Summary Statistics in Approximate Bayesian Computation

Abstract: This document is due to appear as a chapter of the forthcoming Handbook of Approximate Bayesian Computation (ABC) edited by S. Sisson, Y. Fan, and M. Beaumont. Since the earliest work on ABC, it has been recognised that using summary statistics is essential to produce useful inference results. This is because ABC suffers from a curse of dimensionality effect, whereby using high dimensional inputs causes large approximation errors in the output. It is therefore crucial to find low dimensional summaries which are informative about the parameter inference or model choice task at hand. This chapter reviews the methods which have been proposed to select such summaries, extending the previous review paper of Blum et al. (2013) with recent developments. Related theoretical results on the ABC curse of dimensionality and sufficiency are also discussed.