Peskun–Tierney ordering for Markovian Monte Carlo: Beyond the reversible scenario
本文针对物理和统计文献中当前或重新引起兴趣的一类非可逆蒙特卡洛马尔可夫链和过程，发展了与可逆情形紧密对应的比较结果，证明了一些猜想并加强了早期结论。
Historically time-reversibility of the transitions or processes underpinning Markov chain Monte Carlo methods (MCMC) has played a key role in their development, while the self-adjointness of associated operators together with the use of classical functional analysis techniques on Hilbert spaces have led to powerful and practically successful tools to characterise and compare their performance. Similar results for algorithms relying on nonreversible Markov processes are scarce. We show that for a type of nonreversible Monte Carlo Markov chains and processes, of current or renewed interest in the physics and statistical literatures, it is possible to develop comparison results which closely mirror those available in the reversible scenario. We show that these results shed light on earlier literature, proving some conjectures and strengthening some earlier results.