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The likelihood-free sequential Approximate Bayesian Computation (ABC)algorithms, are increasingly popular inference tools for complex biologicalmodels. Such algorithms proceed by constructing a succession of probabilitydistributions over the parameter space conditional upon the simulated datalying in an $\epsilon$--ball around the observed data, for decreasing values ofthe threshold $\epsilon$. While in theory, the distributions (starting from asuitably defined prior) will converge towards the unknown posterior as$\epsilon$ tends to zero, the exact sequence of thresholds can impact upon thecomputational efficiency and success of a particular application. Inparticular, we show here that the current preferred method of choosingthresholds as a pre-determined quantile of the distances between simulated andobserved data from the previous population, can lead to the inferred posteriordistribution being very different to the true posterior. Threshold selectionthus remains an important challenge. Here we propose an automated and adaptivemethod that allows us to balance the need to minimise the threshold withcomputational efficiency. Moreover, our method which centres around predictingthe threshold - acceptance rate curve using the unscented transform, enables usto avoid local minima - a problem that has plagued previous threshold schemes.

Optimizing Threshold - Schedules for Approximate Bayesian Computation Sequential Monte Carlo Samplers: Applications to Molecular Systems