Markov Chain Monte Carlo : Stochastic Simulation for Bayesian Inference /: Stochastic Simulation for Bayesian Inference. (2006)

• Record Type: Book
• Further Information: Note: Dani Gamerman, Hedibert Freitas Lopes.
• Authors: Gamerman, Dani; Lopes, Hedibert F
• Contents: Cover; Half Title; Title Page; Copyright Page; Dedication; Table of Contents; Introduction; Preface to the second edition; Preface to the first edition; 1: Stochastic simulation; 1.1 Introduction; 1.2 Generation of discrete random quantities; 1.2.1 Bernoulli distribution; 1.2.2 Binomial distribution; 1.2.3 Geometric and negative binomial distribution; 1.2.4 Poisson distribution; 1.3 Generation of continuous random quantities; 1.3.1 Probability integral transform; 1.3.2 Bivariate techniques; 1.3.3 Methods based on mixtures; 1.4 Generation of random vectors and matrices 1.4.1 Multivariate normal distribution1.4.2 Wishart distribution; 1.4.3 Multivariate Student's t distribution; 1.5 Resampling methods; 1.5.1 Rejection method; 1.5.2 Weighted resampling method; 1.5.3 Adaptive rejection method; 1.6 Exercises; 2: Bayesian inference; 2.1 Introduction; 2.2 Bayes' theorem; 2.2.1 Prior, posterior and predictive distributions; 2.2.2 Summarizing the information; 2.3 Conjugate distributions; 2.3.1 Conjugate distributions for the exponential family; 2.3.2 Conjugacy and regression models; 2.3.3 Conditional conjugacy; 2.4 Hierarchical models; 2.5 Dynamic models 2.5.1 Sequential inference2.5.2 Smoothing; 2.5.3 Extensions; 2.6 Spatial models; 2.7 Model comparison; 2.8 Exercises; 3: Approximate methods of inference; 3.1 Introduction; 3.2 Asymptotic approximations; 3.2.1 Normal approximations; 3.2.2 Mode calculation; 3.2.3 Standard Laplace approximation; 3.2.4 Exponential form Laplace approximations; 3.3 Approximations by Gaussian quadrature; 3.4 Monte Carlo integration; 3.5 Methods based on stochastic simulation; 3.5.1 Bayes' theorem via the rejection method; 3.5.2 Bayes' theorem via weighted resampling; 3.5.3 Application to dynamic models 3.6 Exercises4: Markov chains; 4.1 Introduction; 4.2 Definition and transition probabilities; 4.3 Decomposition of the state space; 4.4 Stationary distributions; 4.5 Limiting theorems; 4.6 Reversible chains; 4.7 Continuous state spaces; 4.7.1 Transition kernels; 4.7.2 Stationarity and limiting results; 4.8 Simulation of a Markov chain; 4.9 Data augmentation or substitution sampling; 4.10 Exercises; 5: Gibbs sampling; 5.1 Introduction; 5.2 Definition and properties; 5.3 Implementation and optimization; 5.3.1 Forming the sample; 5.3.2 Scanning strategies; 5.3.3 Using the sample 5.3.4 Reparametrization5.3.5 Blocking; 5.3.6 Sampling from the full conditional distributions; 5.4 Convergence diagnostics; 5.4.1 Rate of convergence; 5.4.2 Informal convergence monitors; 5.4.3 Convergence prescription; 5.4.4 Formal convergence methods; 5.5 Applications; 5.5.1 Hierarchical models; 5.5.2 Dynamic models; 5.5.3 Spatial models; 5.6 MCMC-based software for Bayesian modeling; Appendix 5.A: BUGS code for Example 5.7; Appendix 5.B: BUGS code for Example 5.8; 5.7 Exercises; 6: Metropolis-Hastings algorithms; 6.1 Introduction; 6.2 Definition and properties; 6.3 Special cases
• Edition: Second edition
• Publisher Details: Boca Raton, FL : CRC Press
• Publication Date: 2006
• Extent: 1 online resource
• Subjects: 519.282; Mathematical statistics; Mathematical statistics -- Data processing; Probabilities; Mathematical statistics; Mathematical statistics -- Data processing; Probabilities; Electronic books
• Languages: English
• ISBNs: 9781482296426
• Related ISBNs: 148229642X
• Access Rights: Legal Deposit; Only available on premises controlled by the deposit library and to one user at any one time; The Legal Deposit Libraries (Non-Print Works) Regulations (UK).
• Access Usage: Restricted: Printing from this resource is governed by The Legal Deposit Libraries (Non-Print Works) Regulations (UK) and UK copyright law currently in force.