ABC, anytime!

Last June, Alix Marie d’Avigneau, Sumeet Singh, and Lawrence Murray arXived a paper on anytime ABC I intended to review right away but that sat till now on my virtual desk (and pile of to-cover-arXivals!). The notion of anytime MCMC was already covered in earlier ‘Og entries, but this anytime ABC version bypasses the problem of asynchronicity, namely, “randomly varying local move completion times when parallel tempering is implemented on a multi-processor computing resource”. The different temperatures are replaced by different tolerances in ABC. Since switches between tolerances are natural if a proposal for a given tolerance ε happens to be eligible for a lower tolerance ε’. And accounting for the different durations required to simulate a proposal under different tolerances to avoid the induced bias in the stationary distributions. Or the wait for other processors to complete their task. A drawback with the approach stands in calibrating the tolerance levels in advance (or via preliminary runs that may prove costly).