Bayesian analysis of stochastic process models

Description

"A unique book on Bayesian analyses of stochastic process based models"--;1 Stochastic Processes -- 1.1 Introduction -- 1.2 Key Concepts in Stochastic Processes -- 1.3 Main Classes of Stochastic Processes -- 1.4 Inference, Prediction and Decision Making -- 1.5 Discussion -- 2. Bayesian Analysis -- 2.1 Introduction -- 2.2 Bayesian Statistics -- 2.3 Bayesian Decision Analysis -- 2.4 Bayesian Computation -- 2.5 Discussion -- 3. Discrete Time Markov Chains -- 3.1 Introduction -- 3.2 Important Markov Chain Models -- 3.3 Inference for First Order Chains -- 3.4 Special Topics -- 3.5 Case Study: Wind Directions at Gij́on -- 3.6 Markov Decision Processes -- 3.7 Discussion -- 4. Continuous Time Markov Chains and Extensions -- 4.1 Introduction -- 4.2 Basic Setup and Results -- 4.3 Inference and Prediction for CTMCs -- 4.4 Case Study: Hardware Availability through CTMCs -- 4.5 Semi-Markovian Processes -- 4.6 Decision Making with Semi-Markovian Decision Processes -- 4.7 Discussion -- 5. Poisson Processes and Extensions -- 5.1 Introduction -- 5.2 Basics on Poisson Processes -- 5.3 Homogeneous Poisson Processes -- 5.4 Nonhomogeneous Poisson Processes -- 5.5 Compound Poisson Processes -- 5.6 Further Extensions of Poisson Processes -- 5.7 Case Study: Earthquake Occurrences -- 5.8 Discussion -- 6. Continuous Time Continuous Space Processes -- 6.1 Introduction -- 6.2 Gaussian Processes -- 6.3 Brownian Motion and Fractional Brownian Motion -- 6.4 Dilusions -- 6.5 Case Study: Prey-predator Systems -- 6.6 Discussion -- 7. Queueing Analysis -- 7.1 Introduction -- 7.2 Basic Queueing Concepts -- 7.3 The Main Queueing Models -- 7.4 Inference for Queueing Systems -- 7.5 Inference for M=M=1 Systems -- 7.6 Inference for Non Markovian Systems -- 7.7 Decision Problems in Queueing Systems -- 7.8 Case Study: Optimal Number of Beds in a Hospital -- 7.9 Discussion -- 8. Reliability -- 8.1 Introduction -- 8.2 Basic Reliability Concepts -- 8.3 Renewal Processes -- 8.4 Poisson Processes -- 8.5 Other Processes -- 8.6 Maintenance -- 8.7 Case Study: Gas Escapes -- 8.8 Discussion -- 9 Discrete Event Simulation -- 9.1 Introduction -- 9.2 Discrete Event Simulation Methods -- 9.3 A Bayesian View of DES -- 9.4 Case Study: A G=G=1 Queueing System -- 9.5 Bayesian Output Analysis -- 9.6 Simulation and Optimization -- 9.7 Discussion -- 10. Risk Analysis -- 10.1 Introduction -- 10.2 Risk Measures -- 10.3 Ruin Problems -- 10.4 Case Study: Ruin Probability Estimation -- 10.5 Discussion -- Appendix A Main Distributions -- Appendix B Generating Functions and the Laplace-Stieltjes Transform.;"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"--