection. Covers theoretical and methodological aspects, as well as worked out examples with R code provided in the online supplement. Includes contributions by experts in the field. Supported by a website with code, data, and other supplementary material
Download or read book Bayesian Variable Selection Via a Benchmark written by and published by . This book was released on 2013 with total page 84 pages. Available in PDF, EPUB and Kindle. Book excerpt: With increasing appearances of high dimensional data over the past decades, variable selections through likelihood penalization remains a popular yet challenging research area in statistics. Ridge and Lasso, the two of the most popular penalized regression methods, served as the foundation of regularization technique and motivated several extensions to accommodate various circumstances, mostly through frequentist models. These two regularization problems can also be solved by their Bayesian counterparts, via putting proper priors on the regression parameters and then followed by Gibbs sampling. Compared to the frequentist version, the Bayesian framework enables easier interpretation and more straightforward inference on the parameters, based on the posterior distributional results. In general, however, the Bayesian approaches do not provide sparse estimates for the regression coefficients. In this thesis, an innovative Bayesian variable selection method via a benchmark variable in conjunction with a modified BIC is proposed under the framework of linear regression models as the first attempt, to promote both model sparsity and accuracy. The motivation of introducing such a benchmark is discussed, and the statistical properties regarding its role in the model are demonstrated. In short, it serves as a criterion to measure the importance of each variable based on the posterior inference of the corresponding coefficients, and only the most important variables providing the minimal modified BIC value are included. The Bayesian approach via a benchmark is extended to accommodate linear models with covariates exhibiting group structures. An iterative algorithm is implemented to identify both important groups and important variables within the selected groups. What's more, the method is further developed and modified to select variables for generalized linear models, by taking advantage of the normal approximation on the likelihood function. Simulation studies are carried out to assess and compare the performances among the proposed approaches and other state-of-art methods for each of the above three scenarios. The numerical results consistently illustrate our Bayesian variable selection approaches tend to select exactly the true variables or groups, while producing comparable prediction errors as other methods. Besides the numerical work, several real data sets are analyzed by these methods and the corresponding performances are further compared. The variable selection results by our approach are intuitively appealing or consistent with existing literatures in general.
Download or read book Bayesian Model Selection and Statistical Modeling written by Tomohiro Ando and published by CRC Press. This book was released on 2010-05-27 with total page 300 pages. Available in PDF, EPUB and Kindle. Book excerpt: Along with many practical applications, Bayesian Model Selection and Statistical Modeling presents an array of Bayesian inference and model selection procedures. It thoroughly explains the concepts, illustrates the derivations of various Bayesian model selection criteria through examples, and provides R code for implementation. The author shows how to implement a variety of Bayesian inference using R and sampling methods, such as Markov chain Monte Carlo. He covers the different types of simulation-based Bayesian model selection criteria, including the numerical calculation of Bayes factors, the Bayesian predictive information criterion, and the deviance information criterion. He also provides a theoretical basis for the analysis of these criteria. In addition, the author discusses how Bayesian model averaging can simultaneously treat both model and parameter uncertainties. Selecting and constructing the appropriate statistical model significantly affect the quality of results in decision making, forecasting, stochastic structure explorations, and other problems. Helping you choose the right Bayesian model, this book focuses on the framework for Bayesian model selection and includes practical examples of model selection criteria.
Download or read book Bayesian Variable Selection in Linear and Non linear Models written by Arnab Kumar Maity and published by . This book was released on 2016 with total page 124 pages. Available in PDF, EPUB and Kindle. Book excerpt: Appropriate feature selection is a fundamental problem in the field of statistics. Models with large number of features or variables require special attention due to the computational complexity of the huge model space. This is generally known as the variable or model selection problem in the field of statistics whereas in machine learning and other literature, this is also known as feature selection, attribute selection or variable subset selection. The method of variable selection is the process of efficiently selecting an optimal subset of relevant variables for use in model construction. The central assumption in this methodology is that the data contain many redundant variable; those which do not provide any significant additional information than the optimally selected subset of variable. Variable selection is widely used in all application areas of data analytics, ranging from optimal selection of genes in large scale micro-array studies, to optimal selection of biomarkers for targeted therapy in cancer genomics to selection of optimal predictors in business analytics. Under the Bayesian approach, the formal way to perform this optimal selection is to select the model with highest posterior probability. Using this fact the problem may be thought as an optimization problem over the model space where the objective function is the posterior probability of model and the maximization is taken place with respect to the models. We propose an efficient method for implementing this optimization and we illustrate its feasibility in high dimensional problems. By means of various simulation studies, this new approach has been shown to be efficient and to outperform other statistical feature selection methods methods namely median probability model and sampling method with frequency based estimators. Theoretical justifications are provided. Applications to logistic regression and survival regression are discussed.
