This introductory chapter begins by noting how the three key ideas in this volume — hierarchical models, Markov chain Monte Carlo, and sequential Monte Carlo — that have revolutionized Bayesian statistics are in large measure due to the contributions of Adrian Smith. These concepts are now ubiquitous wherever Bayesian models are used. In this volume, broad topic areas have been selected where these ideas come into play in a significant manner. While these topics are by no means exhaustive, they serve to illustrate the impact of Adrian's research on Bayesian statistics in the last four decades or so. An overview of the twelve parts of the book is then presented.
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