使用R和BUGS的贝叶斯数据分析入门教程

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1.3. THE ORGANIZATION OF THIS BOOK

• Section 2.3 introduces R.

• Chapter 4 explains Bayes’ rule.

• Chapter 7 explains Markov chain Monte Carlo methods.

• Section 7.4 introduces BUGS.

• Chapter 9 explains hierarchical models.

• Chapter 13 explains varieties of power analysis.

• Chapter 14 overviews the generalized linear model and various types of data

analyses that can be conducted.

• Section 23.1 summarizes how to report a Bayesian data analysis.

Figure 1.1: Essential sections of the book.

1.3 The organization of this book

This book has three major parts. The ﬁrst part covers foundations: The basic ideas of

probabilities, models, Bayesian reasoning, and programming in R.

The second main part covers all the crucial ideas of modern Bayesian data analy-

sis while using the simplest possible type of data, namely dichotomous data such as

agree/disagree, remember/forget, male/female, etc. Because the data are so simplistic, the

focus can be on the Bayesian techniques. In particular, the modern techniques of “Markov

chain Monte Carlo” (MCMC) are explained thoroughly and intuitively. And, the ideas of

hierarchical models are thoroughly explored. Because the models are kept simple in this

part of the book, intuitions about the meaning of hierarchical dependencies can be devel-

oped in glorious graphic detail. This second part of the book also explores methods for

planning how much data will need to be collected to achieve a desired degree of precision

in the conclusions. This is called “sample size planning” or “power analysis”.

The third main part of the book applies the Bayesian methods to realistic data. The

applications are organized around the type of data being analyzed, and the type of measure-

ments that are used to explain or predict the data. For example, suppose you are trying to

predict college grade point average (GPA) from high school Scholastic Aptitude Test (SAT)

score. In this case the data to be predicted, the GPAs, are values on a metric scale, and the

predictor, the SAT scores, are also values on a metric scale. Suppose, on the other hand,

that you are trying to predict college GPA from gender. In this case the predictor is a di-

chotomous value, namely, male vs. female. Diﬀerent types of measurement scales require

diﬀerent types of mathematical models, but otherwise the underlying concepts are always

the same. Table 14.1 (p. 312) shows various combinations of measurement scales and their

corresponding models that are explored in detail in the third part of this book.

1.3.1 What are the essential chapters?

The foundations established in the ﬁrst part of the book, and the Bayesian ideas of the

second part, are important to understand. The applications to particular types of data, in the

third part, can be more selectively perused as needed. Within those parts, however, there

CHAPTER 1. THIS BOOK’S ORGANIZATION: READ ME FIRST!

are some chapters that are essential:

• Chapter 4 explains Bayes’ rule.

• Chapter 7 explains Markov chain Monte Carlo methods.

• Chapter 9 explains hierarchical models.

• Chapter 14 overviews the generalized linear model and various types of data analyses

that can be conducted.

As an emphasis of the book is doing Bayesian data analysis, it is also essential to learn the

programming languages R and BUGS:

• Section 2.3 introduces R.

• Section 7.4 introduces BUGS.

Finally, the ultimate purpose of data analysis is to convince other people that their beliefs

should be altered by the data. The results need to be communicated to a skeptical audience,

and therefore additional essential reading is

• Section 23.1 summarizes how to report a Bayesian data analysis.

Another important topic is the planning of research, as opposed to the analysis of data

after they have been collected. Bayesian techniques are especially nicely suited for estimat-

ing the probability that speciﬁed research goals can be achieved as a function of the sample

size for the research. Therefore, although it might not be essential on a ﬁrst reading, it is

essential eventually to read

• Chapter 13 regarding power analysis.

Figure 1.1 puts these recommendations in a convenient reference box, re-arranged into the

order of presentation in the book.

1.3.2 Where’s the equivalent of traditional test X in this book?

Because many readers will be coming to this book after having already been exposed to tra-

ditional 20th-century statistics that emphasize null hypothesis signiﬁcance testing (NHST),

this book will provide Bayesian approaches to the usual topics in NHST textbooks. Ta-

ble 1.1 lists various tests covered by standard introductory statistics textbooks, along with

their Bayesian analogues. If you have been previously contaminated by NHST, but want to

know how to do an analogous Bayesian analysis, Table 1.1 may be useful.

A superﬁcial conclusion from Table 1.1 might be, “Gee, the table shows that traditional

statistical tests do something analogous to Bayesian analysis in every case, therefore it’s

pointless to bother with Bayesian analysis.” Such a conclusion would be wrong. First,

traditional NHST has deep problems, some of which are discussed in Chapter 11. Second,

Bayesian analysis yields richer and more informative inferences than NHST, as will be

shown in numerous examples in throughout the book.

1.4. GIMME FEEDBACK (BE POLITE)

Table 1.1: Bayesian analogues of 20th century null hypothesis signiﬁcance tests.

Traditional Analysis Name Bayesian Analogue

t-test for a single mean Chapter 15

t-test for two independent groups Chapter 18 (Section 18.3)

Simple linear regression Chapter 16

Multiple linear regression Chapter 17

Oneway ANOVA Chapter 18

Multi-factor ANOVA Chapter 19

Logistic regression Chapter 20

Ordinal regression Chapter 21

Binomial test Chapters 5–9, 20

Chi-square test (contingency table) Chapter 22

Power analysis (sample size planning) Chapter 13

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 e-mail 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 also 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 cob-

bled 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 e-mail to me. Rhyming couplets are especially appreciated. If I don’t

respond to your e-mail in a timely manner, it is only because I can’t keep up with the deluge

of fan mail, not because I don’t appreciate your input. Thank you in advance!

1.5 Acknowledgments

This book has been six years in the making, and many colleagues and students have pro-

vided helpful comments. The most extensive comments have come from Drs. Luiz Pessoa,

Mike Kalish, Jerry Busemeyer, and Adam Krawitz; thank you all! Particular sections were

insightfully improved by helpful comments from Drs. Michael Erickson, Robert Nosofsky,

and Geoﬀ Iverson. Various parts of the book beneﬁtted indirectly from communications

with Drs. Woojae Kim, Charles Liu, Eric-Jan Wagenmakers and Jeﬀrey Rouder. Leads

to data sets were oﬀered by Drs. Teresa Treat and Michael Trosset, among others. Very

welcome supportive feedback was provided by Dr. Michael Lee, and also by Dr. Adele

Diederich. A Bayesian-supportive working environment was provided by many colleagues

including Drs. Richard Shiﬀrin, 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 Drs. Linda Smith and Amy

Holtzworth-Munroe. Various teaching assistants have provided helpful comments; in par-

ticular I especially thank Drs. Noah Silbert and Thomas Wisdom for their excellent as-

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