Bayesian Inference Using Synthetic Likelihood: Asymptotics and Adjustments
Bayesian Inference Using Synthetic Likelihood: Asymptotics and Adjustments
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DOI：
10.1080/01621459.2022.2086132
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发表时间：
2022-07-08
影响因子：
3.7
通讯作者：
Kohn, Robert
中科院分区：
文献类型：
--
作者：
Frazier, David T.;Nott, David J.;Kohn, Robert
在复杂的模型中实现贝叶斯推理通常在计算上具有挑战性，特别是当计算可能性很困难时。当可能性难以处理时，合成可能性是一种进行推理的方法，但从模型进行模拟是直接的。该方法通过将向量汇总统计量视为多变量正态分布来构造近似似然，其中未知均值和协方差通过模拟估计。以前的研究表明，贝叶斯实现的合成似然比近似贝叶斯计算，一个流行的似然自由的方法，在高维汇总统计量的存在下，可以更有效的计算。本文有三个贡献。第一个表明，如果汇总统计量表现良好，则合成似然后验是渐近正态的，并产生具有正确覆盖水平的可信集。第二个贡献比较贝叶斯合成似然和近似贝叶斯计算的计算效率。我们表明，贝叶斯合成似然比近似贝叶斯计算更有效的计算。基于渐近结果，第三个贡献提出使用调整的推断方法时，可能被误指定的形式假设的协方差矩阵的合成似然，如对角或因子模型，以加快计算。本文的补充材料可在网上查阅。
Implementing Bayesian inference is often computationally challenging in complex models, especially when calculating the likelihood is difficult. Synthetic likelihood is one approach for carrying out inference when the likelihood is intractable, but it is straightforward to simulate from the model. The method constructs an approximate likelihood by taking a vector summary statistic as being multivariate normal, with the unknown mean and covariance estimated by simulation. Previous research demonstrates that the Bayesian implementation of synthetic likelihood can be more computationally efficient than approximate Bayesian computation, a popular likelihood-free method, in the presence of a high-dimensional summary statistic. Our article makes three contributions. The first shows that if the summary statistics are well-behaved, then the synthetic likelihood posterior is asymptotically normal and yields credible sets with the correct level of coverage. The second contribution compares the computational efficiency of Bayesian synthetic likelihood and approximate Bayesian computation. We show that Bayesian synthetic likelihood is computationally more efficient than approximate Bayesian computation. Based on the asymptotic results, the third contribution proposes using adjusted inference methods when a possibly misspecified form is assumed for the covariance matrix of the synthetic likelihood, such as diagonal or a factor model, to speed up computation. Supplementary materials for this article are available online.