Gibbs sampling is one of the most commonly used Markov Chain Monte Carlo (MCMC) algorithms due to its simplicity and efficiency. It cycles through the latent variables, sampling each one from its distribution conditional on the current values of all the other variables. Conventional Gibbs sampling is based on the systematic scan (with a deterministic order of variables). In contrast, in recent years, Gibbs sampling with random scan has shown its advantage in some scenarios. However, almost all the analyses of Gibbs sampling with the random scan are based on uniform selection of variables. In this paper, we focus on a random scan Gibbs sampling method that selects each latent variable non-uniformly. Firstly, we show that this non-uniform scan Gibbs sampling leaves the target posterior distribution invariant. Then we explore how to determine the selection probability for latent variables. In particular, we construct an objective as a function of the selection probability and solve the constrained optimization problem. We further derive an analytic solution of the selection probability, which can be estimated easily. Our algorithm relies on the simple intuition that choosing the variable updates according to their marginal probabilities enhances the mixing time of the Markov chain. Finally, we validate the effectiveness of the proposed Gibbs sampler by conducting a set of experiments on real-world applications.

本研究解决了传统吉布斯抽样在随机扫描中选择变量均匀性的问题。提出了一种非均匀选择的随机扫描吉布斯抽样方法，并通过约束优化构建选择概率的解析解。这种改进显著提高了马尔可夫链的混合时间，并在实际应用中验证了其有效性。

采用自适应加权方案的加速马尔可夫链蒙特卡洛法