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| Statistical Preliminaries | |
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| Common Models | |
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| Exponential Families | |
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| Location-Scale Families | |
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| Regular Family | |
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| Likelihood Function | |
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| Sufficient Statistics and Ancillary Statistics | |
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| Three Basic Problems of Inference in Classical Statistics | |
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| Point Estimates | |
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| Testing Hypotheses | |
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| Interval Estimation | |
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| Inference as a Statistical Decision Problem | |
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| The Changing Face of Classical Inference | |
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| Exercises | |
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| Bayesian Inference and Decision Theory | |
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| Subjective and Frequentist Probability | |
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| Bayesian Inference | |
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| Advantages of Being a Bayesian | |
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| Paradoxes in Classical Statistics | |
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| Elements of Bayesian Decision Theory | |
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| Improper Priors | |
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| Common Problems of Bayesian Inference | |
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| Point Estimates | |
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| Testing | |
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| Credible Intervals | |
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| Testing of a Sharp Null Hypothesis Through Credible Intervals | |
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| Prediction of a Future Observation | |
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| Examples of Cox and Welch Revisited | |
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| Elimination of Nuisance Parameters | |
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| A High-dimensional Example | |
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| Exchangeability | |
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| Normative and Descriptive Aspects of Bayesian Analysis, Elicitation of Probability | |
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| Objective Priors and Objective Bayesian Analysis | |
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| Other Paradigms | |
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| Remarks | |
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| Exercises | |
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| Utility, Prior, and Bayesian Robustness | |
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| Utility, Prior, and Rational Preference | |
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| Utility and Loss | |
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| Rationality Axioms Leading to the Bayesian Approach | |
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| Coherence | |
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| Bayesian Analysis with Subjective Prior | |
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| Robustness and Sensitivity | |
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| Classes of Priors | |
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| Conjugate Class | |
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| Neighborhood Class | |
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| Density Ratio Class | |
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| Posterior Robustness: Measures and Techniques | |
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| Global Measures of Sensitivity | |
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| Belief Functions | |
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| Interactive Robust Bayesian Analysis | |
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| Other Global Measures | |
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| Local Measures of Sensitivity | |
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| Inherently Robust Procedures | |
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| Loss Robustness | |
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| Model Robustness | |
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| Exercises | |
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| Large Sample Methods | |
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| Limit of Posterior Distribution | |
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| Consistency of Posterior Distribution | |
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| Asymptotic Normality of Posterior Distribution | |
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| Asymptotic Expansion of Posterior Distribution | |
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| Determination of Sample Size in Testing | |
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| Laplace Approximation | |
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| Laplace's Method | |
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| Tierney-Kadane-Kass Refinements | |
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| Exercises | |
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| Choice of Priors for Low-dimensional Parameters | |
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| Different Methods of Construction of Objective Priors | |
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| Uniform Distribution and Its Criticisms | |
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| Jeffreys Prior as a Uniform Distribution | |
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| Jeffreys Prior as a Minimizer of Information | |
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| Jeffreys Prior as a Probability Matching Prior | |
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| Conjugate Priors and Mixtures | |
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| Invariant Objective Priors for Location-Scale Families | |
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| Left and Right Invariant Priors | |
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| Properties of the Right Invariant Prior for Location-Scale Families | |
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| General Group Families | |
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| Reference Priors | |
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| Reference Priors Without Entropy Maximization | |
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| Objective Priors with Partial Information | |
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| Discussion of Objective Priors | |
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| Exchangeability | |
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| Elicitation of Hyperparameters for Prior | |
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| A New Objective Bayes Methodology Using Correlation | |
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| Exercises | |
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| Hypothesis Testing and Model Selection | |
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| Preliminaries | |
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| BIC Revisited | |
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| P-value and Posterior Probability of H[subscript 0] as Measures of Evidence Against the Null | |
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| Bounds on Bayes Factors and Posterior Probabilities | |
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| Introduction | |
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| Choice of Classes of Priors | |
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| Multiparameter Problems | |
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| Invariant Tests | |
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| Interval Null Hypotheses and One-sided Tests | |
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| Role of the Choice of an Asymptotic Framework | |
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| Comparison of Decisions via P-values and Bayes Factors in Bahadur's Asymptotics | |
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| Pitman Alternative and Rescaled Priors | |
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| Bayesian P-value | |
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| Robust Bayesian Outlier Detection | |
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| Nonsubjective Bayes Factors | |
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| The Intrinsic Bayes Factor | |
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| The Fractional Bayes Factor | |
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| Intrinsic Priors | |
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| Exercises | |
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| Bayesian Computations | |
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| Analytic Approximation | |
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| The E-M Algorithm | |
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| Monte Carlo Sampling | |
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| Markov Chain Monte Carlo Methods | |
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| Introduction | |
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| Markov Chains in MCMC | |
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| Metropolis-Hastings Algorithm | |
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| Gibbs Sampling | |
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| Rao-Blackwellization | |
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| Examples | |
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| Convergence Issues | |
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| Exercises | |
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| Some Common Problems in Inference | |
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| Comparing Two Normal Means | |
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| Linear Regression | |
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| Logit Model, Probit Model, and Logistic Regression | |
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| The Logit Model | |
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| The Probit Model | |
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| Exercises | |
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| High-dimensional Problems | |
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| Exchangeability, Hierarchical Priors, Approximation to Posterior for Large p, and MCMC | |
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| MCMC and E-M Algorithm | |
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| Parametric Empirical Bayes | |
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| PEB and HB Interval Estimates | |
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| Linear Models for High-dimensional Parameters | |
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| Stein's Frequentist Approach to a High-dimensional Problem | |
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| Comparison of High-dimensional and Low-dimensional Problems | |
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| High-dimensional Multiple Testing (PEB) | |
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| Nonparametric Empirical Bayes Multiple Testing | |
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| False Discovery Rate (FDR) | |
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| Testing of a High-dimensional Null as a Model Selection Problem | |
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| High-dimensional Estimation and Prediction Based on Model Selection or Model Averaging | |
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| Discussion | |
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| Exercises | |
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| Some Applications | |
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| Disease Mapping | |
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| Bayesian Nonparametric Regression Using Wavelets | |
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| A Brief Overview of Wavelets | |
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| Hierarchical Prior Structure and Posterior Computations | |
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| Estimation of Regression Function Using Dirichlet Multinomial Allocation | |
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| Exercises | |
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| Common Statistical Densities | |
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| Continuous Models | |
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| Discrete Models | |
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| Birnbaum's Theorem on Likelihood Principle | |
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| Coherence | |
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| Microarray | |
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| Bayes Sufficiency | |
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| References | |
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| Author Index | |
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| Subject Index | |