Bayesian Analysis of Stochastic Process Models.

By: Insua, DavidContributor(s): Ruggeri, Fabrizio | Wiper, MikeMaterial type: TextTextSeries: Wiley Series in Probability and Statistics SerPublisher: Hoboken : John Wiley & Sons, Incorporated, 2012Copyright date: ©2012Edition: 1st edDescription: 1 online resource (316 pages)Content type: text Media type: computer Carrier type: online resourceISBN: 9780470975923Subject(s): Bayesian statistical decision theory | Stochastic processesGenre/Form: Electronic books.Additional physical formats: Print version:: Bayesian Analysis of Stochastic Process ModelsDDC classification: 519.5/42 LOC classification: QA279.5 -- .R56 2012ebOnline resources: Click to View
Contents:
Intro -- Bayesian Analysis of Stochastic Process Models -- Contents -- Preface -- PART ONE BASIC CONCEPTS AND TOOLS -- 1 Stochastic processes -- 1.1 Introduction -- 1.2 Key concepts in stochastic processes -- 1.3 Main classes of stochastic processes -- 1.3.1 Markovian processes -- 1.3.2 Poisson process -- 1.3.3 Gaussian processes -- 1.3.4 Brownian motion -- 1.3.5 Diffusion processes -- 1.4 Inference, prediction, and decision-making -- 1.5 Discussion -- References -- 2 Bayesian analysis -- 2.1 Introduction -- 2.2 Bayesian statistics -- 2.2.1 Parameter estimation -- 2.2.2 Hypothesis testing -- 2.2.3 Prediction -- 2.2.4 Sensitivity analysis and objective Bayesian methods -- 2.3 Bayesian decision analysis -- 2.4 Bayesian computation -- 2.4.1 Computational Bayesian statistics -- 2.4.2 Computational Bayesian decision analysis -- 2.5 Discussion -- References -- PART TWO MODELS -- 3 Discrete time Markov chains and extensions -- 3.1 Introduction -- 3.2 Important Markov chain models -- 3.2.1 Reversible chains -- 3.2.2 Higher order chains and mixtures -- 3.2.3 Discrete time Markov processes with continuous state space -- 3.2.4 Branching processes -- 3.2.5 Hidden Markov models -- 3.3 Inference for first-order, time homogeneous, Markov chains -- 3.3.1 Advantages of the Bayesian approach -- 3.3.2 Conjugate prior distribution and modifications -- 3.3.3 Forecasting short-term behavior -- 3.3.4 Forecasting stationary behavior -- 3.3.5 Model comparison -- 3.3.6 Unknown initial state -- 3.3.7 Partially observed data -- 3.4 Special topics -- 3.4.1 Reversible Markov chains -- 3.4.2 Higher order chains and mixtures of Markov chains -- 3.4.3 AR processes and other continuous state space processes -- 3.4.4 Branching processes -- 3.4.5 Hidden Markov models -- 3.4.6 Markov chains with covariate information and nonhomogeneous Markov chains.
3.5 Case study: Wind directions at Gijón -- 3.5.1 Modeling the time series of wind directions -- 3.5.2 Results -- 3.6 Markov decision processes -- 3.7 Discussion -- References -- 4 Continuous time Markov chains and extensions -- 4.1 Introduction -- 4.2 Basic setup and results -- 4.3 Inference and prediction for CTMCs -- 4.3.1 Inference for the chain parameters -- 4.3.2 Forecasting short-term behavior -- 4.3.3 Forecasting long-term behavior -- 4.3.4 Predicting times between transitions -- 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 -- References -- 5 Poisson processes and extensions -- 5.1 Introduction -- 5.2 Basics on Poisson processes -- 5.2.1 Definitions and basic results -- 5.2.2 Arrival and interarrival times -- 5.2.3 Some relevant results -- 5.3 Homogeneous Poisson processes -- 5.3.1 Inference on homogeneous Poisson processes -- 5.4 Nonhomogeneous Poisson processes -- 5.4.1 Intensity functions -- 5.4.2 Inference for nonhomogeneous Poisson processes -- 5.4.3 Change points in NHPPs -- 5.5 Compound Poisson processes -- 5.6 Further extensions of Poisson processes -- 5.6.1 Modulated Poisson process -- 5.6.2 Marked Poisson processes -- 5.6.3 Self-exciting processes -- 5.6.4 Doubly stochastic Poisson processes -- 5.7 Case study: Earthquake occurrences -- 5.7.1 Data -- 5.7.2 Poisson model -- 5.7.3 Data analysis -- 5.8 Discussion -- References -- 6 Continuous time continuous space processes -- 6.1 Introduction -- 6.2 Gaussian processes -- 6.2.1 Bayesian inference for Gaussian processes -- 6.2.2 Gaussian process emulators -- 6.3 Brownian motion and FBM -- 6.3.1 Brownian motion -- 6.3.2 Fractional Brownian motion -- 6.4 Diffusions -- 6.5 Case study: Predator-prey systems -- 6.6 Discussion -- References -- PART THREE APPLICATIONS.
7 Queueing analysis -- 7.1 Introduction -- 7.2 Basic queueing concepts -- 7.3 The main queueing models -- 7.3.1 M/M/1 and related systems -- 7.3.2 GI/M/1 and GI/M/c systems -- 7.3.3 The M/G/1 system -- 7.3.4 GI/G/1 systems -- 7.4 Bayesian inference for queueing systems -- 7.5 Bayesian inference for the M/M/1 system -- 7.5.1 The likelihood function and maximum likelihood estimation -- 7.5.2 Bayesian inference with conjugate priors -- 7.5.3 Alternative prior formulations -- 7.5.4 Alternative experiments -- 7.6 Inference for non-Markovian systems -- 7.6.1 GI/M/1 and GI/M/c systems -- 7.6.2 M/G/1 systems -- 7.6.3 G/G/1 systems -- 7.7 Decision problems in queueing systems -- 7.8 Case study: Optimal number of beds in a hospital -- 7.8.1 Modeling the stay times -- 7.8.2 Characteristics of the hospital queueing system -- 7.8.3 Optimizing the number of beds -- 7.9 Discussion -- References -- 8 Reliability -- 8.1 Introduction -- 8.2 Basic reliability concepts -- 8.2.1 Reliability data -- 8.2.2 Basic definitions -- 8.3 Renewal processes -- 8.4 Poisson processes -- 8.4.1 Selection of the intensity function -- 8.4.2 Reliability measures -- 8.4.3 Failure count data -- 8.5 Other processes -- 8.6 Maintenance -- 8.7 Case study: Gas escapes -- 8.7.1 Cast iron pipe models -- 8.7.2 Steel pipes -- 8.7.3 Different causes of corrosion -- 8.8 Discussion -- References -- 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 -- References -- 10 Risk analysis -- 10.1 Introduction -- 10.2 Risk measures -- 10.2.1 Modeling financial time series -- 10.2.2 Bayesian inference for financial time series models -- 10.3 Ruin problems -- 10.3.1 Modeling the claim size distribution.
10.3.2 Bayesian inference -- 10.4 Case study: Estimation of finite-time ruin probabilities in the Sparre Andersen model -- 10.4.1 Data modeling: The Coxian distribution -- 10.4.2 Bayesian inference for the interclaim time and claim size distributions -- 10.4.3 Results -- 10.5 Discussion -- References -- Appendix A Main distributions -- Appendix B Generating functions and the Laplace-Stieltjes transform -- Index.
Summary: Bayesian analysis of complex models based on stochastic processes has seen a surge in research activity in recent years. Bayesian Analysis of Stochastic Process Models 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. Bayesian Analysis of Stochastic Process Models: Explores Bayesian analysis of models based on stochastic processes, providing a unified treatment. Provides a thorough introduction for research students. Includes computational tools to deal with complex problems, illustrated with real life case studies Computational tools to deal with complex problems are illustrated along with real life case studies Examines 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.
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Intro -- Bayesian Analysis of Stochastic Process Models -- Contents -- Preface -- PART ONE BASIC CONCEPTS AND TOOLS -- 1 Stochastic processes -- 1.1 Introduction -- 1.2 Key concepts in stochastic processes -- 1.3 Main classes of stochastic processes -- 1.3.1 Markovian processes -- 1.3.2 Poisson process -- 1.3.3 Gaussian processes -- 1.3.4 Brownian motion -- 1.3.5 Diffusion processes -- 1.4 Inference, prediction, and decision-making -- 1.5 Discussion -- References -- 2 Bayesian analysis -- 2.1 Introduction -- 2.2 Bayesian statistics -- 2.2.1 Parameter estimation -- 2.2.2 Hypothesis testing -- 2.2.3 Prediction -- 2.2.4 Sensitivity analysis and objective Bayesian methods -- 2.3 Bayesian decision analysis -- 2.4 Bayesian computation -- 2.4.1 Computational Bayesian statistics -- 2.4.2 Computational Bayesian decision analysis -- 2.5 Discussion -- References -- PART TWO MODELS -- 3 Discrete time Markov chains and extensions -- 3.1 Introduction -- 3.2 Important Markov chain models -- 3.2.1 Reversible chains -- 3.2.2 Higher order chains and mixtures -- 3.2.3 Discrete time Markov processes with continuous state space -- 3.2.4 Branching processes -- 3.2.5 Hidden Markov models -- 3.3 Inference for first-order, time homogeneous, Markov chains -- 3.3.1 Advantages of the Bayesian approach -- 3.3.2 Conjugate prior distribution and modifications -- 3.3.3 Forecasting short-term behavior -- 3.3.4 Forecasting stationary behavior -- 3.3.5 Model comparison -- 3.3.6 Unknown initial state -- 3.3.7 Partially observed data -- 3.4 Special topics -- 3.4.1 Reversible Markov chains -- 3.4.2 Higher order chains and mixtures of Markov chains -- 3.4.3 AR processes and other continuous state space processes -- 3.4.4 Branching processes -- 3.4.5 Hidden Markov models -- 3.4.6 Markov chains with covariate information and nonhomogeneous Markov chains.

3.5 Case study: Wind directions at Gijón -- 3.5.1 Modeling the time series of wind directions -- 3.5.2 Results -- 3.6 Markov decision processes -- 3.7 Discussion -- References -- 4 Continuous time Markov chains and extensions -- 4.1 Introduction -- 4.2 Basic setup and results -- 4.3 Inference and prediction for CTMCs -- 4.3.1 Inference for the chain parameters -- 4.3.2 Forecasting short-term behavior -- 4.3.3 Forecasting long-term behavior -- 4.3.4 Predicting times between transitions -- 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 -- References -- 5 Poisson processes and extensions -- 5.1 Introduction -- 5.2 Basics on Poisson processes -- 5.2.1 Definitions and basic results -- 5.2.2 Arrival and interarrival times -- 5.2.3 Some relevant results -- 5.3 Homogeneous Poisson processes -- 5.3.1 Inference on homogeneous Poisson processes -- 5.4 Nonhomogeneous Poisson processes -- 5.4.1 Intensity functions -- 5.4.2 Inference for nonhomogeneous Poisson processes -- 5.4.3 Change points in NHPPs -- 5.5 Compound Poisson processes -- 5.6 Further extensions of Poisson processes -- 5.6.1 Modulated Poisson process -- 5.6.2 Marked Poisson processes -- 5.6.3 Self-exciting processes -- 5.6.4 Doubly stochastic Poisson processes -- 5.7 Case study: Earthquake occurrences -- 5.7.1 Data -- 5.7.2 Poisson model -- 5.7.3 Data analysis -- 5.8 Discussion -- References -- 6 Continuous time continuous space processes -- 6.1 Introduction -- 6.2 Gaussian processes -- 6.2.1 Bayesian inference for Gaussian processes -- 6.2.2 Gaussian process emulators -- 6.3 Brownian motion and FBM -- 6.3.1 Brownian motion -- 6.3.2 Fractional Brownian motion -- 6.4 Diffusions -- 6.5 Case study: Predator-prey systems -- 6.6 Discussion -- References -- PART THREE APPLICATIONS.

7 Queueing analysis -- 7.1 Introduction -- 7.2 Basic queueing concepts -- 7.3 The main queueing models -- 7.3.1 M/M/1 and related systems -- 7.3.2 GI/M/1 and GI/M/c systems -- 7.3.3 The M/G/1 system -- 7.3.4 GI/G/1 systems -- 7.4 Bayesian inference for queueing systems -- 7.5 Bayesian inference for the M/M/1 system -- 7.5.1 The likelihood function and maximum likelihood estimation -- 7.5.2 Bayesian inference with conjugate priors -- 7.5.3 Alternative prior formulations -- 7.5.4 Alternative experiments -- 7.6 Inference for non-Markovian systems -- 7.6.1 GI/M/1 and GI/M/c systems -- 7.6.2 M/G/1 systems -- 7.6.3 G/G/1 systems -- 7.7 Decision problems in queueing systems -- 7.8 Case study: Optimal number of beds in a hospital -- 7.8.1 Modeling the stay times -- 7.8.2 Characteristics of the hospital queueing system -- 7.8.3 Optimizing the number of beds -- 7.9 Discussion -- References -- 8 Reliability -- 8.1 Introduction -- 8.2 Basic reliability concepts -- 8.2.1 Reliability data -- 8.2.2 Basic definitions -- 8.3 Renewal processes -- 8.4 Poisson processes -- 8.4.1 Selection of the intensity function -- 8.4.2 Reliability measures -- 8.4.3 Failure count data -- 8.5 Other processes -- 8.6 Maintenance -- 8.7 Case study: Gas escapes -- 8.7.1 Cast iron pipe models -- 8.7.2 Steel pipes -- 8.7.3 Different causes of corrosion -- 8.8 Discussion -- References -- 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 -- References -- 10 Risk analysis -- 10.1 Introduction -- 10.2 Risk measures -- 10.2.1 Modeling financial time series -- 10.2.2 Bayesian inference for financial time series models -- 10.3 Ruin problems -- 10.3.1 Modeling the claim size distribution.

10.3.2 Bayesian inference -- 10.4 Case study: Estimation of finite-time ruin probabilities in the Sparre Andersen model -- 10.4.1 Data modeling: The Coxian distribution -- 10.4.2 Bayesian inference for the interclaim time and claim size distributions -- 10.4.3 Results -- 10.5 Discussion -- References -- Appendix A Main distributions -- Appendix B Generating functions and the Laplace-Stieltjes transform -- Index.

Bayesian analysis of complex models based on stochastic processes has seen a surge in research activity in recent years. Bayesian Analysis of Stochastic Process Models 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. Bayesian Analysis of Stochastic Process Models: Explores Bayesian analysis of models based on stochastic processes, providing a unified treatment. Provides a thorough introduction for research students. Includes computational tools to deal with complex problems, illustrated with real life case studies Computational tools to deal with complex problems are illustrated along with real life case studies Examines 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.

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Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2018. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries.

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