Abstract

This chapter aims to give an overview of recent work on the asymptotics of approximate Bayesian computation (ABC). By asymptotics here we mean how does the ABC posterior, or point estimates obtained by ABC, behave in the limit as we have more data? The chapter summarises results from three papers, Li and Fearnhead (2018a), Frazier et al. (2016) and Li and Fearnhead (2018b). The presentation in this chapter is deliberately informal, with the hope of conveying both the intuition behind the theoretical results from these papers and the practical consequences of this theory. As such, we will not present all the technical conditions for the results we give: The Interested reader should consult the relevant papers for these, and the results we state should be interpreted as holding under appropriate regularity conditions.