Probability Matching Priors: Higher Order Asymptotics

This is the first book on the topic of probability matching priors. The topic has been of substantial current interest with articles in top journals. This book will be the only source covering the most important developments in this area in a single volume.

The first book on the topic of probability matching priors

Inhalt
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.- 2.6 Further examples.- 2.7 Invariance.- 2.8 General parametric functions and 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.- 3.3 C.d.f matching priors for multiple parametric functions.- 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.- 5.3 Frequentist Bartlett adjustment.- 5.4 Matching priors associated with Rao's score and Wald's statistics.- 5.5 Perturbed ellipsoidal and HPD regions.- 6 Matching Priors for Prediction.- 6.1 Introduction.- 6.2 Matching priors for prediction: no auxiliary variable.- 6.3 Matching priors for predicting a dependent variable in regression models1.- 6.4 Concluding remarks.- References.