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.
Table of Contents:
Preface xi
PART ONE BASIC CONCEPTS AND TOOLS
1 Stochastic processes 3
1.1 Introduction 3
1.2 Key concepts in stochastic processes 3
1.3 Main classes of stochastic processes 7
1.4 Inference, prediction, and decision-making 12
1.5 Discussion 13
2 Bayesian analysis 16
2.1 Introduction 16
2.2 Bayesian statistics 16
2.3 Bayesian decision analysis 25
2.4 Bayesian computation 26
2.5 Discussion 37
PART TWO MODELS
3 Discrete time Markov chains and extensions 45
3.1 Introduction 45
3.2 Important Markov chain models 46
3.3 Inference for first-order, time homogeneous, Markov chains 49
3.4 Special topics 58
3.5 Case study: Wind directions at Gijon 68
3.6 Markov decision processes 74
3.7 Discussion 77
4 Continuous time Markov chains and extensions 82
4.1 Introduction 82
4.2 Basic setup and results 83
4.3 Inference and prediction for CTMCs 85
4.4 Case study: Hardware availability through CTMCs 88
4.5 Semi-Markovian processes 93
4.6 Decision-making with semi-Markovian decision processes 97
4.7 Discussion 102
5 Poisson processes and extensions 105
5.1 Introduction 105
5.2 Basics on Poisson processes 106
5.3 Homogeneous Poisson processes 109
5.4 Nonhomogeneous Poisson processes 117
5.5 Compound Poisson processes 122
5.6 Further extensions of Poisson processes 124
5.7 Case study: Earthquake occurrences 126
5.8 Discussion 130
6 Continuous time continuous space processes 135
6.1 Introduction 135
6.2 Gaussian processes 135
6.3 Brownian motion and FBM 139
6.4 Diffusions 144
6.5 Case study: Predator–prey systems 147
6.6 Discussion 153
PART THREE APPLICATIONS
7 Queueing analysis 163
7.1 Introduction 163
7.2 Basic queueing concepts 163
7.3 The main queueing models 165
7.4 Bayesian inference for queueing systems 169
7.5 Bayesian inference for the M/M/1 system 170
7.6 Inference for non-Markovian systems 180
7.7 Decision problems in queueing systems 187
7.8 Case study: Optimal number of beds in a hospital 188
7.9 Discussion 194
8 Reliability 200
8.1 Introduction 200
8.2 Basic reliability concepts 201
8.3 Renewal processes 203
8.4 Poisson processes 205
8.5 Other processes 212
8.6 Maintenance 214
8.7 Case study: Gas escapes 215
8.8 Discussion 222
9 Discrete event simulation 226
9.1 Introduction 226
9.2 Discrete event simulation methods 227
9.3 A Bayesian view of DES 230
9.4 Case study: A G/G/1 queueing system 231
9.5 Bayesian output analysis 233
9.6 Simulation and optimization 237
9.7 Discussion 238
10 Risk analysis 243
10.1 Introduction 243
10.2 Risk measures 243
10.3 Ruin problems 256
10.4 Case study: Estimation of finite-time ruin probabilities in the Sparre Andersen model 261
10.5 Discussion 266
References 268
Appendix A Main distributions 273
Appendix B Generating functions and the Laplace–Stieltjes transform 283
Index 285
About the Author :
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.
