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 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 optimizing a transform of the approximate posterior that maximizes 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，以更真实地反映其知识体系。由于对应似然函数往往难以处理且模型模拟计算负担沉重，使用这些模型进行统计推断颇具挑战性。幸运的是，在许多此类情况下，可采用替代模型或近似似然函数。直接利用替代模型进行贝叶斯推断虽便捷，却可能导致偏差和不确定性量化不准确。本文提出了一种新方法，通过调整近似后验样本来减少偏差并实现更精确的不确定性量化。该方法的实现途径是优化近似后验的变换形式，使其最大化评分规则。本方法仅需（固定）少量复杂模型模拟，且具有数值稳定性。我们通过复杂度递增的多个算例验证了新方法的优异性能。