Approximate Bayesian computation with composite score functions

Abstract

Both Approximate Bayesian Computation (ABC) and composite likelihood methods are useful for Bayesian and frequentist inference, respectively, when the likelihood function is intractable. We propose to use composite likelihood score functions as summary statistics in ABC in order to obtain accurate approximations to the posterior distribution. This is motivated by the use of the score function of the full likelihood, and extended to general unbiased estimating functions in complex models. Moreover, we show that if the composite score is suitably standardised, the resulting ABC procedure is invariant to reparameterisations and automatically adjusts the curvature of the composite likelihood, and of the corresponding posterior distribution. The method is illustrated through examples with simulated data, and an application to modelling of spatial extreme rainfall data is discussed.

Robust approximate Bayesian inference

“…The class of M-estimators is wide and includes a variety of well-known estimators. For example, it includes the maximum likelihood estimator (MLE), the maximum composite likelihood estimator (see, e.g., Ruli et al, 2016, and references therein) and the scoring rule estimator (see e.g. Dawid et al, 2016, and references therein).…”

Approximate Bayesian Computation: A Survey on Recent Results

“…In particular, the data-points are not iid. To bypass this difficulty, [43] resort instead to a composite likelihood formulation [57], approximating for instance a likelihood by a product of pairwise likelihoods over all pairs of genes. In Kingman's coalescent theory [58], the pairwise likelihoods can indeed be expressed in closed form.…”

“…In connection with [43] and their application in population genetics, [57] advocate the use of composite score functions for ABC. While the paper provides a survey of composite likelihood methods, the core idea of the paper is to use the score function (of the composite likelihood) as the summary statistic,…”

ABC model selection for spatial extremes models applied to South Australian maximum temperature data

“…The first application of ABC methods in an extremes context is Bortot et al (2007), where an MCMC ABC algorithm is used for stereological extremes. Subsequent ABC work has focused on spatial extremes (Erhardt and Smith, 2012;Barthelmé et al, 2015;Prangle, 2016;Ruli et al, 2016;Hainy et al, 2016). Barthelmé et al (2015), Prangle (2016) and Ruli et al (2016) use spatial extremes examples to illustrate the performance of their proposed ABC methods for parameter estimation, where the common goal is to alleviate the high computational burden that ABC methods for spatial extremes entail.…”

“…Subsequent ABC work has focused on spatial extremes (Erhardt and Smith, 2012;Barthelmé et al, 2015;Prangle, 2016;Ruli et al, 2016;Hainy et al, 2016). Barthelmé et al (2015), Prangle (2016) and Ruli et al (2016) use spatial extremes examples to illustrate the performance of their proposed ABC methods for parameter estimation, where the common goal is to alleviate the high computational burden that ABC methods for spatial extremes entail. A different perspective of using ABC methods for spatial extremes applications is provided by Hainy et al (2016), where the optimal design for estimating the spatial dependence structure of extremes is sought.…”