用于无似然后验推断的校准核比率估计方法（英文）

Calibration kernel-based ratio estimation for likelihood-free posterior inference

摘要

在贝叶斯推断中常遇到的一个困难是似然函数难以评估或没有显式的表达式，这种情况被称为无似然贝叶斯问题，此时后验分布只能通过基于特定参数生成的样本来间接推断。无似然贝叶斯问题的主要挑战之一是如何在有限的样本生成次数内有效逼近后验分布，现有的计算方法包括近似贝叶斯计算、合成似然及贝叶斯优化等。Miller等（2022）提出了一种新的序贯比率估计方法，创新地将似然与证据比的估计转化为多分类问题，从而高效地推断后验分布。基于此方法，本研究进一步发展了一种基于校准核的比率估计新方法：校准比率后验推断方法，通过校准核为分类任务的样本赋予额外权重，增强了原方法的训练效率和性能。首先说明新方法的收敛性，随后通过数值实验验证了其在有限样本生成条件下在多个指标上对参数后验分布估计的准确度显著提高。

Abstract

Bayesian inference often faces challenges where the likelihood function is difficult to evaluate or lacks explicit expression， known as likelihood-free Bayesian problems， where posterior distributions can only be inferred indirectly through samples generated under specific parameters. Existing methods such as approximate Bayesian computation， synthetic likelihood， and Bayesian optimization focus on addressing these issues. This paper extends Miller et al.’s （2022） sequential neural ratio estimation method for likelihood-free Bayesian problems by transforming likelihood-to-evidence ratio estimation into a multi-class problem for efficient posterior estimation. We introduce a new calibration kernel-based ratio estimation method （CKRE）， to enhance the original method’s training efficiency and performance. The convergence of our proposed method is proven， and numerical experiments demonstrate its significant improvement in accurately estimating posterior distributions under limited sample generation conditions.