| 1 Introduction and the Shrinkage Argument 1.1 Scope of the monograph 1.2 The shrinkage argument 1.3 An example 2 Matching Priors for Posterior Quantiles 2.1 Introduction 2.2 Setup, notation and preliminaries 2.3 Posterior quantile 2.4 Characterization of matching priors 2.5 Special cases 2.5.1 The casep=l 2.5.2 The casep=2 2.5.3 Orthogonal parameterization 2.5.4 Two general classes of models 2.6 Further examples 2.7 Invariance 2.8 General parametric functions and Bayesian tolerance limits . 2.8.1 General parametric functions 2.8.2 Bayesian tolerance limits 2.9 Matching alternative coverage probabilities 2.10 Propriety of posteriors 3 Matching Priors for Distribution Functions 3.1 Introduction 3.2 C.d.f. matching priors for a single parametric function 3.2.1 Scalar interest parameter 3.2.2 Single parametric function 3.3 C.d.f. matching priors for multiple parametric functions 3.3.1 Multiple parametric functions 3.3.2 Regression residuals approach to c.d.f, matching 4 Matching Priors for Highest Posterior Density Regions.. 4.1 Introduction 4.2 Explicit form of an HPD region 4.3 Characterization of HPD matching priors 4.4 Results in the presence of nuisance parameters 5 Matching Priors for Other Credible Regions 5.1 Introduction 5.2 Matching priors associated with the LR statistic 5.2.1 Credible region via the LR statistic 5.2.2 Matching priors 5.2.3 Results in the presence of nuisance parameters 5.3 Frequentist Bartlett adjustment 5.4 Matching priors associated with Rao's score and Wald's statistics 5.5 Perturbed ellipsoidal and HPD regions 5.5.1 Perturbed ellipsoidal region 5.5.2 Perturbed HPD region 6 Matching Priors for Prediction 6.1 Introduction 6.2 Matching priors for prediction: no auxiliary variable 6.2.1 Preliminaries: expansion for the predictive density ... 6.2.2 Frequentist validity of posterior quantiles 6.2.3 Frequentist validity of highest posterior predictive density regions 6.2.4 Prediction intervals 6.3 Matching priors for predicting a dependent variable in regression models 6.3.1 Posterior predictive density 6.3.2 Matching conditions 6.3.3 Examples: applications to regression models 6.4 Concluding remarks References Index |
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