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.

Finite mixture modelling.- Statistical inference for a finite mixture model with known number of components.- Practical bayesian inference for a finite mixture model with known number of components.- Statistical inference for finite mixture models under model specification uncertainty.- Computational tools for Bayesian inference for finite mixture models under model specification uncertainty.- Finite mixture models with normal components.- Data analysis based on finite mixtures.- Finite mixtures of regression models.- Finite mixture models with non-normal components.- Finite Markov mixture modelling.- Statistical inference for Markov switching models.- Non-linear time series analysis based on Markov switching models.- Switching state space models.