The choice of the summary statistics in Bayesian inference and in particular in ABC algorithms is paramount to produce a valid outcome. We derive necessary and sufficient conditions on those statistics for the corresponding Bayes factor to be convergent, namely to asymptotically select the true...

We show that the fact that any uniformly minimum variance unbiased estimator (UMVUE) is uncorrelated with all unbiased estimators of zero implies certain conclusions of the Rao–Blackwell and Lehmann–Scheffe theorems. We also show that the conditional mean and variance of any UMVUE, given any...

This note gives a simple condition for the nonexistence of nontrivial ancillary statistics. The result shows that in sampling from a discrete exponential family with a regression model, usually there is no nontrivial ancillary statistic.