Machine generated contents note: Preface 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 3 Discrete Time Markov Chains 61 3.1 Introduction 61 3.2 Important Markov Chain Models 62 3.3 Inference for First Order, time homogeneous, Markov chains 66 3.4 Special Topics 76 3.5 Case Study: Wind Directions at Gij́on 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 FBM [Fractional Brownian Motion] 174 6.4 Diffusions 181 6.5 Case Study: Predator-prey Systems 184 6.6 Discussion 190 7 Queueing Analysis 201 7.1 Introduction 201 7.2 Basic Queueing Concepts 201 7.3 The Main Queueing Models 204 7.4 Bayesian 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 271 279 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: Estimation of finite-time ruin probabilities in the Sparre Andersen model 320 10.5 Discussion 327 Appendix A Main Distributions 337 Appendix B Generating Functions and the Laplace-Stieltjes Transform 347 Index.
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Bayesian analysis of stochastic process models by Fabrizio Ruggeri. ISBN 9780470744536. Published by Wiley in 2012. Publication and catalogue information, links to buy online and reader comments.
