The central theme of this book concerns Feynman-Kac path distributions, interacting particle systems, and genealogical tree based models. This re- cent theory has been stimulated from different directions including biology, physics, probability, and statistics, as well as from many branches in engi- neering science, such as signal processing, telecommunications, and network analysis. Over the last decade, this subject has matured in ways that make it more complete and beautiful to learn and to use. The objective of this book is to provide a detailed and self-contained discussion on these...