On invariant moment matching priors for Bayesian point prediction

This paper derives objective priors that asymptotically match the mean of the Bayesian predictive distribution with that of the frequentist plug-in predictive distribution. This moment matching criterion was originally proposed by Ghosh and Liu (2011, Sankhya A) for estimation problems; the resulting priors are referred to as moment matching priors. In the predictive context, while the derived priors take a slightly different form from those for estimation, they exhibit a desirable invariance property under one-to-one parameter transformations. This is a feature not typically attained in estimation frameworks. Furthermore, this study characterizes asymptotically unbiased priors for point prediction.