We show that for any multiple-try Metropolis algorithm, one can always accept the proposal and evaluate the importance weight that is needed to correct for the bias without extra computational cost. This results in a general, convenient, and rejection-free Markov chain Monte Carlo (MCMC) sampling scheme. By further leveraging the importance sampling perspective on Metropolis--Hastings algorithms, we propose an alternative MCMC sampler on discrete spaces that is also outside the Metropolis--Hastings framework, along with a general theory on its complexity. Numerical examples suggest that the proposed algorithms are consistently more efficient than the original Metropolis--Hastings versions.

翻译：我们证明，对于任何多重尝试Metropolis算法，总可以在不增加计算成本的情况下接受提议并评估校正偏差所需的重要性权重。这产生了一种通用、便捷且无拒绝的马尔可夫链蒙特卡洛（MCMC）采样方案。通过进一步利用Metropolis–Hastings算法的重要性采样视角，我们提出了一种同样在Metropolis–Hastings框架之外的离散空间替代MCMC采样器，并建立了关于其复杂度的通用理论。数值实验表明，所提算法始终比原始Metropolis–Hastings版本更高效。