The book aims to introduce Bayesian inference methods for stochastic processes. The Bayesian approach has advantages compared to non-Bayesian, among which is the optimal use of prior information via data from previous similar experiments. Examples from biology, economics, and astronomy reinforce the basic concepts of the subject. R a "Readers with a good background in the two areas, probability theory and statistical inference, should be able to master the essential ideas of this book."~ Ludwig Paditz, Dresden". . .All three important types of Bayesian inferences such are estimation, hypothesis testing and forecasting are considered and many examples are worked through using R and WinBUGS codes. . . It will prove useful for students and scientists who want to learn about Bayesian analysis in stochastic processes." ~Miroslav M. Ristic, Stat Papers