Case Studies in Bayesian Statistics (Volume IV).
Ulrich Mansmann · Biometrics · 2004
The present volume consists of 19 articles, presented at the 6th Workshop on Case Studies in Bayesian Statistics held at the Carnegie Mellon University in September 2001. It is divided into two parts: a section of three invited papers is followed by a selection of 16 contributed papers. The majority of case studies emanate from biomedical research. However, the reader will also find studies in psychology, public policy making, environmental pollution, agriculture, and economics. This book is aimed at statisticians to teach them something very important, namely: the beauty of the Bayesian approach, its ability to structure complicated assessments, its guidance to develop appropriate statistical models, and to perform inferences which are based on summaries being properly accounted for relevant uncertainties. Examples show that a properly structured Bayesian approach can objectively produce valid designs and analyses commonly more effective than traditional methods. It is a challenge for the reader to work on these examples by applying competing techniques. Such a critical appraisal of the presented work will show that Bayesian structuring has succeeded in striking an appropriate scientific compromise between modeling and the subject matter problem. The first article by Liu et al. discusses the use of Bayesian methods in genomic research. One specific problem is the identification of short, repetitive patterns in a set of DNA or protein sequences. The authors offer an example in which explicit statistical modeling is the primary tool to reveal subtle patterns within the data. The need to be explicit in the formulation of a statistical model is often criticized because the model captures neither content nor complexity of the subject matter's background. The article is a superb solution how to handle this problem, and how the model building process can be used to come to a deeper understanding of the biological constraints. The second article by Thall et al. deals with complex problems in clinical research in cases of modeling and designing studies. It is an excellent example to be judged against important standards of clinical trials, because the authors brought together many of the difficult issues one can face. They have long-term experience in applying Bayesian methods to clinical reality, and point out convincingly that Bayesian methods have succeeded in striking an appropriate scientific and ethical compromise. The third article by Viele et al. is a case study in model selection. The problem is to determine how two patients compare to controls in their ability to distinguish between similar objects. To exploit the possibility of some underlying systematic structure, probit regression models for ROC analysis are considered with potential predictors. If a large number of potential predictors could be dropped, such a regression would provide improved contrast estimates. A hybrid stepwise-MCMC algorithm together with the BIC is applied to explore the model space and select models. In their discussion of this article Berger and Molina give a thorough report on basic issues of Bayesian model selection: basic tools such as the BIC, the calculation of model posterior probabilities, and their utilization in terms of model selection or model averaging. Gatsonis et al. present many innovative improvements in Bayesian methodology. It is perfectly suited for providing a deep insight to statistical modeling processes. A serious challenger to this book does not yet exist, in spite of the fact that there are some similarities in both topics and presentation in the series on Bayesian Statistics by Bernardo et al. The presentation of papers is excellent, because each contribution gives a detailed subject matter description and a careful discussion on how to derive the statistical model. The careful presentation of problems will help to open the book to a wider readership. The volume demonstrates once again the continued success of the series on Case Studies in Bayesian Statistics. It would be of great advantage to have an easy and direct access to the data and some of the software presented.