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Bayesian Analysis of Stochastic Process Models.
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...
| Clasificación: | Libro Electrónico |
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| Autor principal: | |
| Otros Autores: | , |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Hoboken :
John Wiley & Sons,
2012.
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| Temas: | |
| Acceso en línea: | Texto completo |
Tabla de Contenidos:
- 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 methods2.3 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 approach3.3.2 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 Gijón3.5.1 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 processes4.7 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.