Bayesian inference for stochastic processes
Broemeling, Lyle D.
creator
text
Florida
CRC Press
2018
monographic
| 0
xv, 432p. With index
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 Ornsteinâ€“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.
Features:
Uses the Bayesian approach to make statistical Inferences about stochastic processes
The R package is used to simulate realizations from different types of processes
Based on realizations from stochastic processes, the WinBUGS package will provide the Bayesian analysis (estimation, testing hypotheses, and prediction) for the unknown parameters of stochastic processes
To illustrate the Bayesian inference, many examples taken from biology, economics, and astronomy will reinforce the basic concepts of the subject
A practical approach is implemented by considering realistic examples of interest to the scientific community
WinBUGS and R code are provided in the text, allowing the reader to easily verify the results of the inferential procedures found in the many examples of the book
Readers with a good background in two areas, probability theory and statistical inference, should be able to master the essential ideas of this book.
https://www.crcpress.com/Bayesian-Inference-for-Stochastic-Processes/Broemeling/p/book/9781138196131
Table of Contents
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
Stochastic processes
Bayesian statistical decision theory
Probabilities
519.22 B7B2
9781138196131
190429