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 several examples.
翻译:无隐隐隐性方法是用来推断可以模拟但相应可能性难以解决的隐含模型的基本工具。然而,常见的无概率方法并不十分适合大量的模型参数。 高维无概率推断的一个很有希望的方法是,仅以被认为对低维组成部分具有信息性的简要统计为基础,对低维边边际后遗物进行估计,然后以某种方式将低维近似值合并在一起。在本文中,我们证明,这种低维近似近似在似乎不直观的简要统计选择的实际操作中可能出乎意料地差。我们描述一种理想化的低维生摘要统计,原则上适合边际估计。然而,对理想化选择的直接接近在实践中是困难的。因此,我们建议一种边际估计的替代方法,即仅对低维系组成部分部分进行统计,而这种低维度简要统计最初的选择可能只对边远的后继地点有所了解,因此,新的方法可以改善实绩,首先粗略地对近似近似性进行定位,使用所有摘要统计,以确保全球直观性统计的准确度估计性,然后是采用低维统计的第二步骤。我们度统计的精确度统计,可以表明,在低维统计中以若干次的精确度统计,然后采用。