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WAIC and WBIC with R Stan

WAIC and WBIC with R Stan
Author: Joe Suzuki
Publisher: Springer Nature
Total Pages: 241
Release: 2023-11-25
Genre: Computers
ISBN: 9819938384
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Master the art of machine learning and data science by diving into the essence of mathematical logic with this comprehensive textbook. This book focuses on the widely applicable information criterion (WAIC), also described as the Watanabe-Akaike information criterion, and the widely applicable Bayesian information criterion (WBIC), also described as the Watanabe Bayesian information criterion. This book expertly guides you through relevant mathematical problems while also providing hands-on experience with programming in R and Stan. Whether you’re a data scientist looking to refine your model selection process or a researcher who wants to explore the latest developments in Bayesian statistics, this accessible guide will give you a firm grasp of Watanabe Bayesian Theory. The key features of this indispensable book include: A clear and self-contained writing style, ensuring ease of understanding for readers at various levels of expertise. 100 carefully selected exercises accompanied by solutions in the main text, enabling readers to effectively gauge their progress and comprehension. A comprehensive guide to Sumio Watanabe’s groundbreaking Bayes theory, demystifying a subject once considered too challenging even for seasoned statisticians. Detailed source programs and Stan codes that will enhance readers’ grasp of the mathematical concepts presented. A streamlined approach to algebraic geometry topics in Chapter 6, making Bayes theory more accessible and less daunting. Embark on your machine learning and data science journey with this essential textbook and unlock the full potential of WAIC and WBIC today!

WAIC and WBIC with Python Stan

WAIC and WBIC with Python Stan
Author: Joe Suzuki
Publisher: Springer Nature
Total Pages: 249
Release: 2024-01-09
Genre: Technology & Engineering
ISBN: 9819938414
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Download WAIC and WBIC with Python Stan Book in PDF, ePub and Kindle

Master the art of machine learning and data science by diving into the essence of mathematical logic with this comprehensive textbook. This book focuses on the widely applicable information criterion (WAIC), also described as the Watanabe-Akaike information criterion, and the widely applicable Bayesian information criterion (WBIC), also described as the Watanabe Bayesian information criterion. The book expertly guides you through relevant mathematical problems while also providing hands-on experience with programming in Python and Stan. Whether you’re a data scientist looking to refine your model selection process or a researcher who wants to explore the latest developments in Bayesian statistics, this accessible guide will give you a firm grasp of Watanabe Bayesian Theory. The key features of this indispensable book include: A clear and self-contained writing style, ensuring ease of understanding for readers at various levels of expertise. 100 carefully selected exercises accompanied by solutions in the main text, enabling readers to effectively gauge their progress and comprehension. A comprehensive guide to Sumio Watanabe’s groundbreaking Bayes theory, demystifying a subject once considered too challenging even for seasoned statisticians. Detailed source programs and Stan codes that will enhance readers’ grasp of the mathematical concepts presented. A streamlined approach to algebraic geometry topics in Chapter 6, making Bayes theory more accessible and less daunting. Embark on your machine learning and data science journey with this essential textbook and unlock the full potential of WAIC and WBIC today!

Bayesian Statistical Modeling with Stan, R, and Python

Bayesian Statistical Modeling with Stan, R, and Python
Author: Kentaro Matsuura
Publisher: Springer Nature
Total Pages: 395
Release: 2023-01-24
Genre: Computers
ISBN: 9811947554
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This book provides a highly practical introduction to Bayesian statistical modeling with Stan, which has become the most popular probabilistic programming language. The book is divided into four parts. The first part reviews the theoretical background of modeling and Bayesian inference and presents a modeling workflow that makes modeling more engineering than art. The second part discusses the use of Stan, CmdStanR, and CmdStanPy from the very beginning to basic regression analyses. The third part then introduces a number of probability distributions, nonlinear models, and hierarchical (multilevel) models, which are essential to mastering statistical modeling. It also describes a wide range of frequently used modeling techniques, such as censoring, outliers, missing data, speed-up, and parameter constraints, and discusses how to lead convergence of MCMC. Lastly, the fourth part examines advanced topics for real-world data: longitudinal data analysis, state space models, spatial data analysis, Gaussian processes, Bayesian optimization, dimensionality reduction, model selection, and information criteria, demonstrating that Stan can solve any one of these problems in as little as 30 lines. Using numerous easy-to-understand examples, the book explains key concepts, which continue to be useful when using future versions of Stan and when using other statistical modeling tools. The examples do not require domain knowledge and can be generalized to many fields. The book presents full explanations of code and math formulas, enabling readers to extend models for their own problems. All the code and data are on GitHub.

Advancements in Bayesian Methods and Implementations

Advancements in Bayesian Methods and Implementations
Author:
Publisher: Academic Press
Total Pages: 322
Release: 2022-10-06
Genre: Mathematics
ISBN: 0323952690
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Advancements in Bayesian Methods and Implementation, Volume 47 in the Handbook of Statistics series, highlights new advances in the field, with this new volume presenting interesting chapters on a variety of timely topics, including Fisher Information, Cramer-Rao and Bayesian Paradigm, Compound beta binomial distribution functions, MCMC for GLMMS, Signal Processing and Bayesian, Mathematical theory of Bayesian statistics where all models are wrong, Machine Learning and Bayesian, Non-parametric Bayes, Bayesian testing, and Data Analysis with humans, Variational inference or Functional horseshoe, Generalized Bayes. Provides the authority and expertise of leading contributors from an international board of authors Presents the latest release in the Handbook of Statistics series Updated release includes the latest information on Advancements in Bayesian Methods and Implementation

Bayesian Hierarchical Models

Bayesian Hierarchical Models
Author: Peter D. Congdon
Publisher: CRC Press
Total Pages: 580
Release: 2019-09-16
Genre: Mathematics
ISBN: 1498785913
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An intermediate-level treatment of Bayesian hierarchical models and their applications, this book demonstrates the advantages of a Bayesian approach to data sets involving inferences for collections of related units or variables, and in methods where parameters can be treated as random collections. Through illustrative data analysis and attention to statistical computing, this book facilitates practical implementation of Bayesian hierarchical methods. The new edition is a revision of the book Applied Bayesian Hierarchical Methods. It maintains a focus on applied modelling and data analysis, but now using entirely R-based Bayesian computing options. It has been updated with a new chapter on regression for causal effects, and one on computing options and strategies. This latter chapter is particularly important, due to recent advances in Bayesian computing and estimation, including the development of rjags and rstan. It also features updates throughout with new examples. The examples exploit and illustrate the broader advantages of the R computing environment, while allowing readers to explore alternative likelihood assumptions, regression structures, and assumptions on prior densities. Features: Provides a comprehensive and accessible overview of applied Bayesian hierarchical modelling Includes many real data examples to illustrate different modelling topics R code (based on rjags, jagsUI, R2OpenBUGS, and rstan) is integrated into the book, emphasizing implementation Software options and coding principles are introduced in new chapter on computing Programs and data sets available on the book’s website

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.

Mathematical Theory of Bayesian Statistics

Mathematical Theory of Bayesian Statistics
Author: Sumio Watanabe
Publisher: CRC Press
Total Pages: 331
Release: 2018-04-27
Genre: Mathematics
ISBN: 148223808X
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Mathematical Theory of Bayesian Statistics introduces the mathematical foundation of Bayesian inference which is well-known to be more accurate in many real-world problems than the maximum likelihood method. Recent research has uncovered several mathematical laws in Bayesian statistics, by which both the generalization loss and the marginal likelihood are estimated even if the posterior distribution cannot be approximated by any normal distribution. Features Explains Bayesian inference not subjectively but objectively. Provides a mathematical framework for conventional Bayesian theorems. Introduces and proves new theorems. Cross validation and information criteria of Bayesian statistics are studied from the mathematical point of view. Illustrates applications to several statistical problems, for example, model selection, hyperparameter optimization, and hypothesis tests. This book provides basic introductions for students, researchers, and users of Bayesian statistics, as well as applied mathematicians. Author Sumio Watanabe is a professor of Department of Mathematical and Computing Science at Tokyo Institute of Technology. He studies the relationship between algebraic geometry and mathematical statistics.

The Oxford Handbook of Computational and Mathematical Psychology

The Oxford Handbook of Computational and Mathematical Psychology
Author: Jerome R. Busemeyer
Publisher:
Total Pages: 425
Release: 2015
Genre: Psychology
ISBN: 0199957991
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This Oxford Handbook offers a comprehensive and authoritative review of important developments in computational and mathematical psychology. With chapters written by leading scientists across a variety of subdisciplines, it examines the field's influence on related research areas such as cognitive psychology, developmental psychology, clinical psychology, and neuroscience. The Handbook emphasizes examples and applications of the latest research, and will appeal to readers possessing various levels of modeling experience. The Oxford Handbook of Computational and mathematical Psychology covers the key developments in elementary cognitive mechanisms (signal detection, information processing, reinforcement learning), basic cognitive skills (perceptual judgment, categorization, episodic memory), higher-level cognition (Bayesian cognition, decision making, semantic memory, shape perception), modeling tools (Bayesian estimation and other new model comparison methods), and emerging new directions in computation and mathematical psychology (neurocognitive modeling, applications to clinical psychology, quantum cognition). The Handbook would make an ideal graduate-level textbook for courses in computational and mathematical psychology. Readers ranging from advanced undergraduates to experienced faculty members and researchers in virtually any area of psychology--including cognitive science and related social and behavioral sciences such as consumer behavior and communication--will find the text useful.

Model Selection and Model Averaging

Model Selection and Model Averaging
Author: Gerda Claeskens
Publisher:
Total Pages: 312
Release: 2008-07-28
Genre: Mathematics
ISBN: 9780521852258
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First book to synthesize the research and practice from the active field of model selection.

Algebraic Geometry and Statistical Learning Theory

Algebraic Geometry and Statistical Learning Theory
Author: Sumio Watanabe
Publisher: Cambridge University Press
Total Pages: 295
Release: 2009-08-13
Genre: Computers
ISBN: 0521864674
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Sure to be influential, Watanabe's book lays the foundations for the use of algebraic geometry in statistical learning theory. Many models/machines are singular: mixture models, neural networks, HMMs, Bayesian networks, stochastic context-free grammars are major examples. The theory achieved here underpins accurate estimation techniques in the presence of singularities.