A0405
Title: Improving the accuracy of marginal approximations in likelihood-free inference via localisation
Authors: Christopher Drovandi - Queensland University of Technology (Australia)
David Nott - National University of Singapore (Singapore) [presenting]
David Frazier - Monash University (Australia)
Abstract: Likelihood-free methods are an essential tool for performing inference for implicit models which can be simulated but for which the corresponding likelihood is intractable. However, common likelihood-free methods do not scale well to a large number of model parameters. A promising approach to high-dimensional likelihood-free inference involves estimating low-dimensional marginal posteriors by conditioning only on summary statistics believed to be informative for the low-dimensional component and then combining the low-dimensional approximations in some way. It is demonstrated that such low-dimensional approximations can be surprisingly poor in practice for seemingly intuitive summary statistic choices. Given an initial choice of low-dimensional summary statistic that might only be informative about a marginal posterior location, a new method which improves performance is described by first crudely localising the posterior approximation using all the summary statistics to ensure global identifiability, followed by a second step that hones in on an accurate low-dimensional approximation using the low-dimensional summary statistic. It is shown that the posterior this approach targets can be represented as a logarithmic pool of posterior distributions based on the low-dimensional and full summary statistics, respectively.
