Dr Wentao Li

Optimal combination of composite likelihoods using approximate Bayesian computation with application to state-space models

The composite likelihood (CL) method provides approximate inference when the likelihood is intractable but marginal likelihoods for small subsets of the data can be evaluated easily. Its application is limited by the arbitrary weighting scheme of sub-likelihoods and the lack of calibration of CL-based posterior uncertainty. This work shows that they can be properly addressed by approximate Bayesian computation (ABC) with multiple composite score functions as the summary statistics. First, the summary-based posterior distribution gives optimal Godambe information among a wide class of estimators defined by estimating functions. Second, when marginal likelihoods have no closed form, ABC is computationally feasible using a novel approach to estimate marginal scores of all pseudo datasets using a Monte Carlo sample with size N. Theoretical results show that the additional noise can be negligible with fixed N, therefore the computational cost is O(n), much lower than the typical cost O(n2) of pseudo-marginal methods. Third, an adaptive scheme is proposed to choose the component composite scores, supported by results on asymptotic behaviour of ABC with
summary statistics having heterogeneous convergence rates. Numerical studies show that the new method significantly outperforms existing Bayesian composite likelihood methods and achieves similar statistical efficiency to that of full likelihood. This is a joint work with Rosabeth White (Newcastle) and Dennis Prangle (Bristol).