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Bayesian Model Selection and Statistical Modeling

Bayesian Model Selection and Statistical Modeling
Author: Tomohiro Ando
Publisher: CRC Press
Total Pages: 300
Release: 2010-05-27
Genre: Mathematics
ISBN: 9781439836156

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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.


Model Averaging

Model Averaging
Author: David Fletcher
Publisher: Springer
Total Pages: 107
Release: 2019-01-17
Genre: Mathematics
ISBN: 3662585413

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This book provides a concise and accessible overview of model averaging, with a focus on applications. Model averaging is a common means of allowing for model uncertainty when analysing data, and has been used in a wide range of application areas, such as ecology, econometrics, meteorology and pharmacology. The book presents an overview of the methods developed in this area, illustrating many of them with examples from the life sciences involving real-world data. It also includes an extensive list of references and suggestions for further research. Further, it clearly demonstrates the links between the methods developed in statistics, econometrics and machine learning, as well as the connection between the Bayesian and frequentist approaches to model averaging. The book appeals to statisticians and scientists interested in what methods are available, how they differ and what is known about their properties. It is assumed that readers are familiar with the basic concepts of statistical theory and modelling, including probability, likelihood and generalized linear models.


Bayesian Model Averaging, Learning and Model Selection

Bayesian Model Averaging, Learning and Model Selection
Author:
Publisher:
Total Pages: 0
Release: 2012
Genre: Bayesian statistical decision theory
ISBN:

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Agents have two forecasting models, one consistent with the unique rational expectations equilibrium, another that assumes a time-varying parameter structure. When agents use Bayesian updating to choose between models in a self-referential system, we find that learning dynamics lead to selection of one of the two models. However, there are parameter regions for which the non-rational forecasting model is selected in the long-run. A key structural parameter governing outcomes measures the degree of expectations feedback in Muth's model of price determination.


Calibrated Bayes Factor and Bayesian Model Averaging

Calibrated Bayes Factor and Bayesian Model Averaging
Author: Jiayin Zheng
Publisher:
Total Pages: 150
Release: 2018
Genre: Bayesian statistical decision theory
ISBN:

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There is a rich history of work on model selection and averaging in the statistics literature. The Bayesian paradigm provides an approach to model selection which successfully overcomes the drawbacks for which frequentist hypothesis testing has been criticized. Most commonly, Bayesian model selection methods are based on the Bayes factor. Additionally, the Bayes factor has applications outside the realm of model selection, such as model averaging. In a formal sense, as a supplement to the prior odds, the Bayes factor produces the posterior odds for a pair of models. These posterior odds can be translated to posterior probabilities and yields a full posterior distribution that assigns a probability to each model as well as a distribution over the parameters for each model. Then the Bayesian model averaging provides better prediction by making inferences based on a weighted average over all of the models considered.


Bayesian Theory and Applications

Bayesian Theory and Applications
Author: Paul Damien
Publisher: Oxford University Press
Total Pages: 717
Release: 2013-01-24
Genre: Mathematics
ISBN: 0199695601

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This volume guides the reader along a statistical journey that begins with the basic structure of Bayesian theory, and then provides details on most of the past and present advances in this field.


Statistical Foundations, Reasoning and Inference

Statistical Foundations, Reasoning and Inference
Author: Göran Kauermann
Publisher: Springer Nature
Total Pages: 361
Release: 2021-09-30
Genre: Mathematics
ISBN: 3030698270

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This textbook provides a comprehensive introduction to statistical principles, concepts and methods that are essential in modern statistics and data science. The topics covered include likelihood-based inference, Bayesian statistics, regression, statistical tests and the quantification of uncertainty. Moreover, the book addresses statistical ideas that are useful in modern data analytics, including bootstrapping, modeling of multivariate distributions, missing data analysis, causality as well as principles of experimental design. The textbook includes sufficient material for a two-semester course and is intended for master’s students in data science, statistics and computer science with a rudimentary grasp of probability theory. It will also be useful for data science practitioners who want to strengthen their statistics skills.


Bayesian Averaging, Prediction and Nonnested Model Selection

Bayesian Averaging, Prediction and Nonnested Model Selection
Author: Han Hong
Publisher:
Total Pages: 29
Release: 2008
Genre: Bayesian statistical decision theory
ISBN:

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This paper studies the asymptotic relationship between Bayesian model averaging and post-selection frequentist predictors in both nested and nonnested models. We derive conditions under which their difference is of a smaller order of magnitude than the inverse of the square root of the sample size in large samples. This result depends crucially on the relation between posterior odds and frequentist model selection criteria. Weak conditions are given under which consistent model selection is feasible, regardless of whether models are nested or nonnested and regardless of whether models are correctly specified or not, in the sense that they select the best model with the least number of parameters with probability converging to 1. Under these conditions, Bayesian posterior odds and BICs are consistent for selecting among nested models, but are not consistent for selecting among nonnested models.


Bayesian Averaging, Prediction and Nonnested Model Selection

Bayesian Averaging, Prediction and Nonnested Model Selection
Author: Han Hong
Publisher:
Total Pages: 31
Release: 2013
Genre:
ISBN:

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This paper studies the asymptotic relationship between Bayesian model averaging and post-selection frequentist predictors in both nested and nonnested models. We derive conditions under which their difference is of a smaller order of magnitude than the inverse of the square root of the sample size in large samples. This result depends crucially on the relation between posterior odds and frequentist model selection criteria. Weak conditions are given under which consistent model selection is feasible, regardless of whether models are nested or nonnested and regardless of whether models are correctly specified or not, in the sense that they select the best model with the least number of parameters with probability converging to 1. Under these conditions, Bayesian posterior odds and BICs are consistent for selecting among nested models, but are not consistent for selecting among nonnested models.


Bayesian Data Analysis, Third Edition

Bayesian Data Analysis, Third Edition
Author: Andrew Gelman
Publisher: CRC Press
Total Pages: 677
Release: 2013-11-01
Genre: Mathematics
ISBN: 1439840954

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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.