The Use of a Single Pseudo-Sample in Approximate Bayesian Computation

Understand

We analyze the computational efficiency of approximate Bayesian computation (ABC), which approximates a likelihood function by drawing pseudo-samples from the associated model.

• For the rejection sampling version of ABC, it is known that multiple pseudo-samples cannot substantially increase (and can substantially decrease) the efficiency of the algorithm as compared to employing a high-variance estimate based on a single pseudo-sample.
• We show that this conclusion also holds for a Markov chain Monte Carlo version of ABC, implying that it is unnecessary to tune the number of pseudo-samples used in ABC-MCMC.
• This conclusion is in contrast to particle MCMC methods, for which increasing the number of particles can provide large gains in computational efficiency.