Scientists continue to develop increasingly complex mechanistic models to reflect their knowledge more realistically. Statistical inference using these models can be challenging since the corresponding likelihood function is often intractable and model simulation may be computationally burdensome. Fortunately, in many of these situations it is possible to adopt a surrogate model or approximate likelihood function. It may be convenient to conduct Bayesian inference directly with a surrogate, but this can result in a posterior with poor uncertainty quantification. In this paper, we propose a new method for adjusting approximate posterior samples to reduce bias and improve posterior coverage properties. We do this by optimizing a transformation of the approximate posterior, the result of which maximizes a scoring rule. Our approach requires only a (fixed) small number of complex model simulations and is numerically stable. We develop supporting theory for our method and demonstrate beneficial corrections to approximate posteriors across several examples of increasing complexity.

翻译：科学家们持续开发日益复杂的机理模型，以更真实地反映其知识体系。由于这类模型对应的似然函数通常难以处理，且模型仿真可能计算负担沉重，使用这些模型进行统计推断颇具挑战。所幸在许多情况下，采用代理模型或近似似然函数是可行的。虽然直接使用代理模型进行贝叶斯推断可能较为便捷，但这可能导致后验分布的不确定性量化效果不佳。本文提出一种调整近似后验样本的新方法，旨在减少偏差并改善后验覆盖特性。该方法通过对近似后验进行变换优化来实现，优化结果使评分规则最大化。我们的方法仅需（固定）少量复杂模型仿真，且具有数值稳定性。我们为此方法建立了支撑理论，并通过多个复杂度递增的案例展示了其对近似后验的有效校正。