Bayesian Analysis of Stochastic Process Models

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.

• Preface xiPART ONE BASIC CONCEPTS AND TOOLS1 Stochastic processes 31.1 Introduction 31.2 Key concepts in stochastic processes 31.3 Main classes of stochastic processes 71.4 Inference, prediction, and decision-making 121.5 Discussion 132 Bayesian analysis 162.1 Introduction 162.2 Bayesian statistics 162.3 Bayesian decision analysis 252.4 Bayesian computation 262.5 Discussion 37PART TWO MODELS3 Discrete time Markov chains and extensions 453.1 Introduction 453.2 Important Markov chain models 463.3 Inference for first-order, time homogeneous, Markov chains 493.4 Special topics 583.5 Case study: Wind directions at Gijon 683.6 Markov decision processes 743.7 Discussion 774 Continuous time Markov chains and extensions 824.1 Introduction 824.2 Basic setup and results 834.3 Inference and prediction for CTMCs 854.4 Case study: Hardware availability through CTMCs 884.5 Semi-Markovian processes 934.6 Decision-making with semi-Markovian decision processes 974.7 Discussion 1025 Poisson processes and extensions 1055.1 Introduction 1055.2 Basics on Poisson processes 1065.3 Homogeneous Poisson processes 1095.4 Nonhomogeneous Poisson processes 1175.5 Compound Poisson processes 1225.6 Further extensions of Poisson processes 1245.7 Case study: Earthquake occurrences 1265.8 Discussion 1306 Continuous time continuous space processes 1356.1 Introduction 1356.2 Gaussian processes 1356.3 Brownian motion and FBM 1396.4 Diffusions 1446.5 Case study: Predator–prey systems 1476.6 Discussion 153PART THREE APPLICATIONS7 Queueing analysis 1637.1 Introduction 1637.2 Basic queueing concepts 1637.3 The main queueing models 1657.4 Bayesian inference for queueing systems 1697.5 Bayesian inference for the M/M/1 system 1707.6 Inference for non-Markovian systems 1807.7 Decision problems in queueing systems 1877.8 Case study: Optimal number of beds in a hospital 1887.9 Discussion 1948 Reliability 2008.1 Introduction 2008.2 Basic reliability concepts 2018.3 Renewal processes 2038.4 Poisson processes 2058.5 Other processes 2128.6 Maintenance 2148.7 Case study: Gas escapes 2158.8 Discussion 2229 Discrete event simulation 2269.1 Introduction 2269.2 Discrete event simulation methods 2279.3 A Bayesian view of DES 2309.4 Case study: A G/G/1 queueing system 2319.5 Bayesian output analysis 2339.6 Simulation and optimization 2379.7 Discussion 23810 Risk analysis 24310.1 Introduction 24310.2 Risk measures 24310.3 Ruin problems 25610.4 Case study: Estimation of finite-time ruin probabilities in the Sparre Andersen model 26110.5 Discussion 266References 268Appendix A Main distributions 273Appendix B Generating functions and the Laplace–Stieltjes transform 283Index 285