The past decade has seen powerful new computational tools for modeling which combine a Bayesian approach with recent Monte simulation techniques based on Markov chains. This book reviews these techniques and covers advances in the field. This is the first book to offer a systematic presentation of the Bayesian perspective of finite mixture modelling. Focusing mainly on Bayesian inference, the author reviews several frequentist techniques, especially selecting the number of components of a finite mixture model, and discusses some of their shortcomings compared to the Bayesian approach. The book is designed to show how finite mixture and Markov switching models are formulated, what structures they imply on the data, their potential uses, and how they are estimated. Presenting its concepts informally without sacrificing mathematical correctness, the book will serve a wide readership including statisticians as well as biologists, economists, engineers, financial and market researchers.
Rezensionen / Stimmen
From the reviews:
"At first glance, the numerous equations and formulas may seem to be daunting for psychologists with limited statistical background; however, the descriptions and explanations of the various models are actually quite reader friendly (more so than many advanced statistical textbooks). The author has done an excellent job of inviting newcomers to enter the world of mixture models, more impressively, the author did so without sacrificing mathematical and statistical rigor. Mixture models are appealing in many applications in social and psychological studies. This book not only offers a gentle introduction to mixture models but also provides more in depth coverage for those who look beyond the surface. I believe that psychologists who are interested in related models (e.g., latent class models, latent Markov models, and latent class regression models) will benefit greatly from this book. I highly recommend this book to all psychologists who are interested in mixture models." (Hsiu-Ting Yu, PSYCHOMETRIKA-VOL. 74, NO. 3, 559-560 SEPTEMBER 2009)
"The book is impressive in its mathematical and formal correctness, in generality and in details....it would be helfpful as an additional reference among a wider range of available textbooks in the area. [I]t will find many friends among experts and newcomers to the world of mixture models." (Atanu Biswas, Biometrics, Issue 63, September 2007)
"Finite mixture distributions are important for many models. Therefore they constitute a very active field of research. This book gives an up to date overview over the various models of this kind. . The aim of this book is to impart the finite mixture and Markov switching approach to statistical modeling to a wide-ranging community. . For the frequentists, it offers a good opportunity to explore the advantages of the Bayesian approach in the context of mixing models." (Gheorghe Pitis, Zentralblatt MATH, Vol. 1108(10), 2007)
"Readership: Statisticians, biologists, economists, engineers, financial agents, market researchers, medical researchers or any other frequent user of statistical models. The first nine chapters of the book are concerned with static mixture models, and the last four with Markov switching models. . especially valuable for students, serving to demonstrate how different statistical techniques, which superficially appear to be unrelated, are in fact part of an integrated whole. This book struck me as being particularly clearly written - it is a pleasure to read." (David J. Hand, International Statistical Review, Vol. 75 (2), 2007)
"The book is excellent, giving a most readable overview of the topic of finite mixtures, aimed at a broad readership . . Students will like the text because of the pedagogical writing style; researchers will definitely welcome the broad treatment of the subject. Both will benefit from the extensive and up-to-date bibliography . as well as the well-organized index. No doubt, this book is a valuable addition to the field of statistics and will surely find its rightful place in many a statistician's library." (Valerie Chavez-Demoulin, Journal of the American Statistical Association, Vol. 104 (485), March, 2009)
