Probability Matching Priors: Higher Order Asymptotics

"...This monograph will likely prove valuable in promoting probability matching priors among the practitioners and applied statisticians." Journal of the American Statistical Association, March 2006

• 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.