Robust Approximate Bayesian Inference With Synthetic Likelihood

Bayesian synthetic likelihood (BSL) is now an established method for conducting approximate Bayesian inference in models where, due to the intractability of the likelihood function, exact Bayesian approaches are either infeasible or computationally too demanding. Implicit in the application of BSL is the assumption that the data-generating process (DGP) can produce simulated summary statistics that capture the behaviour of the observed summary statistics. We demonstrate that if this compatibility between the actual and assumed DGP is not satisfied, that is, if the model is misspecified, BSL can yield unreliable parameter inference. To circumvent this issue, we propose a new BSL approach that can detect the presence of model misspecification, and simultaneously deliver useful inferences even under significant model misspecification. Two simulated and two real data examples demonstrate the performance of this new approach to BSL, and document its superior accuracy over standard BSL when the assumed model is misspecified. Supplementary materials for this article are available online.

贝叶斯合成似然（Bayesian synthetic likelihood，BSL）现已成为一种成熟的方法，用于在似然函数不可处理，导致精确贝叶斯方法要么不可行、要么计算成本过高的模型中开展近似贝叶斯推断。BSL的应用隐含了一项核心假设：数据生成过程（data-generating process，DGP）能够生成可复现观测摘要统计量特征的模拟摘要统计量。本文证明，若实际数据生成过程与预设数据生成过程之间的兼容性不满足，即模型存在误设时，BSL可能会得到不可靠的参数推断结果。为规避这一问题，本文提出一种新型BSL方法，该方法不仅能够检测模型误设的存在性，即便在模型存在显著误设的场景下，仍可输出可靠的推断结果。通过两个模拟数据集与两个真实数据集的算例，本文验证了该新型BSL方法的性能，并证实了当预设模型存在误设时，其精度优于标准BSL方法。本文配套补充材料可在线获取。