This book provides a unified introduction to a variety of computational algorithms for Bayesian and likelihood inference. In this third edition, I have attempted to expand the treatment of many of the techniques discussed. I have added some new examples, as well as included recent results. Exercises have been added at the end of each chapter. Prerequisites for this book include an understanding of mathematical statistics at the level of Bickel and Doksum (1977), some understanding of the Bayesian approach as in Box and Tiao (1973), some exposure to statistical models as found in McCullagh and NeIder (1989), and for Section 6. 6 some experience with condi tional inference at the level of Cox and Snell (1989). I have chosen not to present proofs of convergence or rates of convergence for the Metropolis algorithm or the Gibbs sampler since these may require substantial background in Markov chain theory that is beyond the scope of this book. However, references to these proofs are given. There has been an explosion of papers in the area of Markov chain Monte Carlo in the past ten years. I have attempted to identify key references-though due to the volatility of the field some work may have been missed."

Drawing upon the recent explosion of research in the field, a diverse group of scholars surveys the latest strategies for solving ecological inference problems, the process of trying to infer individual behavior from aggregate data. The uncertainties and information lost in aggregation make ecological inference one of the most difficult areas of statistical inference, but these inferences are required in many academic fields, as well as by legislatures and the Courts in redistricting, marketing research by business, and policy analysis by governments. This wide-ranging collection of essays offers many fresh and important contributions to the study of ecological inference.

Drawing upon the explosion of research in the field, a diverse group of scholars surveys strategies for solving ecological inference problems, the process of trying to infer individual behavior from aggregate data. The uncertainties and information lost in aggregation make ecological inference one of the most difficult areas of statistical inference, but these inferences are required in many academic fields, as well as by legislatures and the Courts in redistricting, marketing research by business, and policy analysis by governments. This wide-ranging collection of essays, first published in 2004, offers many important contributions to the study of ecological inference.

Exactly what is the state of the art in statistics as we move forward into the 21st century? What promises, what trends does its future hold? Through the reflections of 70 of the world's leading statistical methodologists, researchers, theorists, and practitioners, Statistics in the 21st Century answers those questions.

Originally published in the Journal of the American Statistical Association, this collection of vignettes examines our statistical past, comments on our present, and speculates on our future. Although the coverage is broad and the topics diverse, it reveals the essential intellectual unity of the field as we see the same themes recurring in different contexts. We see how the development of statistics has been driven by the unprecedented and still growing range of applications, by the explosion in computer technology, and by the new types of data that continue to emerge and advance the discipline.

Organized around major areas of application and leading up to vignettes on theory and methods, Statistics in the 21st Century forms a landmark record of the progress and perceived future of the discipline. No student, researcher, or practitioner of statistics should miss this extraordinary opportunity to view the past, present, and future world of statistics through the eyes of its foremost thinkers.