Finite mixtures are a cornerstone of Bayesian modelling, and it is well-known that sampling from the resulting posterior distribution can be a hard task. In particular, popular reversible Markov chain Monte Carlo schemes are often slow to converge when the number of observations $n$ is large. In this paper we introduce a novel and simple non-reversible sampling scheme for Bayesian finite mixture models, which is shown to drastically outperform classical samplers in many scenarios of interest, especially during convergence phase and when components in the mixture have non-negligible overlap. At the theoretical level, we show that the performance of the proposed non-reversible scheme cannot be worse than the standard one, in terms of asymptotic variance, by more than a factor of four; and we provide a scaling limit analysis suggesting that the non-reversible sampler can reduce the convergence time from O$(n^2)$ to O$(n)$. We also discuss why the statistical features of mixture models make them an ideal case for the use of non-reversible discrete samplers.

翻译：有限混合模型是贝叶斯建模的基石，众所周知，从其后验分布中采样可能是一项困难的任务。特别是，当观测数量$n$较大时，流行的可逆马尔可夫链蒙特卡罗方案通常收敛缓慢。本文针对贝叶斯有限混合模型提出了一种新颖且简单的非可逆采样方案，该方案被证明在许多关注场景中显著优于经典采样器，尤其在收敛阶段以及当混合模型中各成分存在不可忽略的重叠时。在理论层面，我们证明所提出的非可逆方案在渐近方差方面的性能不会比标准方案差超过四倍；同时我们提供的尺度极限分析表明，非可逆采样器可将收敛时间从O$(n^2)$缩短至O$(n)$。我们还讨论了混合模型的统计特性为何使其成为使用非可逆离散采样器的理想场景。