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| Preface | |
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| Introduction to Bayesian Statistics | |
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| The Frequentist Approach to Statistics | |
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| The Bayesian Approach to Statistics | |
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| Comparing Likelihood and Bayesian Approaches to Statistics | |
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| Computational Bayesian Statistics | |
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| Purpose and Organization of This Book | |
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| Monte Carlo Sampling from the Posterior | |
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| Acceptance-Rejection-Sampling | |
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| Sampling-Importance-Resampling | |
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| Adaptive-Rejection-Sampling from a Log-Concave Distribution | |
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| Why Direct Methods Are Inefficient for High-Dimension Parameter Space | |
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| Bayesian Inference | |
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| Bayesian Inference from the Numerical Posterior | |
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| Bayesian Inference from Posterior Random Sample | |
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| Bayesian Statistics Using Conjugate Priors | |
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| One-Dimensional Exponential Family of Densities | |
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| Distributions for Count Data | |
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| Distributions for Waiting Times | |
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| Normally Distributed Observations with Known Variance | |
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| Normally Distributed Observations with Known Mean | |
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| Normally Distributed Observations with Unknown Mean and Variance | |
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| Multivariate Normal Observations with Known Covariance Matrix | |
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| Observations from Normal Linear Regression Model | |
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| Appendix: Proof of Poisson Process Theorem | |
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| Markov Chains | |
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| Stochastic Processes | |
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| Markov Chains | |
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| Time-Invariant Markov Chains with Finite State Space | |
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| Classification of States of a Markov Chain | |
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| Sampling from a Markov Chain | |
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| Time-Reversible Markov Chains and Detailed-Balance | |
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| Markov Chains with Continuous State Space | |
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| Markov Chain Monte Carlo Sampling from Posterior | |
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| Metropolis-Hastings Algorithm for a Single Parameter | |
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| Metropolis-Hastings Algorithm for Multiple Parameters | |
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| Blockwise Metropolis Hastings Algorithm | |
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| Gibbs Sampling | |
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| Summary | |
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| Statistical Inference from a Markov Chain Monte Carlo Sample | |
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| Mixing Properties of the Chain | |
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| Finding a Heavy-Tailed Matched Curvature Candidate Density | |
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| Obtaining An Approximate Random Sample For Inference | |
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| Appendix: Procedure for Finding the Matched Curvature Candidate Density for a Multivariate Parameter | |
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| Logistic Regression | |
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| Logistic Regression Model | |
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| Computational Bayesian Approach to the Logistic Regression Model | |
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| Modelling with the Multiple Logistic Regression Model | |
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| Poisson Regression and Proportional Hazards Model | |
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| Poisson Regression Model | |
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| Computational Approach to Poisson Regression Model | |
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| The Proportional Hazards Model | |
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| Computational Bayesian Approach to Proportional Hazards Model | |
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| Gibbs Sampling and Hierarchical Models | |
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| Gibbs Sampling Procedure | |
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| The Gibbs Sampler for the Normal Distribution | |
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| Hierarchical Models and Gibbs Sampling | |
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| Modelling Related Populations with Hierarchical Models | |
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| Appendix: Proof That Improper Jeffrey's Prior Distribution for the Hypervariance Can Lead to an Improper Posterior | |
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| Going Forward with Markov Chain Monte Carlo | |
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| Using the Included Minitab Macros | |
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| Using the Included R Functions | |
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| References | |
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| Topic Index | |