tempered后验分布的外推
Extrapolation of Tempered Posteriors
AI总结：
本文针对贝叶斯计算中后验分布近似问题，提出基于回火期望外推与平滑的新方法，可作为序贯蒙特卡洛的后处理方差缩减工具，无需高质量近似$p_1$即可得到所需后验量。
摘要：
回火（tempering）是贝叶斯计算中常用的工具，用于将后验分布$p_1$转换为更易近似的参考分布$p_0$。已有多种算法先近似$p_0$，再通过一系列中间分布$p_t$逐步得到$p_1$的近似。本文研究发现，对$p_1$的项进行高质量近似并非必要，因为中间分布的知识可用于外推得到感兴趣的后验量。具体而言，本文确定了后验期望由其关联的任意非空$t$区间上的回火期望决定的条件。利用该结果，本文提出了一种基于回火期望外推与平滑的后验期望近似新方法，并将其作为序贯蒙特卡洛（Sequential Monte Carlo）的后处理方差缩减工具实现。
英文摘要：
Tempering is a popular tool in Bayesian computation, being used to transform a posterior distribution $p_1$ into a reference distribution $p_0$ that is more easily approximated. Several algorithms exist that start by approximating $p_0$ and proceed through a sequence of intermediate distributions $p_t$ until an approximation to $p_1$ is obtained. Our contribution reveals that high-quality approximation of terms up to $p_1$ is not essential, as knowledge of the intermediate distributions enables posterior quantities of interest to be extrapolated. Specifically, we establish conditions under which posterior expectations are determined by their associated tempered expectations on any non-empty $t$ interval. Harnessing this result, we propose novel methodology for approximating posterior expectations based on extrapolation and smoothing of tempered expectations, which we implement as a post-processing variance-reduction tool for sequential Monte Carlo.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
