In sampling tasks, it is common for target distributions to be known up to a normalising constant. However, in many situations, evaluating even the unnormalised distribution can be costly or infeasible. This issue arises in scenarios such as sampling from the Bayesian posterior for tall datasets and the 'doubly-intractable' distributions. In this paper, we begin by observing that seemingly different Markov chain Monte Carlo (MCMC) algorithms, such as the exchange algorithm, PoissonMH, and TunaMH, can be unified under a simple common procedure. We then extend this procedure into a novel framework that allows the use of auxiliary variables in both the proposal and acceptance-rejection steps. We develop the theory of the new framework, applying it to existing algorithms to simplify and extend their results. Several new algorithms emerge from this framework, with improved performance demonstrated on both synthetic and real datasets.

翻译：在采样任务中，目标分布通常仅已知一个归一化常数。然而，在许多情况下，即使评估未归一化的分布也可能成本高昂或不可行。这一问题出现在诸如高维数据集的贝叶斯后验采样以及"双难解"分布等场景中。本文首先指出，诸如交换算法、PoissonMH 和 TunaMH 等看似不同的马尔可夫链蒙特卡洛（MCMC）算法，均可通过一个简单的通用流程进行统一。随后，我们将此流程扩展为一个新颖的框架，允许在提议和接受-拒绝步骤中使用辅助变量。我们发展了新框架的理论，并将其应用于现有算法以简化和扩展其结果。该框架衍生出若干新算法，在合成和真实数据集上均展现出更优的性能。