Abstract

Likelihood-free methods are an established approach for performing approximate Bayesian inference for models with intractable likelihood functions. However, they can be computationally demanding. Bayesian synthetic likelihood (BSL) is a popular such method that approximates the likelihood function of the summary statistic with a known, tractable distribution—typically Gaussian—and then performs statistical inference using standard likelihood-based techniques. However, as the number of summary statistics grows, the number of model simulations required to accurately estimate the covariance matrix for this likelihood rapidly increases. This poses a significant challenge for the application of BSL, especially in cases where model simulation is expensive. In this article, we propose whitening BSL (wBSL)—an efficient BSL method that uses approximate whitening transformations to decorrelate the summary statistics at each algorithm iteration. We show empirically that this can reduce the number of model simulations required to implement BSL by more than an order of magnitude, without much loss of accuracy. We explore a range of whitening procedures and demonstrate the performance of wBSL on a range of simulated and real modeling scenarios from ecology and biology. Supplementary materials for this article are available online.

摘要

无似然方法是一种既定方法，用于对具有难以处理的似然函数的模型执行近似贝叶斯推理。但是，它们的计算要求可能很高。贝叶斯合成似然 (BSL) 是一种流行的此类方法，它使用已知的、易处理的分布（通常是高斯分布）近似汇总统计量的似然函数，然后使用标准的基于似然的技术进行统计推断。然而，随着汇总统计量的增加，准确估计这种可能性的协方差矩阵所需的模型模拟数量迅速增加。这对 BSL 的应用提出了重大挑战，尤其是在模型模拟成本高昂的情况下。在本文中，我们提出了白化 BSL (wBSL)——一种有效的 BSL 方法，它使用近似白化变换在每次算法迭代时对汇总统计信息进行去相关。我们凭经验表明，这可以将实现 BSL 所需的模型模拟数量减少一个数量级以上，而不会损失太多准确性。我们探索了一系列美白程序，并展示了 wBSL 在生态学和生物学的一系列模拟和真实建模场景中的性能。本文的补充材料可在线获取。我们探索了一系列美白程序，并展示了 wBSL 在生态学和生物学的一系列模拟和真实建模场景中的性能。本文的补充材料可在线获取。我们探索了一系列美白程序，并展示了 wBSL 在生态学和生物学的一系列模拟和真实建模场景中的性能。本文的补充材料可在线获取。