Jean-Michel Marin - Bayesian Essentials with R

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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 users (or instructors) 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 Rankins 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 () used the same skeleton as in Bayesian Core and as we restarted from their version.

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 parameter 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 distributions, 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 corresponding model, and the statistical analysis is provided with detailed comments. 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.

We thus expect readers to place themselves in a realistic situation to conduct this analysis in life-threatening (or job-threatening) situations. As detailed 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!

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 () 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 programs 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 ().

Besides Robert (), 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 perspective, and thus do not assume prior knowledge of Monte Carlo methods, detailed references are Robert and Casella ().

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. ).

Presentation often matters almost as much as content towards a better understanding, 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 LaTeX, as follows.