Bayesian Analysis of Stochastic Process Models

by Insua , David; Ruggeri, Fabrizio; Wiper, Mike

• ISBN13: 9780470744536
• ISBN10: 0470744537
• Edition: 1st
• Format: Hardcover
• Copyright: 2012-05-07
• Publisher: Wiley

Summary

This book provides a unique opportunity to provide a unified view on analysis of stochastic processes from a Bayesian perspective. Covering the main classes of stochastic processing including modeling, computational, inference, prediction, decision-making and important applied models based on stochastic processes.

Author Biography

Fabrizio Ruggeri, Research Director, CNR IMATI, Milano, Italy.

Michael P. Wiper, Associate Professor in Statistics, Department of Statistics, Universidad Carlos III de Madrid, Spain.

David Rios Insua, Professor of Statistics and Operations Research, Department of Statistics and Operations Research, Universidad Rey Juan Carlos, Spain.

Table of Contents

Preface
Stochastic Processes	p. 11
Introduction	p. 11
Key Concepts in Stochastic Processes	p. 11
Main Classes of Stochastic Processes	p. 16
Inference, Prediction and Decision Making	p. 21
Discussion	p. 23
Bayesian Analysis	p. 27
Introduction	p. 27
Bayesian Statistics	p. 28
Bayesian Decision Analysis	p. 37
Bayesian Computation	p. 39
Discussion	p. 51
Discrete Time Markov Chains	p. 61
Introduction	p. 61
Important Markov Chain Models	p. 62
Inference for First Order Chains	p. 66
Special Topics	p. 76
Case Study: Wind Directions at Gijon	p. 87
Markov Decision Processes	p. 94
Discussion	p. 97
Continuous Time Markov Chains and Extensions	p. 105
Introduction	p. 105
Basic Setup and Results	p. 106
Inference and Prediction for CTMCs	p. 108
Case Study: Hardware Availability through CTMCs	p. 112
Semi-Markovian Processes	p. 118
Decision Making with Semi-Markovian Decision Processes	p. 122
Discussion	p. 128
Poisson Processes and Extensions	p. 133
Introduction	p. 133
Basics on Poisson Processes	p. 134
Homogeneous Poisson Processes	p. 138
Nonhomogeneous Poisson Processes	p. 147
Compound Poisson Processes	p. 153
Further Extensions of Poisson Processes	p. 154
Case Study: Earthquake Occurrences	p. 157
Discussion	p. 162
Continuous Time Continuous Space Processes	p. 169
Introduction	p. 169
Gaussian Processes	p. 170
Brownian Motion and Fractional Brownian Motion	p. 174
Di®usions	p. 181
Case Study: Prey-predator Systems	p. 184
Discussion	p. 190
Queueing Analysis	p. 201
Introduction	p. 201
Basic Queueing Concepts	p. 201
The Main Queueing Models	p. 204
Inference for Queueing Systems	p. 208
Inference for M=M=1 Systems	p. 209
Inference for Non Markovian Systems	p. 220
Decision Problems in Queueing Systems	p. 229
Case Study: Optimal Number of Beds in a Hospital	p. 230
Discussion	p. 235
Reliability	p. 245
Introduction	p. 245
Basic Reliability Concepts	p. 246
Renewal Processes	p. 249
Poisson Processes	p. 251
Other Processes	p. 259
Maintenance	p. 262
Case Study: Gas Escapes	p. 263
Discussion	p. 271
Discrete Event Simulation	p. 279
Introduction	p. 279
Discrete Event Simulation Methods	p. 280
A Bayesian View of DES	p. 283
Case Study: A G=G=1 Queueing System	p. 286
Bayesian Output Analysis	p. 288
Simulation and Optimization	p. 292
Discussion	p. 294
Risk Analysis	p. 301
Introduction	p. 301
Risk Measures	p. 302
Ruin Problems	p. 316
Case Study: Ruin Probability Estimation	p. 320
Discussion	p. 327
Main Distributions	p. 337
Generating Functions and the Laplace-Stieltjes Transform	p. 347
Index
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