On the use of ABC-MCMC with inflated tolerance and post-correction
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Approximate Bayesian computation (ABC) allows for inference of complicated probabilistic models with intractable likelihoods using model simulations. The ABC Markov chain Monte Carlo (MCMC) inference is often sensitive to the tolerance parameter: low tolerance leads to poor mixing and large tolerance entails excess bias. We consider an approach using a relatively large tolerance for the ABC-MCMC to ensure sufficient mixing, and post-processing the output of ABC-MCMC leading to estimators for a range of finer tolerances. We introduce an approximate confidence interval for the related post-corrected estimators, which can be calculated from any run of ABC-MCMC, with little extra cost. We propose an adaptive ABC-MCMC, which finds a `balanced' tolerance level automatically, based on acceptance rate optimisation. Tolerance adaptation, combined with proposal covariance adaptation, leads to an easy-to-use adaptive ABC-MCMC, with subsequent post-correction over a range of tolerances. Our experiments show that post-processing based estimators can perform better than direct ABC-MCMC, that our confidence intervals are reliable, and that our adaptive ABC-MCMC leads to reliable inference with little user specification.
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