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 PART ONE BASIC CONCEPTS AND TOOLS 1 Stochastic Processes 111.1 Introduction 111.2 Key Concepts in Stochastic Processes 111.3 Main Classes of Stochastic Processes 161.4 Inference, Prediction and Decision Making 211.5 Discussion 232 Bayesian Analysis 272.1 Introduction 272.2 Bayesian Statistics 282.3 Bayesian Decision Analysis 372.4 Bayesian Computation 392.5 Discussion 51PART TWO MODELS3 Discrete Time Markov Chains 613.1 Introduction 613.2 Important Markov Chain Models 623.3 Inference for First Order Chains 663.4 Special Topics 763.5 Case Study: Wind Directions at Gijon 873.6 Markov Decision Processes 943.7 Discussion 974 Continuous Time Markov Chains and Extensions 1054.1 Introduction 1054.2 Basic Setup and Results 1064.3 Inference and Prediction for CTMCs 1084.4 Case Study: Hardware Availability through CTMCs 1124.5 Semi-Markovian Processes 1184.6 Decision Making with Semi-Markovian Decision Processes 1224.7 Discussion 1285 Poisson Processes and Extensions 1335.1 Introduction 1335.2 Basics on Poisson Processes 1345.3 Homogeneous Poisson Processes 1385.4 Nonhomogeneous Poisson Processes 1475.5 Compound Poisson Processes 1535.6 Further Extensions of Poisson Processes 1545.7 Case Study: Earthquake Occurrences 1575.8 Discussion 1626 Continuous Time Continuous Space Processes 1696.1 Introduction 1696.2 Gaussian Processes 1706.3 Brownian Motion and Fractional Brownian Motion 1746.4 Di®usions 1816.5 Case Study: Prey-predator Systems 1846.6 Discussion 190PART THREE APPLICATIONS7 Queueing Analysis 2017.1 Introduction 2017.2 Basic Queueing Concepts 2017.3 The Main Queueing Models 2047.4 Inference for Queueing Systems 2087.5 Inference for M=M=1 Systems 2097.6 Inference for Non Markovian Systems 2207.7 Decision Problems in Queueing Systems 2297.8 Case Study: Optimal Number of Beds in a Hospital 2307.9 Discussion 2358 Reliability 2458.1 Introduction 2458.2 Basic Reliability Concepts 2468.3 Renewal Processes 2498.4 Poisson Processes 2518.5 Other Processes 2598.6 Maintenance 2628.7 Case Study: Gas Escapes 2638.8 Discussion 2719 Discrete Event Simulation 2799.1 Introduction 2799.2 Discrete Event Simulation Methods 2809.3 A Bayesian View of DES 2839.4 Case Study: A G=G=1 Queueing System 2869.5 Bayesian Output Analysis 2889.6 Simulation and Optimization 2929.7 Discussion 29410 Risk Analysis 30110.1 Introduction 30110.2 Risk Measures 30210.3 Ruin Problems 31610.4 Case Study: Ruin Probability Estimation 32010.5 Discussion 327Appendix A Main Distributions 337Appendix B Generating Functions and the Laplace-Stieltjes Transform 347Index