Bayesian Model Selection and Statistical Modeling
Bayesian Model Selection and Statistical Modeling

Author: Tomohiro Ando

Publisher: CRC Press

Published: 2010-05-27

Total Pages: 300

ISBN-13: 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.

Information Criteria and Statistical Modeling
Information Criteria and Statistical Modeling

Author: Sadanori Konishi

Publisher: Springer Science & Business Media

Published: 2008

Total Pages: 282

ISBN-13: 0387718869

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Statistical modeling is a critical tool in scientific research. This book provides comprehensive explanations of the concepts and philosophy of statistical modeling, together with a wide range of practical and numerical examples. The authors expect this work to be of great value not just to statisticians but also to researchers and practitioners in various fields of research such as information science, computer science, engineering, bioinformatics, economics, marketing and environmental science. It’s a crucial area of study, as statistical models are used to understand phenomena with uncertainty and to determine the structure of complex systems. They’re also used to control such systems, as well as to make reliable predictions in various natural and social science fields.

Bayesian Statistical Modelling
Bayesian Statistical Modelling

Author: P. Congdon

Publisher:

Published: 2001-05-02

Total Pages: 568

ISBN-13:

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Bayesian methods draw upon previous research findings and combine them with sample data to analyse problems and modify existing hypotheses. The calculations are often extremely complex, with many only now possible due to recent advances in computing technology. Bayesian methods have as a result gained wider acceptance, and are applied in many scientific disciplines, including applied statistics, public health research, medical science, the social sciences and economics. Bayesian Statistical Modelling presents an accessible overview of modelling applications from a Bayesian perspective. * Provides an integrated presentation of theory, examples and computer algorithms * Examines model fitting in practice using Bayesian principles * Features a comprehensive range of methodologies and modelling techniques * Covers recent innovations in bayesian modelling, including Markov Chain Monte Carlo methods * Includes extensive applications to health and social sciences * Features a comprehensive collection of nearly 200 worked examples * Data examples and computer code in WinBUGS are available via ftp Whilst providing a general overview of Bayesian modelling, the author places emphasis on the principles of prior selection, model identification and interpretation of findings, in a range of modelling innovations, focussing on their implementation with real data, with advice as to appropriate computing choices and strategies. Researchers in applied statistics, medical science, public health and the social sciences will benefit greatly from the examples and applications featured. The book will also appeal to graduate students of applied statistics, data analysis and Bayesian methods, and will provide a good reference source for both researchers and students.

Bayesian Models
Bayesian Models

Author: N. Thompson Hobbs

Publisher: Princeton University Press

Published: 2015-08-04

Total Pages: 315

ISBN-13: 1400866553

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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 probability and develops a step-by-step sequence of connected ideas, including basic distribution theory, network diagrams, hierarchical models, Markov chain Monte Carlo, and inference from single and multiple models. This unique book places less emphasis on computer coding, favoring instead a concise presentation of the mathematical statistics needed to understand how and why Bayesian analysis works. It also explains how to write out properly formulated hierarchical Bayesian models and use them in computing, research papers, and proposals. This primer enables ecologists to understand the statistical principles behind Bayesian modeling and apply them to research, teaching, policy, and management. Presents the mathematical and statistical foundations of Bayesian modeling in language accessible to non-statisticians Covers basic distribution theory, network diagrams, hierarchical models, Markov chain Monte Carlo, and more Deemphasizes computer coding in favor of basic principles Explains how to write out properly factored statistical expressions representing Bayesian models

Bayesian Data Analysis, Third Edition
Bayesian Data Analysis, Third Edition

Author: Andrew Gelman

Publisher: CRC Press

Published: 2013-11-01

Total Pages: 677

ISBN-13: 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.

Case Studies in Bayesian Statistical Modelling and Analysis
Case Studies in Bayesian Statistical Modelling and Analysis

Author: Clair L. Alston

Publisher: John Wiley & Sons

Published: 2012-12-17

Total Pages: 0

ISBN-13: 9781119941828

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Provides an accessible foundation to Bayesian analysis using real world models This book aims to present an introduction to Bayesian modelling and computation, by considering real case studies drawn from diverse fields spanning ecology, health, genetics and finance. Each chapter comprises a description of the problem, the corresponding model, the computational method, results and inferences as well as the issues that arise in the implementation of these approaches. Case Studies in Bayesian Statistical Modelling and Analysis: Illustrates how to do Bayesian analysis in a clear and concise manner using real-world problems. Each chapter focuses on a real-world problem and describes the way in which the problem may be analysed using Bayesian methods. Features approaches that can be used in a wide area of application, such as, health, the environment, genetics, information science, medicine, biology, industry and remote sensing. Case Studies in Bayesian Statistical Modelling and Analysis is aimed at statisticians, researchers and practitioners who have some expertise in statistical modelling and analysis, and some understanding of the basics of Bayesian statistics, but little experience in its application. Graduate students of statistics and biostatistics will also find this book beneficial.

Statistical Modeling for Naturalists
Statistical Modeling for Naturalists

Author: Pedro F. Quintana Ascencio

Publisher: Cambridge Scholars Publishing

Published: 2022-01-31

Total Pages: 210

ISBN-13: 1527579530

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This book will allow naturalists, nature stewards, and graduate students to appreciate and comprehend basic statistical concepts as a bridge to more complex themes relevant to their daily work. Although there are excellent sources on more specialized analytical topics relevant to naturalists, this introductory book makes a connection with the experience and needs of field practitioners. It uses aspects of the natural history of the Florida scrub relevant for conservation and management as examples of analytical issues pertinent to the naturalist in a broader context. Each chapter identifies important ecological questions and then provides approaches to evaluate data, focusing on the analytical decision-making process. The book guides the reader on frequently overlooked aspects such as the understanding of model assumptions, alternative model specifications, model output interpretation, and model limitations.

Statistical Rethinking
Statistical Rethinking

Author: Richard McElreath

Publisher: CRC Press

Published: 2018-01-03

Total Pages: 488

ISBN-13: 1315362619

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Statistical Rethinking: A Bayesian Course with Examples in R and Stan builds readers’ knowledge of and confidence in statistical modeling. Reflecting the need for even minor programming in today’s model-based statistics, the book pushes readers to perform step-by-step calculations that are usually automated. This unique computational approach ensures that readers understand enough of the details to make reasonable choices and interpretations in their own modeling work. The text presents generalized linear multilevel models from a Bayesian perspective, relying on a simple logical interpretation of Bayesian probability and maximum entropy. It covers from the basics of regression to multilevel models. The author also discusses measurement error, missing data, and Gaussian process models for spatial and network autocorrelation. By using complete R code examples throughout, this book provides a practical foundation for performing statistical inference. Designed for both PhD students and seasoned professionals in the natural and social sciences, it prepares them for more advanced or specialized statistical modeling. Web Resource The book is accompanied by an R package (rethinking) that is available on the author’s website and GitHub. The two core functions (map and map2stan) of this package allow a variety of statistical models to be constructed from standard model formulas.

Bayesian Data Analysis in Ecology Using Linear Models with R, BUGS, and Stan
Bayesian Data Analysis in Ecology Using Linear Models with R, BUGS, and Stan

Author: Franzi Korner-Nievergelt

Publisher: Academic Press

Published: 2015-04-04

Total Pages: 329

ISBN-13: 0128016787

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Bayesian Data Analysis in Ecology Using Linear Models with R, BUGS, and STAN examines the Bayesian and frequentist methods of conducting data analyses. The book provides the theoretical background in an easy-to-understand approach, encouraging readers to examine the processes that generated their data. Including discussions of model selection, model checking, and multi-model inference, the book also uses effect plots that allow a natural interpretation of data. Bayesian Data Analysis in Ecology Using Linear Models with R, BUGS, and STAN introduces Bayesian software, using R for the simple modes, and flexible Bayesian software (BUGS and Stan) for the more complicated ones. Guiding the ready from easy toward more complex (real) data analyses ina step-by-step manner, the book presents problems and solutions—including all R codes—that are most often applicable to other data and questions, making it an invaluable resource for analyzing a variety of data types. - Introduces Bayesian data analysis, allowing users to obtain uncertainty measurements easily for any derived parameter of interest - Written in a step-by-step approach that allows for eased understanding by non-statisticians - Includes a companion website containing R-code to help users conduct Bayesian data analyses on their own data - All example data as well as additional functions are provided in the R-package blmeco