Scientists continue to develop increasingly complex mechanistic models to reflect their knowledge more realistically. Statistical inference using these models can be highly 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 base Bayesian inference directly on the surrogate, but this can result in bias and poor uncertainty quantification. In this paper we propose a new method for adjusting approximate posterior samples to reduce bias and produce more accurate uncertainty quantification. We do this by optimising a transform of the approximate posterior that maximises a scoring rule. Our approach requires only a (fixed) small number of complex model simulations and is numerically stable. We demonstrate good performance of the new method on several examples of increasing complexity.

翻译：科学家们持续开发日益复杂的机理模型，以更真实地体现其知识。使用这些模型进行统计推断极具挑战性，因为相应的似然函数通常难以处理，且模型模拟可能计算负担沉重。幸运的是，在许多此类情形下，可以采用替代模型或近似似然函数。将贝叶斯推断直接基于替代模型或许很方便，但这可能导致偏差和较差的不确定性量化。本文提出一种新方法，用于调整近似后验样本以减少偏差并产生更精确的不确定性量化。我们通过优化近似后验的变换来实现这一目标，该变换最大化评分规则。该方法仅需（固定的）少量复杂模型模拟，且数值稳定。我们在多个复杂度递增的示例上展示了新方法的良好性能。