Runs and Scans With Applications

TLDR: This text is a revision of the book by Arnold, Costillo, and Sarabia (1992), but with much more depth than the original, and comprises a lively overview of conditionally speciŽ ed models of the conditional distribution.

Abstract: of the conditional distribution speciŽ cations. Chapters 8 and 10 extend these methods from two to more dimensions. Chapter 9 investigates estimation in conditionally speciŽ ed models. Chapter 11 considers models speciŽ ed by conditioning on events speciŽ ed by one variable exceeding a value rather than equaling a value, and Chapter 12 considers models for extreme-value data. Chapter 13 extends conditional speciŽ cation to Bayesian analysis. Chapter 14 describes the related simultaneous-equation models, and Chapter 15 ties in some additional topics. An appendix describes methods of simulation from conditionally speciŽ ed models. Chapters 1–4, plus Chapters 9 and 13, comprise a lively overview of conditionally speciŽ ed models. The remainder of the text constitutes a detailed catalog of results speciŽ c to different conditional distributions. Although this catalog is certainly of value, the reader desiring a briefer and less detailed introduction to the subject might skip the remainder at Ž rst reading. This text is a revision of the book by Arnold, Costillo, and Sarabia (1992). The current version is of similar breadth, but with much more depth than the original. The text is clearly written and accessible with relatively few mathematical prerequisites. I found surprisingly few typographical errors; the authors are to be congratulated for this. In a few cases, regularity conditions for results are not given in full. Generally, this causes little confusion, although something does appear to be missing in the statement of Aczél’s key theorem (Theorem 1.3). Fortunately, most of the results in the sequel are derived from corollaries to this theorem, and the corollaries are stated more precisely. I noted few gaps in the material covered. The only area that I thought was insufŽ ciently represented was application to Markov chain Monte Carlo. Conditional speciŽ cation is particularly important in Gibbs sampling. I believe that many practitioners would beneŽ t from a discussion of the issues involved in these sampling schemes. Each chapter contains numerous exercises. These exercises appear to be at an appropriate level for a graduate course in statistics, and appear to provide appropriate reinforcement for the material in the preceding chapters.