贝叶斯数据分析第二版：R、JAGS与Stan教程

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"Doing Bayesian Data Analysis 第二版" 是一本由 John K. Kruschke 编写的教程，专注于介绍贝叶斯数据分析的方法，并结合R、JAGS和Stan等工具进行实践教学。本书深入探讨了贝叶斯统计学的核心概念，它是统计学的一个重要分支，特别是在数据科学和机器学习领域中应用广泛。贝叶斯方法允许我们直接对参数的概率分布进行建模，而不仅仅是观测数据的概率。这种思维方式使得在处理不确定性时更加灵活，并且能够随着新数据的引入不断更新我们的信念。第二版的内容可能包括了自第一版以来的最新发展和改进，例如在软件工具（如Stan）上的更新，这是一款用于贝叶斯推断的现代马尔科夫链蒙特卡洛（MCMC）模拟软件。R和JAGS是另外两个常用的贝叶斯分析工具，R是一种强大的统计编程语言，JAGS（Just Another Gibbs Sampler）则是一个实现MCMC采样的程序，便于用户编写贝叶斯模型。书中可能涵盖了以下关键知识点： 1. 贝叶斯定理基础：解释了贝叶斯定理的数学形式和直观含义，它是贝叶斯统计学的核心。 2. 贝叶斯模型构建：如何根据问题背景建立适当的先验分布和似然函数，形成完整的贝叶斯模型。 3. 后验推断：通过MCMC方法（如JAGS和Stan）进行后验概率分布的模拟，提取模型参数的估计。 4. 数据可视化：如何用图形展示数据和模型结果，帮助理解模型性能和数据特征。 5. 贝叶斯决策：利用后验分布进行决策，如区间估计、假设检验和预测。 6. 贝叶斯模型比较：介绍贝叶斯因子和 DIC（Deviance Information Criterion）等方法，用于比较不同模型的优劣。 7. 应用案例：可能包含多个实际领域的应用示例，如心理学、生物学、社会科学等，以展示贝叶斯分析在解决实际问题中的应用。此外，本书还可能强调了贝叶斯方法的哲学和解释性优势，以及它如何在不确定性分析中提供更全面的理解。书中可能还包括了如何寻求和获得版权许可的信息，以及关于出版商权限政策的详细说明，确保读者在引用和分享内容时遵循正确的规定。 "Doing Bayesian Data Analysis 第二版" 是一个全面的指南，适合想要掌握贝叶斯分析理论和实践的读者，无论他们是初学者还是有经验的研究者。通过这本书，读者将有机会深入理解贝叶斯统计学，并学会使用现代工具进行有效的数据分析。

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6 Doing Bayesian Data Analysis

1.3. WHAT’S NEW IN THE SECOND EDITION?

The basic progression of topics remains the same as the rst edition, but all the details have

been changed, from cover to cover. The book and its programs have been completely

rewritten. Here are just a few highlights of the changes:

• There are all new programs in JAGS and Stan. The new programs are designed to be

much easier to use than the scripts in the rst edition. In particular, there are now

compact high-level scripts that make it easy to run the programs on your own data.

This new programming was a major undertaking by itself.

• The introductory Chapter 2, regarding the basic ideas of how Bayesian inference re-

allocates credibility across possibilities, is completely rewritten and greatly expanded.

• There are completely new chapters on the programming languages R (Chapter 3),

JAGS (Chapter 8), and Stan (Chapter 14). The lengthy new chapter on R includes

explanations of data les and structures such as lists and data frames, along with

several utility functions. (It also has a new poem that I am particularly pleased

with.) The new chapter on JAGS includes explanation of the RunJAGS package

which executes JAGS on parallel computer cores. The new chapter on Stan

provides a novel explanation of the concepts of Hamiltonian Monte Carlo. The

chapteronStanalsoexplainsconceptual dierences in program ow between Stan

and JAGS.

• Chapter 5 on Bayes’ rule is greatly revised, with a new emphasis on how Bayes’ rule

re-allocates credibility across parameter values from prior to posterior. The material

on model comparison has been removed from all the early chapters and integrated

into a compact presentation in Chapter 10.

• What were two separate chapters on the Metropolis algorithm and Gibbs sampling

have been consolidated into a single chapter on MCMC methods (as Chapter 7).

• There is extensive new material on MCMC convergence diagnostics in Chapters 7

and 8. There are explanations of autocorrelation and eective sample size. There is

also exploration of the stability of the estimates of the highest density interval (HDI)

limits. New computer programs display the diagnostics, as well.

• Chapter 9 on hierarchical models includes extensive new and unique material on the

crucial concept of shrinkage, along with new examples.

• All the material on model comparison, which was spread across various chapters in

the rst edition, in now consolidated into a single focused chapter (Chapter 10)that

emphasizes its conceptualization as a case of hierarchical modeling.

• Chapter 11 on null hypothesis signicance testing is extensively revised. It has new

material for introducing the concept of sampling distribution. It has new illustrations

of sampling distributions for various stopping rules, and for multiple tests.

• Chapter 12, regarding Bayesian approaches to null value assessment, has new material

about the region of practical equivalence (ROPE), new examples of accepting the

What’s in This Book (Read This First!) 7

null value by Bayes factors, and new explanation of the Bayes factor in terms of the

Savage-Dickey method.

• Chapter 13, regarding statistical power and sample size, has an extensive new section

on sequential testing, and recommends making the research goal be precision of

estimation instead of rejecting or accepting a particular value.

• Chapter 15, which introduces the generalized linear model, is fully revised, with

more complete tables showing combinations of predicted and predictor variable

types.

• Chapter 16, regarding estimation of means, now includes extensive discussion of

comparing two groups, along with explicit estimation of eect size.

• Chapter 17, regarding regression on a single metric predictor, now includes extensive

examples of robust regression in JAGS and Stan. New examples of hierarchical

regression, including quadratic trend, graphically illustrate shrinkage in estimates of

individual slopes and curvatures. The use of weighted data is also illustrated.

• Chapter 18, on multiple linear regression, includes a new section on Bayesian variable

selection, in which various candidate predictors are probabilistically included in the

regression model.

• Chapter 19, on one-factor ANOVA-like analysis, has all new examples, including

a completely worked out example analogous to analysis of covariance (ANCOVA),

and a new example involving heterogeneous variances.

• Chapter 20, on multi-factor ANOVA-like analysis, has all new examples, including

a completely worked out example of a split-plot design that involves a combination

of a within-subjects factor and a between-subjects factor.

• Chapter 21, on logistic regression, is expanded to include examples of robust logistic

regression, and examples with nominal predictors.

• There is a completely new chapter (Chapter 22) on multinomial logistic regression.

This chapter lls in a case of the generalized linear model (namely, a nominal

predicted variable) that was missing from the rst edition.

• Chapter 23, regarding ordinal data, is greatly expanded. New examples illustrate

single-group and two-group analyses, and demonstrate how interpretations dier

from treating ordinal data as if they were metric.

• There is a new section (25.4) that explains how to model censored data in JAGS.

• Many exercises are new or revised.

Oh, and did I mention that the cover is dierent? The correspondence of the doggies

to Bayes’ rule is now made explicit: The folded ears of the posterior doggie are a

compromise between the perky ears and oppy ears of the likelihood and prior doggies.

The marginal likelihood is not usually computed in MCMC methods, so the doggie in

the denominator gets sleepy with nothing much to do. I hope that what’s between the

covers of this book is as friendly and engaging as the doggies on the cover.

8 Doing Bayesian Data Analysis

1.4. GIMME FEEDBACK (BE POLITE)

I have worked thousands of hours on this book, and I want to make it better. If

you have suggestions regarding any aspect of this book, please do email me:

johnkruschke@gmail.com. Let me know if you’ve spotted egregious errors or innocuous

infelicities, typo’s or thoughto’s. Let me know if you have a suggestion for how to clarify

something. Especially let me know if you have a good example that would make things

more interesting or relevant. I’m interested in complete raw data from research that

is interesting to a broad audience, and which can be used with acknowledgement but

without fee. Let me know also if you have more elegant programming code than what

I’ve cobbled together. The outside margins of these pages are intentionally made wide

so that you have room to scribble your ridicule and epithets before re-phrasing them

into kindly stated suggestions in your email to me. Rhyming couplets are especially

appreciated.

Since the publication of the rst edition I have received hundreds of email messages

from readers. I have replied to many, but I am truly embarrassed by the fact that I have

not been able to reply to all of them, and some have gone unacknowledged. If I don’t

respond to your email in a timely manner, it is likely that your message got buried under

the avalanche of subsequent emails. You are welcome to send a follow-up email to try

to provoke a response from me. In any case, if your email is lengthy or has attachments

or asks about a problem in some complicated analysis you are trying, chances are that I’ll

react by saying to myself, “That’s very interesting, but I’ll have to think about it when

I have more time and reply later.” Then, no matter what time it is, later never comes.

Whether I am able to reply or not, I appreciate all your messages.

1.5. THANK YOU!

I would like to thank the many readers who posted reviews and recommendations

of the rst edition on sites such as Amazon.com, Goodreads.com,blogs,andsocial

networking sites. At the time of this writing, there were 46 reviews on Amazon.com,

6atAmazon.co.uk (United Kingdom), 2 at Amazon.ca (Canada), and 1 at Amazon.cn

(China). There were 4 reviews at Goodreads.com plus many ratings. Numerous people

have reviewed or recommended the book on their blogs. Many people have given a

“shout out” to the book on social networking sites. I am very grateful to all of you for

taking the time to write reviews, and pleased that your reviews have generally been very

positive! I hope that this second edition elicits continued impulse to post new reviews

about the second edition, as the revisions have been a huge eort to make the book even

better.

I also thank the authors of professional reviews of rst edition, including

Andrews (2011), Barry (2011), Colvin (2013), Ding (2011), Fellingham (2012),

Goldstein (2011), Smithson (2011), and Vanpaemel and Tuerlinckx (2012). My apologies

What’s in This Book (Read This First!) 9

to any reviewers whom I have missed; please let me know. I think it is valuable to raise

the visibility of Bayesian methods in professional circles, and I am very grateful to all

these authors for taking the time and eort to compose reviews.

Several people have written computer programs that extended or improved programs

related to the rst edition of the book. In particular, the programs for Bayesian estimation

of two groups (“BEST”; Kruschke, 2013a,cf.Chapter 16 of this book) were re-

packaged in R by Mike Meredith, in JavaScript by Rasmus Bååth, and in Python by

Andrew Straw. For links to their work, see http://www.indiana.edu/~kruschke/BEST/.

Systems for creating hierarchical diagrams, akin to Figure 9.13 (p. 252), were created

by Rasmus Bååth for LibreOce and R, and by Tinu Schneider for L

X and TikZ.

For links to their work, see http://doingbayesiandataanalysis.blogspot.com/2013/10/

diagrams-for-hierarchical-models-new.html. Thank you all for your extensive eorts

and contributions to making Bayesian methods accessible to a wider audience.

Many colleagues have organized workshops or courses for Doing Bayesian

Data Analysis. A list of workshops appears at https://sites.google.com/site/

doingbayesiandataanalysis/. At each of those workshops many more people were

involved than I can possibly mention by name here, but they include William Jacoby

and Dieter Burrell at the Interuniversity Consortium for Political and Social Research

Summer Program at the University of Michigan; William Pridemore, James Russell,

James Walker, and Je DeWitt at the Indiana University Social Science Research

Commons; Hans-Joachim Knopf at the University of St. Gallen Summer School in

Empirical Research Methods, Switzerland; Hans Olav Melberg at the University of

Oslo, Norway; Mark Nawrot and colleagues at North Dakota State University; Ulf

Ahlstrom and colleagues at the Federal Aviation Administration Human Factors Lab,

New Jersey; Tim Pleskac and colleagues at Michigan State University; John Curtin at the

University of Wisconsin, Madison; Michael Roberts and colleagues including Chester

Fornari, Bryan Hanson, and Humberto Barreto at DePauw University; Jan Andrews,

Ming-Wen An, and colleagues at Vassar College; Kelly Goedert and colleagues at Seton

Hall University; Gregory Francis and Zygmunt Pizlo at Purdue University; Boicho

Kokinov and colleagues at the New Bulgarian University, Soa; Nathalie Rothert and

the workshop program committees at the Association for Psychological Science; Duncan

Brumby and the tutorials program committees of the Cognitive Science Society; Andrew

Delamater at the Eastern Psychological Association (and thanks to James McClelland

for introducing my talk there); William Merriman at the Midwestern Psychological

Association; Xiangen Hu and Michael Jones at the Society for Computers in Psychology.

My apologies to those whom I have inadvertently left o this list. I thank you all for

your time and eort. I hope that the workshops and courses genuinely facilitate doing

Bayesian data analysis by the attendees.

The book has been used by a number of instructors in their courses, and a few of

them have sent me notes of their experiences. In particular, Jerey Witmer at Oberlin

10 Doing Bayesian Data Analysis

College sent extensive comments. Adrian Brasoveanu at the University of California,

Santa Cruz, and John Miyamoto at the University of Washington, also conveyed or

posted information about their courses. The review by Vanpaemel and Tuerlinckx (2012)

reported experiences from classroom use. Thanks to all the instructors who have boldly

tried the rst edition in their courses. I hope that the second edition is even more useful

for the classroom and self study.

Over recent years there have been many students in my classes who have made

insightful comments and suggestions. Some of these include Young Ahn, Gregory Cox,

Junyi Dai, Josh de Lueew, Andrew Jahn, Arash Khodadadi, and Torrin Liddell. Thanks

to Torrin Liddell also for help with checking the proofs of the book. I thank Anne

Standish for researching and recommending a discussion forum for the book’s blog.

I am grateful to the many people who have left thoughtful comments at the blog and

discussion forum. Thanks also to several careful readers who reported errors in the rst

edition. And thanks to Jacob Hodes for being so interested in Bayesian analysis that he

would travel to a conference to talk with me about it.

The rst edition of this book was 6 years in the making, and many colleagues and

students provided helpful comments during that period. The most extensive comments

came from Luiz Pessoa, Michael Kalish, Jerome Busemeyer, and Adam Krawitz; thank

you all! Particular sections were insightfully improved by helpful comments from Michael

Erickson, Robert Nosofsky, Geo Iverson, and James L. (Jay) McClelland. Various

parts of the book beneted indirectly from communications with Woojae Kim, Charles

Liu, Eric-Jan Wagenmakers, and Jerey Rouder. Pointers to data sets were oered by

Teresa Treat and Michael Trosset, among others. Very welcome supportive feedback

was provided by Michael D. Lee, and also by Adele Diederich. A Bayesian-supportive

working environment was provided by many colleagues including Richard Shirin,

Jerome Busemeyer, Peter Todd, James Townsend, Robert Nosofsky, and Luiz Pessoa.

Other department colleagues have been very supportive of integrating Bayesian statistics

into the curriculum, including Linda Smith and Amy Holtzworth-Munroe. Various

teaching assistants have provided helpful comments; in particular I especially thank Noah

Silbert and Thomas Wisdom for their excellent assistance. As this book has evolved over

the years, suggestions have been contributed by numerous students, including Aaron

Albin, Thomas Smith, Sean Matthews, Thomas Parr, Kenji Yoshida, Bryan Bergert, and

perhaps dozens of others who have contributed insightful questions or comments that

helped me tune the presentation in the book.

Gratefully acknowledged are the creators of the software R (RCoreTeam, 2013),

RStudio (RStudio, 2013), JAGS (Plummer, 2003, 2012), RunJAGS (Denwood, 2013),

BUGS (Lunn, Thomas, Best, & Spiegelhalter, 2000; A. Thomas, O’Hara, Ligges, &

Sturtz, 2006), and Stan (Stan Development Team, 2012). Also gratefully acknowledged

are the creators of the typesetting software L

X(http://www.latex-project.org/)

and MikTeX (http://miktex.org/), the editor TeXmaker (http://www.xm1math.net/

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