Chapman and Hall/CRC
432 pages | 30 B/W Illus.
This is the first book designed to introduce Bayesian inference procedures for stochastic processes. There are clear advantages to the Bayesian approach (including the optimal use of prior information). Initially, the book begins with a brief review of Bayesian inference and uses many examples relevant to the analysis of stochastic processes, including the four major types, namely those with discrete time and discrete state space and continuous time and continuous state space. The elements necessary to understanding stochastic processes are then introduced, followed by chapters devoted to the Bayesian analysis of such processes. It is important that a chapter devoted to the fundamental concepts in stochastic processes is included. Bayesian inference (estimation, testing hypotheses, and prediction) for discrete time Markov chains, for Markov jump processes, for normal processes (e.g. Brownian motion and the Ornstein–Uhlenbeck process), for traditional time series, and, lastly, for point and spatial processes are described in detail. Heavy emphasis is placed on many examples taken from biology and other scientific disciplines. In order analyses of stochastic processes, it will use R and WinBUGS.
Readers with a good background in two areas, probability theory and statistical inference, should be able to master the essential ideas of this book.
"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
1. Introduction to Bayesian Inference for Stochastic Processes
2. Bayesian Analysis
3. Introduction to Stochastic Processes
4. Bayesian Inference for Discrete Markov Chains
5. Examples of Markov Chains in Biology
6. Inferences for Markov Chains in Continuous Time
7. Bayesian Inference: Examples of Continuous-Time Markov Chains
8. Bayesian Inferences for Normal Processes
9. Queues and Time Series