Author: Richard A. Chechile
Publisher: MIT Press
ISBN: 0262044587
Category : Mathematics
Languages : en
Pages : 473
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Book Description
An introduction to the Bayesian approach to statistical inference that demonstrates its superiority to orthodox frequentist statistical analysis. This book offers an introduction to the Bayesian approach to statistical inference, with a focus on nonparametric and distribution-free methods. It covers not only well-developed methods for doing Bayesian statistics but also novel tools that enable Bayesian statistical analyses for cases that previously did not have a full Bayesian solution. The book's premise is that there are fundamental problems with orthodox frequentist statistical analyses that distort the scientific process. Side-by-side comparisons of Bayesian and frequentist methods illustrate the mismatch between the needs of experimental scientists in making inferences from data and the properties of the standard tools of classical statistics. The book first covers elementary probability theory, the binomial model, the multinomial model, and methods for comparing different experimental conditions or groups. It then turns its focus to distribution-free statistics that are based on having ranked data, examining data from experimental studies and rank-based correlative methods. Each chapter includes exercises that help readers achieve a more complete understanding of the material. The book devotes considerable attention not only to the linkage of statistics to practices in experimental science but also to the theoretical foundations of statistics. Frequentist statistical practices often violate their own theoretical premises. The beauty of Bayesian statistics, readers will learn, is that it is an internally coherent system of scientific inference that can be proved from probability theory.
Author: Richard A. Chechile
Publisher: MIT Press
ISBN: 0262360705
Category : Mathematics
Languages : en
Pages : 473
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Book Description
An introduction to the Bayesian approach to statistical inference that demonstrates its superiority to orthodox frequentist statistical analysis. This book offers an introduction to the Bayesian approach to statistical inference, with a focus on nonparametric and distribution-free methods. It covers not only well-developed methods for doing Bayesian statistics but also novel tools that enable Bayesian statistical analyses for cases that previously did not have a full Bayesian solution. The book's premise is that there are fundamental problems with orthodox frequentist statistical analyses that distort the scientific process. Side-by-side comparisons of Bayesian and frequentist methods illustrate the mismatch between the needs of experimental scientists in making inferences from data and the properties of the standard tools of classical statistics.
Author: Andrew Gelman
Publisher: CRC Press
ISBN: 1439840954
Category : Mathematics
Languages : en
Pages : 677
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Book Description
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.
Author: William M. Bolstad
Publisher: John Wiley & Sons
ISBN: 1118593227
Category : Mathematics
Languages : en
Pages : 608
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Book Description
"...this edition is useful and effective in teaching Bayesian inference at both elementary and intermediate levels. It is a well-written book on elementary Bayesian inference, and the material is easily accessible. It is both concise and timely, and provides a good collection of overviews and reviews of important tools used in Bayesian statistical methods." There is a strong upsurge in the use of Bayesian methods in applied statistical analysis, yet most introductory statistics texts only present frequentist methods. Bayesian statistics has many important advantages that students should learn about if they are going into fields where statistics will be used. In this third Edition, four newly-added chapters address topics that reflect the rapid advances in the field of Bayesian statistics. The authors continue to provide a Bayesian treatment of introductory statistical topics, such as scientific data gathering, discrete random variables, robust Bayesian methods, and Bayesian approaches to inference for discrete random variables, binomial proportions, Poisson, and normal means, and simple linear regression. In addition, more advanced topics in the field are presented in four new chapters: Bayesian inference for a normal with unknown mean and variance; Bayesian inference for a Multivariate Normal mean vector; Bayesian inference for the Multiple Linear Regression Model; and Computational Bayesian Statistics including Markov Chain Monte Carlo. The inclusion of these topics will facilitate readers' ability to advance from a minimal understanding of Statistics to the ability to tackle topics in more applied, advanced level books. Minitab macros and R functions are available on the book's related website to assist with chapter exercises. Introduction to Bayesian Statistics, Third Edition also features: Topics including the Joint Likelihood function and inference using independent Jeffreys priors and join conjugate prior The cutting-edge topic of computational Bayesian Statistics in a new chapter, with a unique focus on Markov Chain Monte Carlo methods Exercises throughout the book that have been updated to reflect new applications and the latest software applications Detailed appendices that guide readers through the use of R and Minitab software for Bayesian analysis and Monte Carlo simulations, with all related macros available on the book's website Introduction to Bayesian Statistics, Third Edition is a textbook for upper-undergraduate or first-year graduate level courses on introductory statistics course with a Bayesian emphasis. It can also be used as a reference work for statisticians who require a working knowledge of Bayesian statistics.
Author: Deborah G. Mayo
Publisher: Cambridge University Press
ISBN: 1139485369
Category : Science
Languages : en
Pages : 491
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Book Description
Although both philosophers and scientists are interested in how to obtain reliable knowledge in the face of error, there is a gap between their perspectives that has been an obstacle to progress. By means of a series of exchanges between the editors and leaders from the philosophy of science, statistics and economics, this volume offers a cumulative introduction connecting problems of traditional philosophy of science to problems of inference in statistical and empirical modelling practice. Philosophers of science and scientific practitioners are challenged to reevaluate the assumptions of their own theories - philosophical or methodological. Practitioners may better appreciate the foundational issues around which their questions revolve and thereby become better 'applied philosophers'. Conversely, new avenues emerge for finally solving recalcitrant philosophical problems of induction, explanation and theory testing.
Author: Devinderjit Sivia
Publisher: OUP Oxford
ISBN: 0191546704
Category : Mathematics
Languages : en
Pages : 259
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Book Description
One of the strengths of this book is the author's ability to motivate the use of Bayesian methods through simple yet effective examples. - Katie St. Clair MAA Reviews.
Author: Kenji Doya
Publisher: MIT Press
ISBN: 026204238X
Category : Bayesian statistical decision theory
Languages : en
Pages : 341
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Book Description
Experimental and theoretical neuroscientists use Bayesian approaches to analyze the brain mechanisms of perception, decision-making, and motor control.
Author: Tony Pourmohamad
Publisher: Springer Nature
ISBN: 3030824586
Category : Mathematics
Languages : en
Pages : 113
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Book Description
This book introduces readers to Bayesian optimization, highlighting advances in the field and showcasing its successful applications to computer experiments. R code is available as online supplementary material for most included examples, so that readers can better comprehend and reproduce methods. Compact and accessible, the volume is broken down into four chapters. Chapter 1 introduces the reader to the topic of computer experiments; it includes a variety of examples across many industries. Chapter 2 focuses on the task of surrogate model building and contains a mix of several different surrogate models that are used in the computer modeling and machine learning communities. Chapter 3 introduces the core concepts of Bayesian optimization and discusses unconstrained optimization. Chapter 4 moves on to constrained optimization, and showcases some of the most novel methods found in the field. This will be a useful companion to researchers and practitioners working with computer experiments and computer modeling. Additionally, readers with a background in machine learning but minimal background in computer experiments will find this book an interesting case study of the applicability of Bayesian optimization outside the realm of machine learning.
Author: Todd E. Hudson
Publisher: Cambridge University Press
ISBN: 9781108812900
Category : Psychology
Languages : en
Pages : 500
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Book Description
This textbook bypasses the need for advanced mathematics by providing in-text computer code, allowing students to explore Bayesian data analysis without the calculus background normally considered a prerequisite for this material. Now, students can use the best methods without needing advanced mathematical techniques. This approach goes beyond "frequentist" concepts of p-values and null hypothesis testing, using the full power of modern probability theory to solve real-world problems. The book offers a fully self-contained course, which demonstrates analysis techniques throughout with worked examples crafted specifically for students in the behavioral and neural sciences. The book presents two general algorithms that help students solve the measurement and model selection (also called "hypothesis testing") problems most frequently encountered in real-world applications.
Author: Deborah G. Mayo
Publisher: University of Chicago Press
ISBN: 9780226511979
Category : Mathematics
Languages : en
Pages : 520
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Book Description
Preface1: Learning from Error 2: Ducks, Rabbits, and Normal Science: Recasting the Kuhn's-Eye View of Popper 3: The New Experimentalism and the Bayesian Way 4: Duhem, Kuhn, and Bayes 5: Models of Experimental Inquiry 6: Severe Tests and Methodological Underdetermination7: The Experimental Basis from Which to Test Hypotheses: Brownian Motion8: Severe Tests and Novel Evidence 9: Hunting and Snooping: Understanding the Neyman-Pearson Predesignationist Stance10: Why You Cannot Be Just a Little Bit Bayesian 11: Why Pearson Rejected the Neyman-Pearson (Behavioristic) Philosophy and a Note on Objectivity in Statistics12: Error Statistics and Peircean Error Correction 13: Toward an Error-Statistical Philosophy of Science ReferencesIndex Copyright © Libri GmbH. All rights reserved.
