Accept-reject based Markov chain Monte Carlo (MCMC) methods are the workhorse algorithm for Bayesian inference. These algorithms, like Metropolis-Hastings, require choosing a proposal distribution which is typically informed by the desired target distribution. Surprisingly, proposal distributions with unknown normalizing constants are not uncommon, even though for such a choice of a proposal, the Metropolis-Hastings acceptance ratio cannot be evaluated exactly. Across the literature, authors resort to approximation methods that yield inexact MCMC or develop specialized algorithms to combat this problem. We show how Bernoulli factory MCMC algorithms, originally proposed for doubly intractable target distributions, can quite naturally be adapted to yield an exact MCMC sampling method. We present three diverse and relevant examples demonstrating the usefulness of the Bernoulli factory approach to this problem.

翻译：基于接受-拒绝的马尔可夫链蒙特卡洛（MCMC）方法是贝叶斯推断的主力算法。这些算法（如Metropolis-Hastings算法）需要选择一个通常由目标分布指导的提议分布。令人惊讶的是，具有未知归一化常数的提议分布并不罕见，尽管对于此类提议分布的选择，Metropolis-Hastings接受率无法被精确评估。在相关文献中，作者们采用近似方法来生成非精确MCMC，或开发专门算法来解决这一问题。我们展示了最初为双重难处理目标分布提出的伯努利工厂MCMC算法，如何能够自然地适应从而产生精确MCMC采样方法。我们给出了三个多样且相关的例子，证明了伯努利工厂方法对解决这一问题的有效性。