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Bayesian Analysis of Stochastic Process Models

Book Description

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

  1. Cover
  2. Series
  3. Title Page
  4. Copyright
  5. Preface
  6. Part One: Basic Concepts and Tools
    1. 1: Stochastic processes
      1. 1.1 Introduction
      2. 1.2 Key concepts in stochastic processes
      3. 1.3 Main classes of stochastic processes
      4. 1.4 Inference, prediction, and decision-making
      5. 1.5 Discussion
      6. References
    2. 2: Bayesian analysis
      1. 2.1 Introduction
      2. 2.2 Bayesian statistics
      3. 2.3 Bayesian decision analysis
      4. 2.4 Bayesian computation
      5. 2.5 Discussion
      6. References
  7. Part Two: Models
    1. 3: Discrete time Markov chains and extensions
      1. 3.1 Introduction
      2. 3.2 Important Markov chain models
      3. 3.3 Inference for first-order, time homogeneous, Markov chains
      4. 3.4 Special topics
      5. 3.5 Case study: Wind directions at Gijón
      6. 3.6 Markov decision processes
      7. 3.7 Discussion
      8. References
    2. 4: Continuous time Markov chains and extensions
      1. 4.1 Introduction
      2. 4.2 Basic setup and results
      3. 4.3 Inference and prediction for CTMCs
      4. 4.4 Case study: Hardware availability through CTMCs
      5. 4.5 Semi-Markovian processes
      6. 4.6 Decision-making with semi-Markovian decision processes
      7. 4.7 Discussion
      8. References
    3. 5: Poisson processes and extensions
      1. 5.1 Introduction
      2. 5.2 Basics on Poisson processes
      3. 5.3 Homogeneous Poisson processes
      4. 5.4 Nonhomogeneous Poisson processes
      5. 5.5 Compound Poisson processes
      6. 5.6 Further extensions of Poisson processes
      7. 5.7 Case study: Earthquake occurrences
      8. 5.8 Discussion
      9. References
    4. 6: Continuous time continuous space processes
      1. 6.1 Introduction
      2. 6.2 Gaussian processes
      3. 6.3 Brownian motion and FBM
      4. 6.4 Diffusions
      5. 6.5 Case study: Predator–prey systems
      6. 6.6 Discussion
      7. References
  8. Part Three: Applications
    1. 7: Queueing analysis
      1. 7.1 Introduction
      2. 7.2 Basic queueing concepts
      3. 7.3 The main queueing models
      4. 7.4 Bayesian inference for queueing systems
      5. 7.5 Bayesian inference for the system
      6. 7.6 Inference for non-Markovian systems
      7. 7.7 Decision problems in queueing systems
      8. 7.8 Case study: Optimal number of beds in a hospital
      9. 7.9 Discussion
      10. References
    2. 8: Reliability
      1. 8.1 Introduction
      2. 8.2 Basic reliability concepts
      3. 8.3 Renewal processes
      4. 8.4 Poisson processes
      5. 8.5 Other processes
      6. 8.6 Maintenance
      7. 8.7 Case study: Gas escapes
      8. 8.8 Discussion
      9. References
    3. 9: Discrete event simulation
      1. 9.1 Introduction
      2. 9.2 Discrete event simulation methods
      3. 9.3 A Bayesian view of DES
      4. 9.4 Case study: A queueing system
      5. 9.5 Bayesian output analysis
      6. 9.6 Simulation and optimization
      7. 9.7 Discussion
      8. References
    4. 10: Risk analysis
      1. 10.1 Introduction
      2. 10.2 Risk measures
      3. 10.3 Ruin problems
      4. 10.4 Case study: Estimation of finite-time ruin probabilities in the Sparre Andersen model
      5. 10.5 Discussion
      6. References
  9. Appendix A: Main distributions
    1. Discrete distributions
    2. Continuous distributions
    3. Multivariate distributions
    4. References
  10. Appendix B: Generating functions and the Laplace–Stieltjes transform
    1. Probability generating function
    2. Moment generating function
    3. Laplace–Stieltjes transform
    4. References
  11. Index
  12. Series List