Improving the Accuracy of Marginal Approximations in Likelihood-Free Inference via Localization
针对高维无似然推断中边际后验近似效果差的问题，提出一种两步法：先用所有统计量粗定位确保全局可识别性，再用低维统计量精修，提升近似准确性。
Likelihood-free methods are an essential tool for performing inference for implicit models which can be simulated from, 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. In this paper, we demonstrate that such low-dimensional approximations can be surprisingly poor in practice for seemingly intuitive summary statistic choices. We describe an idealized low-dimensional summary statistic that is, in principle, suitable for marginal estimation. However, a direct approximation of the idealized choice is difficult in practice. We thus suggest an alternative approach to marginal estimation which is easier to implement and automate. Given an initial choice of low-dimensional summary statistic that might only be informative about a marginal posterior location, the new method improves performance 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. We show 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. The good performance of our method is illustrated in low to moderate dimensional examples. Computer code to implement the methods for the examples of this paper is available at https://github.com/cdrovandi/ABC-marginal-approximations. Supplementary materials including appendices for this article are available online.