Probability matching priors, ensuring frequentist validity of posterior credible sets up to the desired order of asymptotics, are of substantial current interest. They can form the basis of an objective Bayesian analysis. In addition, they provide a route for obtaining accurate frequentist confidence sets, which are meaningful also to a Bayesian. This monograph presents, for the first time in book form, an up-to-date and comprehensive account of probability matching priors addressing the problems of both estimation and prediction. Apart from being useful to researchers, it can be the core of a one-semester graduate course in Bayesian asymptotics.
Gauri Sankar Datta is a professor of statistics at the University of Georgia. He has published extensively in the fields of Bayesian analysis, likelihood inference, survey sampling, and multivariate analysis.
Rahul Mukerjee is a professor of statistics at the Indian Institute of Management Calcutta. He co-authored three other research monographs, including "A Calculus for Factorial Arrangements" in this series. A fellow of the Institute of Mathematical Statistics, Dr. Mukerjee is on the editorial boards of several international journals.
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.
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.
