ABSTRACT
This chapter gives an overview of recent work on the asymptotics of approximate Bayesian computation (ABC). It reviews results on the behaviour of the ABC posterior, the ABC posterior mean, and Monte Carlo estimates of this mean as n → ∞. The chapter accepts a much larger ABC posterior variance for the same width of the region in which the summary statistics. It suggests choosing the number of summary statistics to be close to, or equal to, the number of parameters and choosing a distance for measuring the discrepancy in summary statistics that is based on the variance of the summary statistics. The chapter considers the limiting form of the ABC posterior and the frequentist asymptotic distribution of the ABC posterior. The identifiability condition on the binding function is used to ensure that concentration of accepted summaries around b results in ABC posterior concentration around θ0.
