Probability matching priors : higher order asymptotics 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. TOC:Introduction and the Shrinkage Argument * Matching Priors forPosterior Quantiles* Matching Priors for Distribution Functions * Matching Priors for Highest Posterior Density Regions * Matching Priors for Other Credible Regions * Matching Priors for Prediction