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Preface to the Third Edition | |
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Approaches for statistical inference | |
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Introduction | |
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Motivating vignettes | |
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Personal probability | |
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Missing data | |
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Bioassay | |
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Attenuation adjustment | |
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Defining the approaches | |
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The Bayes-frequentist controversy | |
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Some basic Bayesian models | |
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A Gaussian/Gaussian (normal/normal) model | |
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A beta/binomial model | |
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Exercises | |
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The Bayes approach | |
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Introduction | |
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Prior distributions | |
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Elicited priors | |
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Conjugate priors | |
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Noninformative priors | |
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Other prior construction methods | |
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Bayesian inference | |
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Point estimation | |
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Interval estimation | |
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Hypothesis testing and Bayes factors | |
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Hierarchical modeling | |
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Normal linear models | |
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Effective model size and the DIC criterion | |
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Model assessment | |
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Diagnostic measures | |
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Model averaging | |
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Nonparametric methods | |
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Exercises | |
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Bayesian computation | |
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Introduction | |
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Asymptotic methods | |
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Normal approximation | |
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Laplace's method | |
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Noniterative Monte Carlo methods | |
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Direct sampling | |
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Indirect methods | |
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Markov chain Monte Carlo methods | |
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Gibbs sampler | |
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Metropolis-Hastings algorithm | |
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Slice sampler | |
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Hybrid forms, adaptive MCMC, and other algorithms | |
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Variance estimation | |
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Convergence monitoring and diagnosis | |
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Exercises | |
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Model criticism and selection | |
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Bayesian modeling | |
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Linear models | |
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Nonlinear models | |
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Binary data models | |
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Bayesian robustness | |
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Sensitivity analysis | |
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Prior partitioning | |
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Model assessment | |
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Bayes factors via marginal density estimation | |
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Direct methods | |
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Using Gibbs sampler output | |
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Using Metropolis-Hastings output | |
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Bayes factors via sampling over the model space | |
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Product space search | |
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"Metropolized" product space search | |
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Reversible jump MCMC | |
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Using partial analytic structure | |
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Other model selection methods | |
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Penalized likelihood criteria: AIC, BIC, and DIC | |
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Predictive model selection | |
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Exercises | |
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The empirical Bayes approach | |
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Introduction | |
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Parametric EB (PEB) point estimation | |
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Gaussian/Gaussian models | |
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Computation via the EM algorithm | |
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EB performance of the PEB | |
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Stein estimation | |
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Nonparametric EB (NPEB) point estimation | |
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Compound sampling models | |
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Simple NPEB (Robbins' method) | |
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Interval estimation | |
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Morris' approach | |
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Marginal posterior approach | |
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Bias correction approach | |
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Bayesian processing and performance | |
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Univariate stretching with a two-point prior | |
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Multivariate Gaussian model | |
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Frequentist performance | |
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Gaussian/Gaussian model | |
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Beta/binomial model | |
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Empirical Bayes performance | |
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Point estimation | |
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Interval estimation | |
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Exercises | |
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Bayesian design | |
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Principles of design | |
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Bayesian design for frequentist analysis | |
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Bayesian design for Bayesian analysis | |
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Bayesian clinical trial design | |
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Classical versus Bayesian trial design | |
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Bayesian assurance | |
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Bayesian indifference zone methods | |
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Other Bayesian approaches | |
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Extensions | |
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Applications in drug and medical device trials | |
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Binary endpoint drug trial | |
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Cox regression device trial with interim analysis | |
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Exercises | |
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Special methods and models | |
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Estimating histograms and ranks | |
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Bayesian ranking | |
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Histogram and triple goal estimates | |
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Robust prior distributions | |
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Order restricted inference | |
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Longitudinal data models | |
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Continuous and categorical time series | |
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Survival analysis and frailty models | |
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Statistical models | |
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Treatment effect prior determination | |
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Computation and advanced models | |
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Sequential analysis | |
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Model and loss structure | |
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Backward induction | |
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Forward sampling | |
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Spatial and spatio-temporal models | |
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Point source data models | |
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Regional summary data models | |
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Exercises | |
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Case studies | |
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Analysis of longitudinal AIDS data | |
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Introduction and background | |
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Modeling of longitudinal CD4 counts | |
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CD4 response to treatment at two months | |
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Survival analysis | |
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Discussion | |
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Robust analysis of clinical trials | |
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Clinical background | |
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Interim monitoring | |
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Prior robustness and prior scoping | |
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Sequential decision analysis | |
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Discussion | |
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Modeling of infectious diseases | |
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Introduction and data | |
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Stochastic compartmental model | |
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Parameter estimation and model building | |
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Results | |
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Discussion | |
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Appendices | |
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Distributional catalog | |
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Discrete | |
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Univariate | |
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Multivariate | |
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Continuous | |
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Univariate | |
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Multivariate | |
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Decision theory | |
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Introduction | |
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Risk and admissibility | |
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Unbiased rules | |
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Bayes rules | |
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Minimax rules | |
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Procedure evaluation and other unifying concepts | |
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Mean squared error (MSE) | |
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The variance-bias tradeoff | |
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Other loss functions | |
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Generalized absolute loss | |
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Testing with a distance penalty | |
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A threshold loss function | |
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Multiplicity | |
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Multiple testing | |
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Additive loss | |
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Non-additive loss | |
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Exercises | |
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Answers to selected exercises | |
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References | |
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Author index | |
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Subject index | |