实用贝叶斯统计：R语言版

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"Bayesian Essentials with R" 是一本专注于实践和计算贝叶斯统计学的书籍，主要使用通用示例来介绍最常见的模型。这本书适用于大约13-15周的教学课程，适合每周三小时讲座的研究生课程。内容涵盖贝叶斯方法、R语言以及相关的算法，目标读者是需要使用贝叶斯统计分析实验或数据集的研究生。在贝叶斯统计学中，关键概念是概率的主观解释，即先验概率与观测数据结合形成后验概率。这本书通过R语言提供实践指导，帮助读者理解和应用这一理论。R语言是一种广泛用于统计分析的编程语言，具有丰富的包和工具，特别适合进行贝叶斯分析。书中涉及的贝叶斯方法包括贝叶斯公式，它允许我们将先验知识（即对参数的初步理解）与观测数据相结合，更新我们的信念以得到后验分布。此外，还可能探讨了马尔科夫链蒙特卡洛（MCMC）算法，如Gibbs采样和Metropolis-Hastings算法，这些是解决复杂贝叶斯模型中计算后验分布的常用技术。标签中的“bayes Algorithm”指的是贝叶斯算法，这是一类基于贝叶斯定理的统计决策规则，常用于分类、预测和估计。例如，在机器学习中，朴素贝叶斯分类器是一种简单但有效的算法，它假设特征之间相互独立，并利用贝叶斯定理进行预测。本书第二版可能更新了内容，以反映近年来贝叶斯统计学和R语言在应用上的最新发展，包括新的贝叶斯软件包和更高效的数据处理方法。此外，对于初学者来说，书中可能包含了大量的实例和练习，以帮助他们掌握贝叶斯方法，并通过实际编程练习来巩固理论知识。 “Bayesian Essentials with R”是一本面向实践的教材，旨在让读者掌握贝叶斯统计学的核心原理，并能运用R语言解决实际问题。书中的案例和练习将有助于读者建立起对贝叶斯分析的深入理解和应用能力，不论是在学术研究还是在数据分析工作中都将大有裨益。

User’s Manual

The bare essentials, in other words.

—Ian Rankin, Tooth & Nai l.—

Roadmap

The Roadmap is a section that will start each chapter by providing a commented

table of contents. It also usually contains indications on the purpose of the chapter.

For instance, in this initial chapter, we explain the typographical notations that

we adopted to distinguish between the diﬀerent semantic levels of the course.

We also try to detail how one should work with this book and how one could

best beneﬁt from this work. This chapter is to be understood as a user’s (or

instructor’s) manual that details our pedagogical choices. It also seems the right

place to introduce the programming language R, which we use to illustrate all the

introduced concepts.

In each chapter, both Ian Rankin’s quotation and the ﬁgure on top of the title

page are (at best) vaguely related to the topic of the chapter, and one should not

waste too much time pondering their implications and multiple meanings. The

similarity with the introductory chapter of Introducing Monte Carlo Methods with

R is not coincidental, as Robert and Casella (2009) used the same skeleton as in

Bayesian Core and as we restarted from their version.

J.-M. Marin and C.P. Robert, Bayesian Essentials with R, Springer Texts

in Statistics, DOI 10.1007/978-1-4614-8687-9

21User’sManual

1.1 Expectations

The key word associated with this book is modeling, that is, the ability to

build up a probabilistic interpretation of an observed phenomenon and the

“story” that goes with it. The “grand scheme” is to get anyone involved in

analyzing data to process a dataset within this coherent methodology. This

means picking a parameterized probability distribution, denoted by f

,and

extracting information about (shortened in “estimating”) the unknown pa-

rameter θ of this probability distribution in order to provide a convincing

interpretation of the reasons that led to the phenomenon at the basis of the

dataset (and/or to be able to draw predictions about upcoming phenomena

of the same nature). Before starting the description of the probability distri-

butions, we want to impose on the reader the essential feature that a model

is an interpretation of a real phenomenon that ﬁts its characteristics up to

some degree of approximation rather than an explanation that would require

the model to be “true”. In short, there is no such thing as a “true model”,

even though some models are more appropriate than others!

In this book, we chose to describe the use of “classical” probability models

for several reasons: First, it is often better to start a trip on well-traveled

paths because they are less likely to give rise to unexpected surprises and

misinterpretations. Second, they can serve as references for more advanced

modelings: Quantities that appear in both simple and advanced modelings

should get comparable estimators or, if not, the more advanced modeling

should account for that diﬀerence. At last, the deliberate choice of an artiﬁcial

model should give a clearer meaning to the motto that all models are false

in that it illustrates the fact that a model is not necessarily justiﬁed by the

theory beyond the modeled phenomenon but that its corresponding inference

can nonetheless be exploited as if it were a true model. By the end of the book,

the reader should also be in a position to assess the relevance of a particular

model for a given dataset.

Working with this book should not appear as a major endeavor: The

datasets are described along with the methods that are relevant for the cor-

responding model, and the statistical analysis is provided with detailed com-

ments. The R code that backs up this analysis is included and commented

throughout the text. If there is a diﬃculty with this scheme, it actually starts

at this point: Once the reader has seen the analysis, it should be possible

for her or him to repeat this analysis or a similar analysis with no further

assistance. Even better, the reader should try to read as little as possible of

the analysis proposed in this book and on the opposite hand should try to

conduct the following stage of the analysis before reading the proposed (but

not unique) solution. The ultimate lesson here is that there are indeed many

ways to analyze a dataset and to propose modeling scenarios and inferential

schemes. It is beyond the purpose of this book to provide all of those analyses,

and the reader (or the instructor) is supposed to look for alternatives on her

or his own.

1.2 Prerequisites and Further Reading 3

We thus expect readers to place themselves in a realistic situation to con-

duct this analysis in life-threatening (or job-threatening) situations. As de-

tailed in the preface, the course was originally intended for students in the

last year of study toward a professional degree, and it seems quite reasonable

to insist that they face similar situations before entering their incoming job!

1.2 Prerequisites and Further Reading

This being a textbook about statistical modeling, the students are supposed to

have a background in both probability and statistics, at the level, for instance,

of Casella and Berger (2001). In particular, a knowledge of standard sampling

distributions and their properties is desirable. Lab work in the spirit of Nolan

and Speed (2000) is also a plus. (One should read in particular their Ap-

pendix A on “How to write lab reports?”) Further knowledge about Bayesian

statistics is not a requirement, although using Robert (2007)orHoﬀ (2009)

as further references would bring a better insight into the topics treated here.

Similarly, we expect students to be able to understand the bits of R pro-

grams provided in the analysis, mostly because the syntax of R is very simple.

We include an introduction to this language in this chapter and we refer to

Dalgaard (2002) for a deeper entry and also to Venables and Ripley (2002).

Besides Robert (2007), the philosophy of which is obviously reﬂected in this

book, other reference books pertaining to applied Bayesian statistics include

Gelman et al. (2013), Carlin and Louis (1996), and Congdon (2001, 2003).

More speciﬁc books that cover parts of the topics of a given chapter are

mentioned (with moderation) in the corresponding chapter, but we can quote

here the relevant books of Holmes et al. (2002), Pole et al. (1994), and Gill

(2002). We want to stress that the citations are limited for eﬃciency purposes:

There is no extensive coverage of the literature as in, e.g., Robert (2007)or

Gelman et al. (2013), because the prime purpose of the book is to provide

a working methodology, for which incremental improvements and historical

perspectives are not directly relevant.

While we also cover simulation-based techniques in a self-contained per-

spective, and thus do not assume prior knowledge of Monte Carlo methods,

detailed references are Robert and Casella (2004, 2009)andChen et al. (2000).

Although we had at some stage intended to write a new chapter about

hierarchical Bayes analysis, we ended up not including this chapter in the

current edition and this for several reasons. First, we were not completely

convinced about the relevance of a speciﬁc hierarchical chapter, given that

the hierarchical theme is somehow transversal to the book and pops in the

mixture (Chap. 6), dynamic (Chap. 7) and image (Chap. 8) chapters. Second,

the revision took already too long and creating a brand new chapter did not

sound a manageable goal. Third, managing realistic hierarchical models meant

relying on codes written in JAGS and BUGS, which clashed with the philoso-

phy of backing the whole book on R codes. This was subsumed by the recent

and highly relevant publication of The BUGS Book (Lunn et al., 2012)andby

the incoming new edition of Bayesian Data Analysis (Gelman et al., 2013).

41User’sManual

1.3 Styles and Fonts

Presentation often matters almost as much as content towards a better und-

erstanding, and this is particularly true for data analyzes, since they aim

to reproduce a realistic situation of a consultancy job where the consultant

must report to a customer the results of an analysis. An equilibrated use

of graphics, tables, itemized comments, and short paragraphs is, for instance,

quite important for providing an analysis that stresses the diﬀerent conclusions

of the work, as well as the points that are yet unclear and those that could

be expanded.

In particular, because this book is doing several things at once (that is,

to introduce theoretical and computational concepts and to implement them

in realistic situations), it needs to diﬀerentiate between the purposes and the

levels of the parts of the text so that it is as obvious as possible to the reader.

To this eﬀect, we take advantage of the many possibilities of modern computer

editing, and in particular of L

X, as follows.

First, a minimal amount of theoretical bases is required for dealing with

the model introduced in each chapter, either for Bayesian statistics or for

Monte Carlo theory. This aspect of the material is necessarily part of the

main text, but it is also kept to a minimum—just enough for the book to

be self-contained—and therefore occasional references to more detailed books

such as Robert (2007)andRobert and Casella (2004) are necessary. These

sections need be well-understood before handling the following applications

or realistic cases. This book is primarily intended for those without a strong

background in the theory of Bayesian statistics or computational methods,

and “theoretical” sections are essential for them, hence the need to keep those

sections within the main text.

Statistics is as much about data processing as about mathemat-

ical and probabilistic modeling. To enforce this principle, we center

each chapter around one or two speciﬁc realistic datasets that are de-

scribed early enough in the chapter to be used extensively through-

out the chapter. These datasets are available on the book’s Website

(http://www.ceremade.dauphine.fr/~xian/BCS/) and are part of the cor-

responding R package bayess,asnormaldata, capturedata, and so on, the

name being chosen in reference to the case/chapter heading. (Some of these

datasets are already available as datasets in the R language.) In particu-

lar, we explain the “how and why” of the corresponding dataset in a separate

paragraph in this shaded format. This style is also used for illustrating theoret-

ical developments for the corresponding dataset and for speciﬁc computations

related to this dataset. For typographical convenience, large graphs and tables

may appear outside these sections, in subsequent pages, but are obviously

mentioned and identiﬁed within them.

1.4 An Introduction to R 5

Example 1.1. There may also be a need for detailed examples in addition

to the main datasets, although we strived to keep them to a minimum and

only for very speciﬁc issues where the reference dataset was not appropriate.

They follow this numbered style, the sideways triangle indicating the end of

the example. 

 The last style used in the book is the warning, represented by a lightning 

symbol in the margin: This entry is intended to signal major warnings about

things that can (and do) go wrong “otherwise”; that is, if the warning is not

taken into account. Needless to say, these paragraphs must be given the utmost

attention!

A diverse collection of exercises is proposed at the end of each chapter, with

solutions to all those exercises freely available on Springer-Verlag webpage.

1.4 An Introduction to R

This section attempts at introducing R to newcomers in a few pages and,

as such, it should not be considered as a proper introduction to R. Entire

volumes, such as the monumental RBookby Crawley (2007), and the intro-

duction by Dalgaard (2002), are dedicated to the practice of this language,

and therefore additional eﬀorts (besides reading this chapter) will be required

from the reader to suﬃciently master the language.

However, before discour-

aging anyone, let us comfort you with the fact that:

(a) The syntax of R is simple and logical enough to quickly allow for a basic

understanding of simple R programs, as should become obvious in a few

paragraphs.

(b) The best, and in a sense the only, way to learn R is through trial-and-

error on simple and then more complex examples. Reading the book with

a computer available nearby is therefore the best way of implementing

this recommendation.

In particular, the embedded help commands help() and help.search() are

very good starting points to gather information about a speciﬁc function or

a general issue, even though more detailed manuals are available both locally

and on-line. Note that help.start() opens a Web browser linked to the local

manual pages.

One may ﬁrst wonder why we support using R as the programming int-

erface for this introduction to Monte Carlo methods, since there exist other

If you decide to skip this chapter, be sure to at least print the handy RRef-

erence Card available at http://cran.r-project.org/doc/contrib/Short-refcard.pdf that

summarizes, in four pages, the major commands of R.

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