ABC with inflated tolerance

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For the last One World ABC seminar of the year 2020, this coming Thursday, Matti Vihola is speaking from Finland on his recent Biometrika paper “On the use of ABC-MCMC with inflated tolerance and post-correction”. To attend the talk, all is required is a registration on the seminar webpage.

The Markov chain Monte Carlo (MCMC) implementation of ABC is often sensitive to the tolerance parameter: low tolerance leads to poor mixing and large tolerance entails excess bias. We propose an approach that involves using a relatively large tolerance for the MCMC sampler to ensure sufficient mixing, and post-processing of the output which leads to estimators for a range of finer tolerances. We introduce an approximate confidence interval for the related post-corrected estimators and propose an adaptive ABC-MCMC algorithm, which finds a balanced tolerance level automatically based on acceptance rate optimization. Our experiments suggest that post-processing-based estimators can perform better than direct MCMC targeting a fine tolerance, that our confidence intervals are reliable, and that our adaptive algorithm can lead to reliable inference with little user specification.

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