A well-known difficult problem regarding Metropolis-Hastings algorithms is to get sharp bounds on their convergence rates. Moreover, a fundamental but often overlooked problem in Markov chain theory is to study the convergence rates for different initializations. In this paper, we study the two issues mentioned above of the Independent Metropolis-Hastings (IMH) algorithms on both general and discrete state spaces. We derive the exact convergence rate and prove that the IMH algorithm's different deterministic initializations have the same convergence rate. We get the exact convergence speed for IMH algorithms on general state spaces.

翻译：有关大都会-哈斯廷斯算法的一个众所周知的难题是其趋同率的清晰界限。 此外,Markov连锁理论中一个基本但经常被忽视的问题是研究不同初始化的趋同率。在本文中,我们研究了上文提到的独立大都会-哈斯廷斯算法在一般和离散州空间的两个问题。我们得出了确切的趋同率,并证明IMH算法的不同确定性初始化的趋同率相同。我们获得了通用州空间上IMH算法的精确趋同速度。