Automatic Tolerance Selection for Approximate Bayesian Computation

Approximate Bayesian Computation (ABC) provides Monte Carlo inference of the posterior distribution, even for models with intractable likelihoods. The quality of ABC inference relies on the choice of tolerance for the distance between the observed data summary statistics, and the summary statistics of pseudo-data simulated from the given model likelihood. However, there is no fully automatic method to select the best tolerance level, and finding the best tolerance level can be non-trivial and time consuming. This article introduces a fast, simple, and automatic bootstrap estimator of the tolerance, with the aim of making ABC a more automatic and broadly applicable Bayesian data analysis method. The tolerance estimate can be input into any suitable Monte Carlo algorithm to sample and infer the target approximate posterior distribution. This tolerance estimator can be still quickly computed even for any model for which it is computationally costly to sample directly from its exact likelihood, if its summary statistics are specified as consistent point-estimator of the model parameters with estimated asymptotic normal distribution that can be easily sampled from. The new tolerance estimator is illustrated through a simulation study of tractable models and intractable likelihood models, and through the Bayesian intractable likelihood analysis of a real 23,000-node network dataset involving stochastic search model selection