David Insua, Fabrizio Ruggeri, Mike Wiper

Bayesian Analysis of Stochastic Process Models

• Gebundenes Buch

Produktbeschreibung

This book provides analysis of stochastic processes from a Bayesian perspective with coverage of the main classes of stochastic processing, including modeling, computational, inference, prediction, decision-making and important applied models based on stochastic processes. In offers an introduction of MCMC and other statistical computing machinery that have pushed forward advances in Bayesian methodology. Addressing the growing interest for Bayesian analysis of more complex models, based on stochastic processes, this book aims to unite scattered information into one comprehensive and reliable volume.

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Bayesian analysis of complex models based on stochastic processes has in recent years become a growing area. This book provides a unified treatment of Bayesian analysis of models based on stochastic processes, covering the main classes of stochastic processing including modeling, computational, inference, forecasting, decision making and important applied models.

Key features:
Explores Bayesian analysis of models based on stochastic processes, providing a unified treatment.
Provides a thorough introduction for research students.
Computational tools to deal with complex problems are illustrated along with real life case studies
Looks at inference, prediction and decision making.

Researchers, graduate and advanced undergraduate students interested in stochastic processes in fields such as statistics, operations research (OR), engineering, finance, economics, computer science and Bayesian analysis will benefit from reading this book. With numerous applications included, practitioners of OR, stochastic modelling and applied statistics will also find this book useful.

Produktdetails

• Wiley Series in Probability and Statistics .
• Verlag: Wiley & Sons
• 1. Auflage
• Seitenzahl: 316
• Erscheinungstermin: 7. Mai 2012
• Englisch
• Abmessung: 235mm x 157mm x 22mm
• Gewicht: 590g
• ISBN-13: 9780470744536
• ISBN-10: 0470744537
• Artikelnr.: 30589121

Autorenporträt

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.

Inhaltsangabe

Preface PART ONE BASIC CONCEPTS AND TOOLS 1 Stochastic Processes 11 1.1
Introduction 11 1.2 Key Concepts in Stochastic Processes 11 1.3 Main
Classes of Stochastic Processes 16 1.4 Inference, Prediction and Decision
Making 21 1.5 Discussion 23 2 Bayesian Analysis 27 2.1 Introduction 27 2.2
Bayesian Statistics 28 2.3 Bayesian Decision Analysis 37 2.4 Bayesian
Computation 39 2.5 Discussion 51 PART TWO MODELS 3 Discrete Time Markov
Chains 61 3.1 Introduction 61 3.2 Important Markov Chain Models 62 3.3
Inference for First Order Chains 66 3.4 Special Topics 76 3.5 Case Study:
Wind Directions at Gijon 87 3.6 Markov Decision Processes 94 3.7 Discussion
97 4 Continuous Time Markov Chains and Extensions 105 4.1 Introduction 105
4.2 Basic Setup and Results 106 4.3 Inference and Prediction for CTMCs 108
4.4 Case Study: Hardware Availability through CTMCs 112 4.5 Semi-Markovian
Processes 118 4.6 Decision Making with Semi-Markovian Decision Processes
122 4.7 Discussion 128 5 Poisson Processes and Extensions 133 5.1
Introduction 133 5.2 Basics on Poisson Processes 134 5.3 Homogeneous
Poisson Processes 138 5.4 Nonhomogeneous Poisson Processes 147 5.5 Compound
Poisson Processes 153 5.6 Further Extensions of Poisson Processes 154 5.7
Case Study: Earthquake Occurrences 157 5.8 Discussion 162 6 Continuous Time
Continuous Space Processes 169 6.1 Introduction 169 6.2 Gaussian Processes
170 6.3 Brownian Motion and Fractional Brownian Motion 174 6.4 Di(r)usions
181 6.5 Case Study: Prey-predator Systems 184 6.6 Discussion 190 PART THREE
APPLICATIONS 7 Queueing Analysis 201 7.1 Introduction 201 7.2 Basic
Queueing Concepts 201 7.3 The Main Queueing Models 204 7.4 Inference for
Queueing Systems 208 7.5 Inference for M=M=1 Systems 209 7.6 Inference for
Non Markovian Systems 220 7.7 Decision Problems in Queueing Systems 229 7.8
Case Study: Optimal Number of Beds in a Hospital 230 7.9 Discussion 235 8
Reliability 245 8.1 Introduction 245 8.2 Basic Reliability Concepts 246 8.3
Renewal Processes 249 8.4 Poisson Processes 251 8.5 Other Processes 259 8.6
Maintenance 262 8.7 Case Study: Gas Escapes 263 8.8 Discussion 271 9
Discrete Event Simulation 279 9.1 Introduction 279 9.2 Discrete Event
Simulation Methods 280 9.3 A Bayesian View of DES 283 9.4 Case Study: A
G=G=1 Queueing System 286 9.5 Bayesian Output Analysis 288 9.6 Simulation
and Optimization 292 9.7 Discussion 294 10 Risk Analysis 301 10.1
Introduction 301 10.2 Risk Measures 302 10.3 Ruin Problems 316 10.4 Case
Study: Ruin Probability Estimation 320 10.5 Discussion 327 Appendix A Main
Distributions 337 Appendix B Generating Functions and the Laplace-Stieltjes
Transform 347 Index