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| Preface to the second edition | |
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| Preface to the first edition | |
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| Introduction | |
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| Stochastic simulation | |
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| Introduction | |
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| Generation of discrete random quantities | |
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| Bernoulli distribution | |
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| Binomial distribution | |
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| Geometric and negative binomial distribution | |
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| Poisson distribution | |
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| Generation of continuous random quantities | |
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| Probability integral transform | |
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| Bivariate techniques | |
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| Methods based on mixtures | |
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| Generation of random vectors and matrices | |
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| Multivariate normal distribution | |
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| Wishart distribution | |
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| Multivariate Student's t distribution | |
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| Resampling methods | |
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| Rejection method | |
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| Weighted resampling method | |
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| Adaptive rejection method | |
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| Exercises | |
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| Bayesian inference | |
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| Introduction | |
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| Bayes' theorem | |
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| Prior, posterior and predictive distributions | |
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| Summarizing the information | |
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| Conjugate distributions | |
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| Conjugate distributions for the exponential family | |
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| Conjugacy and regression models | |
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| Conditional conjugacy | |
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| Hierarchical models | |
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| Dynamic models | |
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| Sequential inference | |
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| Smoothing | |
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| Extensions | |
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| Spatial models | |
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| Model comparison | |
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| Exercises | |
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| Approximate methods of inference | |
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| Introduction | |
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| Asymptotic approximations | |
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| Normal approximations | |
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| Mode calculation | |
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| Standard Laplace approximation | |
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| Exponential form Laplace approximations | |
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| Approximations by Gaussian quadrature | |
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| Monte Carlo integration | |
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| Methods based on stochastic simulation | |
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| Bayes' theorem via the rejection method | |
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| Bayes' theorem via weighted resampling | |
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| Application to dynamic models | |
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| Exercises | |
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| Markov chains | |
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| Introduction | |
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| Definition and transition probabilities | |
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| Decomposition of the state space | |
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| Stationary distributions | |
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| Limiting theorems | |
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| Reversible chains | |
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| Continuous state spaces | |
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| Transition kernels | |
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| Stationarity and limiting results | |
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| Simulation of a Markov chain | |
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| Data augmentation or substitution sampling | |
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| Exercises | |
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| Gibbs sampling | |
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| Introduction | |
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| Definition and properties | |
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| Implementation and optimization | |
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| Forming the sample | |
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| Scanning strategies | |
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| Using the sample | |
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| Reparametrization | |
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| Blocking | |
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| Sampling from the full conditional distributions | |
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| Convergence diagnostics | |
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| Rate of convergence | |
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| Informal convergence monitors | |
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| Convergence prescription | |
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| Formal convergence methods | |
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| Applications | |
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| Hierarchical models | |
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| Dynamic models | |
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| Spatial models | |
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| MCMC-based software for Bayesian modeling | |
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| BUGS code for Example 5.7 | |
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| BUGS code for Example 5.8 | |
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| Exercises | |
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| Metropolis-Hastings algorithms | |
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| Introduction | |
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| Definition and properties | |
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| Special cases | |
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| Symmetric chains | |
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| Random walk chains | |
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| Independence chains | |
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| Other forms | |
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| Hybrid algorithms | |
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| Componentwise transition | |
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| Metropolis within Gibbs | |
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| Blocking | |
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| Reparametrization | |
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| Applications | |
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| Generalized linear mixed models | |
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| Dynamic linear models | |
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| Dynamic generalized linear models | |
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| Spatial models | |
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| Exercises | |
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| Further topics in MCMC | |
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| Introduction | |
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| Model adequacy | |
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| Estimates of the predictive likelihood | |
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| Uses of the predictive likelihood | |
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| Deviance information criterion | |
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| Model choice: MCMC over model and parameter spaces | |
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| Markov chain for supermodels | |
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| Markov chain with jumps | |
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| Further issues related to RJMCMC algorithms | |
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| Convergence acceleration | |
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| Alterations to the chain | |
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| Alterations to the equilibrium distribution | |
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| Auxiliary variables | |
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| Exercises | |
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| References | |
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| Author index | |
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| Subject index | |