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Preface | |
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Preface to the First Edition | |
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A Bayesian Hall of Fame | |
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Foundations and Principles | |
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Background | |
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Rationale for Bayesian Inference and Preliminary Views of Bayes' Theorem | |
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Example: Observing a Desired Experimental Effect | |
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Thomas Bayes | |
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Brief Descriptions of the Chapters | |
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A Bayesian Perspective on Probability | |
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Introduction | |
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Types of Probability | |
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Coherence | |
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Operationalizing Subjective Probability Beliefs | |
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Calibration of Probability Assessors | |
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Comparing Probability Definitions | |
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The Likelihood Function | |
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Introduction | |
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Likelihood Function | |
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Likelihood Principle | |
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Likelihood Principle and Conditioning | |
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Likelihood and Bayesian Inference | |
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Development of the Likelihood Function Using Histograms and Other Graphical Methods | |
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Bayes' Theorem | |
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Introduction | |
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General Form of Bayes' Theorem for Events | |
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Bayes' Theorem for Discrete Data and Discrete Parameter | |
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Bayes' Theorem for Continuous Data and Discrete Parameter | |
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Bayes' Theorem for Discrete Data and Continuous Parameter | |
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Bayes' Theorem for Continuous Data and Continuous Parameter | |
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Prior Distributions | |
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Introduction | |
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Objective and Subjective Prior Distributions | |
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(Univariate) Prior Distributions for a Single Parameter | |
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Prior Distributions for Vector and Matrix Parameters | |
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Data-Mining Priors | |
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Wrong Priors | |
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Numerical Implementation of the Bayesian Paradigm | |
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Markov Chain Monte Carlo Methods | |
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Introduction | |
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Metropolis-Hastings (M-H) Algorithm | |
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Multiple-Block M-H Algorithm | |
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Some Techniques Useful in MCMC Sampling | |
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Examples | |
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Comparing Models Using MCMC Methods | |
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Large Sample Posterior Distributions and Approximations | |
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Introduction | |
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Large-Sample Posterior Distributions | |
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Approximate Evaluation of Bayesian Integrals | |
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Importance Sampling | |
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Bayesian Statistical Inference and Decision Making | |
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Bayesian Estimation | |
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Introduction | |
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Univariate (Point) Bayesian Estimation | |
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Multivariate (Point) Bayesian Estimation | |
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Interval Estimation | |
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Empirical Bayes' Estimation | |
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Robustness in Bayesian Estimation | |
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Bayesian Hypothesis Testing | |
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Introduction | |
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A Brief History of Scientific Hypothesis Testing | |
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Problems with Frequentist Methods of Hypothesis Testing | |
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Lindley's Vague Prior Procedure for Bayesian Hypothesis Testing | |
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Jeffreys' Procedure for Bayesian Hypothesis Testing | |
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Predictivism | |
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Introduction | |
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Philosophy of Predictivism | |
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Predictive Distributions/Comparing Theories | |
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Exchangeability | |
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De Finetti's Theorem | |
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The De Finetti Transform | |
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Predictive Distributions in Classification and Spatial and Temporal Analysis | |
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Bayesian Neural Nets | |
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Bayesian Decision Making | |
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Introduction | |
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Loss Functions | |
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Admissibility | |
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Models and Applications | |
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Bayesian Inference in the General Linear Model | |
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Introduction | |
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Simple Linear Regression | |
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Multivariate Regression Model | |
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Multivariate Analysis of Variance Model | |
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Bayesian Inference in the Multivariate Mixed Model | |
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Model Averaging | |
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Introduction | |
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Model Averaging and Subset Selection in Linear Regression | |
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Prior Distributions | |
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Posterior Distributions | |
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Choice of Hyperparameters | |
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Implementing BMA | |
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Examples | |
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Hierarchical Bayesian Modeling | |
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Introduction | |
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Fundamental Concepts and Nomenclature | |
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Applications and Examples | |
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Inference in Hierarchical Models | |
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Relationship to Non-Bayesian Approaches | |
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Computation for Hierarchical Models | |
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Software for Hierarchical Models | |
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Bayesian Factor Analysis | |
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Introduction | |
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Background | |
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Bayesian Factor Analysis Model for Fixed Number of Factors | |
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Choosing the Number of Factors | |
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Additional Model Considerations | |
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Bayesian Inference in Classification and Discrimination | |
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Introduction | |
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Likelihood Function | |
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Prior Density | |
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Posterior Density | |
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Predictive Density | |
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Posterior Classification Probability | |
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Example: Two Populations | |
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Second Guessing Undecided Respondents: An Application | |
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Extensions of the Basic Classification Problem | |
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Description of Appendices | |
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Bayes, Thomas | |
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Thomas Bayes. A Bibliographical Note | |
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Communication of Bayes' Essay to the Philosophical Transactions of the Royal Society of London | |
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An Essay Towards Solving a Problem in the Doctrine of Chances | |
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Applications of Bayesian Statistical Science | |
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Selecting the Bayesian Hall of Fame | |
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Solutions to Selected Exercises | |
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Bibliography | |
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Subject Index | |
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Author Index | |