Bayesian Artificial Intelligence

TLDR: This book would have been more useful had some more detailed discussion on the choices of ranked set size k and cycle number m been added, however, overall I would highly recommend this well-written and reasonably priced book to researchers and practitioners.

Abstract: The book comprises eight chapters of varying length. The inclusion of sections at the end of the main chapters to collect more technical arguments and to give bibliographic notes works well and helps the readers explore in more depth aspects of RSS in which they are interested. Chapter 1 introduces the notion and general procedure of RSS. This very useful chapter will enable readers to quickly enter into the realm of RSS, learn about its historical developments, and identify applications of particular interest. Chapters 2 and 3 discuss balanced RSS. In particular, Chapter 2 focuses on nonparametric RSS, in which no assumption on the underlying distribution of the variable of interest is made. This chapter studies in detail the relative efficiency of RSS with respect to SRS in the estimation of a population mean, a smooth function of means, and population quantiles. The authors also consider the inference procedures, such as the construction of confidence intervals and hypothesis testing. To facilitate the inference procedures based on RSS sample quantiles, they also discuss the kernel method of density estimation. This section is quite interesting. The chapter also presents some robust procedure based on M-estimates with RSS data. Chapter 3 addresses parametric RSS, where the underlying distribution of the variable of interest is assumed to belong to some parametric family (e.g., location-scale family and shape-scale family) of distributions. The authors nicely lay out the theoretical foundation for the parametric RSS via Fisher information. The maximum likelihood estimate (MLE) based on RSS and its relative efficiency with respect to MLE based on SRS are studied, and the best linear unbiased estimate for location family of distributions is dealt with. Chapter 4 studies unbalanced RSS. This chapter first develops the methodology of analyzing RSS data for the inferences on distribution functions and quantiles, as well as general statistical functionals. The optimal designs for the parametric location-scale family and for nonparametric estimation of quantiles are discussed in detail. This chapter also contains methods of Bayes design and adaptive design. Chapter 5 explores classical distribution-free tests in the context of RSS. The authors consider the sign test, signed rank test, and Mann–Whitney– Wilcoxon tests and revisit the issue of the optimal design for distribution-free tests. Readers with a prior knowledge of nonparametric tests at the level of Gibbons and Chakraborti (2003) will find this chapter informative and easy to understand. For readers not familiar with these standard topics, some brief additional explanation and references might have been beneficial for the wider accessibility. Chapter 6 describes RSS with concomitant variables. A multilayer RSS scheme and an adaptive RSS scheme using multiple concomitant variables are developed; the general regression analysis using RSS is discussed; and the design of optimal RSS schemes for regression analysis, on the basis of the concomitant variables, is explored. Chapter 7 illustrates RSS as a data reduction tool for data mining, whereas Chapter 8 exemplifies the practical features of RSS via case studies. The inclusion of this last chapter on case studies with RSS further enhances the value of this monograph for practitioners and applied statisticians. In the development of RSS, the choices of ranked set size k and cycle number m are directly pertinent to practical problems. This book would have been more useful had some more detailed discussion on the choices been added. However, overall I would highly recommend this well-written and reasonably priced book to researchers and practitioners, all of whom are likely to use one or more of the methods it discusses.