论文标题
双重分配的稳定性
Stability of doubly-intractable distributions
论文作者
论文摘要
每当可能包含标准化函数$ z $时，双重折扣的分布自然而然地作为贝叶斯推理框架中的后验分布。拥有两个这样的功能$ z $和$ \ widetilde z $，我们提供了总变化的估计，以及由此产生的后验概率度量的瓦斯坦距离。结果，这导致了本地Lipschitz的连续性W.R.T. $ z $。在随机函数$ \ widetilde z $的更一般框架中，我们在预期的总变化和预期的瓦斯坦距离上得出了界限。在两个代表性的蒙特卡洛恢复方案的设置中说明了估计值的适用性。
Doubly-intractable distributions appear naturally as posterior distributions in Bayesian inference frameworks whenever the likelihood contains a normalizing function $Z$. Having two such functions $Z$ and $\widetilde Z$ we provide estimates of the total variation and Wasserstein distance of the resulting posterior probability measures. As a consequence this leads to local Lipschitz continuity w.r.t. $Z$. In the more general framework of a random function $\widetilde Z$ we derive bounds on the expected total variation and expected Wasserstein distance. The applicability of the estimates is illustrated within the setting of two representative Monte Carlo recovery scenarios.
