We investigate the increase in efficiency of simulated and parallel tempering MCMC algorithms when using non-reversible updates to give them "momentum". By making a connection to a certain simple discrete Markov chain, we show that, under appropriate assumptions, the non-reversible algorithms still exhibit diffusive behaviour, just on a different time scale. We use this to argue that the optimally scaled versions of the non-reversible algorithms are indeed more efficient than the optimally scaled versions of their traditional reversible counterparts, but only by a modest speed-up factor of about 42%.

翻译：本研究探讨了当采用非可逆更新为模拟回火与并行回火MCMC算法注入"动量"时，其效率的提升程度。通过建立与某一简单离散马尔可夫链的关联，我们证明在适当假设下，非可逆算法仍呈现扩散行为，仅时间尺度有所不同。基于此，我们论证了经最优尺度调整的非可逆算法确实比传统可逆版本的最优尺度调整算法更高效，但加速幅度较为有限，约为42%。