One Pseudo-Sample is Enough in Approximate Bayesian Computation MCMC

We analyze the efficiency of approximate Bayesian computation (ABC), which approximates the likelihood function by drawing pseudo-samples from the model. We address both the rejection sampling and Markov chain Monte Carlo versions of ABC, presenting the surprising result that multiple pseudo-samples typically do not improve the efficiency of the algorithm as compared to employing a high-variance estimate computed using a single pseudo-sample. This result means that it is unnecessary to tune the number of pseudo-samples, and is in contrast to particle MCMC methods, in which many particles are often required to provide sufficient accuracy.