@article{Marin2011RelevantSF,
title={Relevant statistics for Bayesian model choice},
author={J. Marin and N. Pillai and C. Robert and J. Rousseau},
journal={Quality Engineering},
year={2011},
volume={60},
pages={349-352}
}

The choice of the summary statistics used in Bayesian inference and in particular in ABC algorithms has bearings on the validation of the resulting inference. Those statistics are nonetheless customarily used in ABC algorithms without consistency checks. We derive necessary and sufficient conditions on summary statistics for the corresponding Bayes factor to be convergent, namely to asymptotically select the true model. Those conditions, which amount to the expectations of the summary… CONTINUE READING