Abstract

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.

摘要

贝叶斯合成似然 (BSL) 现在是在模型中进行近似贝叶斯推理的既定方法，由于似然函数的难处理性，精确贝叶斯方法要么不可行，要么计算要求过高。隐含在 BSL 应用中的假设是数据生成过程 (DGP) 可以生成模拟汇总统计数据，这些汇总统计数据可以捕捉观察到的汇总统计数据的行为。我们证明，如果不满足实际和假设 DGP 之间的这种兼容性，即如果模型指定错误，BSL 会产生不可靠的参数推断。为了规避这个问题，我们提出了一种新的 BSL 方法，它可以检测模型错误指定的存在，并同时即使在严重的模型错误指定下也能提供有用的推理。两个模拟和两个真实数据示例证明了这种新的 BSL 方法的性能，并证明了当假设模型被错误指定时，它比标准 BSL 具有更高的准确性。本文的补充材料可在线获取。