Highest posterior density regions with approximate frequentist validity: The role of data-dependent priors

For the general multiparameter case, we consider the problem of ensuring frequentist validity of highest posterior density regions with margin of error o(n(-1)), where n is the sample size. The role of data-dependent priors is investigated and it is seen that the resulting probability matching condition readily allows solutions, in contrast to what happens with data-free priors. Moreover, use of data-dependent priors is seen to be helpful even for models, such as mixture models, where closed form expressions for the expected information elements do not exist. (c) 2010 Elsevier B.V. All rights reserved.