ABSTRACT
This introduction presents an overview of the key concepts discussed in the subsequent chapters of this book. The book introduces the fundamental ideas of computing the posterior distribution via simulation methods. In particular, Monte Carlo Markov chain (MCMC) methods are described and illustrated with WinBUGS for the normal and binomial populations. The book describes the theory that is necessary to understand the probability ideas of stochastic processes beginning with the definition. It deals with a discussion of stochastic calculus, where the derivative and integral of Wiener processes are defined and illustrated with many examples. The book also deals with a presentation of irreducible chains and Bayesian inferences for transient and recurrent states and the estimation of the period of a state. It provides the Poisson process, an important case of continuous-time Markov chains (CTMCs). The book also presents the Bayesian inferences for general CTMC.
