It is commonly admitted that non-reversible Markov chain Monte Carlo (MCMC) algorithms usually yield more accurate MCMC estimators than their reversible counterparts. In this note, we show that in addition to their variance reduction effect, some non-reversible MCMC algorithms have also the undesirable property to slow down the convergence of the Markov chain. This point, which has been overlooked by the literature, has obvious practical implications. We illustrate this phenomenon for different non-reversible versions of the Metropolis-Hastings algorithm on several discrete state space examples and discuss ways to mitigate the risk of a small asymptotic variance/slow convergence scenario.

中文翻译：

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一些不可逆马尔可夫链蒙特卡罗方法的收敛时间

通常公认的是，不可逆的马尔可夫链蒙特卡罗（MCMC）算法通常比可逆的对应算法产生更准确的MCMC估计量。在此注释中，我们表明，除了其方差减少效果外，某些不可逆的MCMC算法还具有不理想的特性，从而降低了马尔可夫链的收敛速度。这一点已被文献所忽略，具有明显的实际意义。我们在几个离散的状态空间示例中说明了Metropolis-Hastings算法的不同不可逆版本的这一现象，并讨论了减轻小渐近方差/慢收敛场景风险的方法。