Preface to
Bayesian Computation Using Minitab
By Jim Albert

WHY WAS THIS BOOK AND SOFTWARE WRITTEN?

This book describes the use of a package of Minitab programs for implementing Bayesian methods for a wide range of elementary statistical inference problems. The motivation for this project was my interest in using Bayesian ideas in teaching statistical inference at an elementary level. I have had difficulties in teaching the frequentist notion of inference and believe that the basic tenets of statistical inference may be better communicated using the Bayesian paradigm. I was encouraged to develop Bayesian teaching materials with the publication of Don Berry's text
Statistics: A Bayesian Perspective. This book presents the basic inferential methods for proportions and means using Bayes' rule with a discussion of many real-life applications of these methods. One aspect of the Berry's text that I found attractive is its focus on discrete models. In teaching Bayes' rule, I believe it is essential that the student get some experience specifying subjective probabilities, and prior probability distributions can be easier to assess when there are only a few values of the parameter of interest.

Although Bayes' rule is simple conceptually, it can be cumbersome to implement. For example, it can be tedious and time consuming to compute posterior probabilities for two proportions when there are a large number of discrete models. Without the use of the computer, the instructor is forced in this situation to only discuss very simple models where only a couple of values of each proportion are used. This setting is not very realistic, and doesn't motivate the more general setting where continuous models for the proportions are used. Thus, a general goal of these Minitab programs is to remove the computational burden in implementing Bayes' rule.

WHAT TOPICS ARE COVERED IN THIS BOOK?

This text describes and illustrates computer programs to perform Bayesian calculations for the inference topics in the standard one semester introductory statistics course. Chapter 3 uses a program 'bayes' to introduce Bayesian inference when the unknown model is categorical. Chapters 4-8 describe the use of Minitab programs to address basic inference problems for one and two proportions, one and two normal means, and simple linear regression and contingency tables. These programs should help the instructor focus on the conceptual aspects of Bayesian inference. For example, in the case of learning about a proportion with discrete models, the instructor can focus his/her discussion on the specification of prior information and the summarization and interpretation of the posterior distribution rather than on the computation details.

Bayes' rule provides a simple mechanism to help us learn from data, and Bayesian methods can be used in a broad range of applications. In addition to the basic inference topics described above, this text also provides general algorithms and corresponding Minitab programs that can be used to implement Bayes' rule. Chapter 9 gives a general program for learning about a parameter when the prior is concentrated on a finite collection of values. This program is used to illustrate inference problems outside of the realm of the usual binomial and normal problems. In particular, inference about Poisson, exponential, uniform, and hypergeometric populations is illustrated.

Simulation methods are demonstrated in this text for a range of problems. In Chapter 4, simulation is used to update probabilities about a proportion when the prior distribution is in the form of a histogram. The sampling-importance-resampling (sir) algorithm is used in Chapter 5 in estimating two proportions when the proportions are believed exchangeable. Chapter 10 and 11 implement simple algorithms for simulating from arbitrary prior/likelihood combinations. One nice feature of simulation methods is that a simulated sample of values from the posterior distribution is obtained and data analysis techniques can be used to display and summarize this simulated sample.

HOW CAN THIS BOOK BE USED?

This book can be used in a number of ways. It would be a suitable companion software text for those instructors who plan to introduce some Bayesian inferential methods at an elementary level. It would also be suitable for instructors who wish to introduce Bayesian ideas and computing briefly in a statistical inference class for undergraduate or graduate students. The chapters of the book are independently presented, so an instructor can select out particular chapters and programs that are of interest. An instructor teaching probability may enjoy the programs that simulate games of chance in Chapter 2. The programs that implement basic summarization methods in Chapter 11 may be useful for a graduate class that is learning about Bayesian computation.

Each chapter of this book presents a particular inference method or computing strategy. After outlining the method, the computer programs are illustrated for a particular example. Further illustrations of the use of the programs are contained in the exercises. Due to space limitations, the book provides a limited explanation of Bayesian inference. See Berry (1995), Antleman (1995) or Lee (1988) for basic expositions of Bayesian inference. However, it should be easy for an instructor to understand the methods and software after some exposure with Bayesian methods.

WHY MINITAB?

Finally, why are these programs written in Minitab? I decided to use Minitab since it is the most popular statistics package in teaching statistics. Many instructors are familiar with the basic syntax of Minitab, so it will not be difficult for them to learn how to use these new Bayesian commands. The programs are written using the 'exec' type of Minitab macros and the higher resolution graphics that are available in Release 10 of Minitab and the Student Edition of Minitab of Windows. Included in this disk is a second version of the programs which use the older style of character graphics. These programs work essentially the same as the ones described in the text and will run on Release 7 or later of Minitab.