Posterior sampling is a task of central importance in Bayesian inference. For many applications in Bayesian meta-analysis and Bayesian transfer learning, the prior distribution is unknown and needs to be estimated from samples. In practice, the prior distribution can be high-dimensional, adding to the difficulty of efficient posterior inference. In this paper, we propose a novel Markov chain Monte Carlo algorithm, which we term graph-enabled MCMC, for posterior sampling with unknown and potentially high-dimensional prior distributions. The algorithm is based on constructing a geometric graph from prior samples and subsequently uses the graph structure to guide the transition of the Markov chain. Through extensive theoretical and numerical studies, we demonstrate that our graph-enabled MCMC algorithm provides reliable approximation to the posterior distribution and is highly computationally efficient.

翻译：后验采样是贝叶斯推断中的核心任务。在贝叶斯元分析和贝叶斯迁移学习的许多应用中，先验分布未知且需要从样本中估计。实际应用中，先验分布可能具有高维特性，这增加了高效后验推断的难度。本文提出一种新颖的马尔可夫链蒙特卡洛算法——我们称之为图启发的MCMC算法——用于处理具有未知且可能高维先验分布的后验采样问题。该算法基于先验样本构建几何图，并利用图结构指导马尔可夫链的状态转移。通过系统的理论分析与数值实验，我们证明所提出的图启发MCMC算法能够可靠地逼近后验分布，并具有极高的计算效率。