标题： 关于混合空间的Metropolis-Hastings接受概率的注记 显示英文标题

标题： A note on the Metropolis-Hastings acceptance probabilities for mixture spaces

摘要： 本研究的动力源于对Metropolis-Hastings算法和可逆跳算法在跨维采样背景下能力和贡献的普遍争议。 我们通过深入研究Metropolis-Hastings接受概率在一般混合空间中的实现来揭开这一主题的神秘面纱。 尽管从理论角度来看并不引人注目，但混合空间提出了关于有效探索的严峻挑战。 一种经常使用但未被广泛研究的用于在不同空间之间过渡的工具被称为所谓的平移函数。 我们对该主题进行了启发性的处理，这导致了可逆跳算法的推广，并揭示了另一种有前景的平移技术。 此外，通过重新考虑著名的Gibbs内Metropolis方法，我们发现了开发Metropolis-Hastings采样器的双重策略。 我们通过断点示例验证了我们的发现并比较了我们方法的性能。 之后，在更理论化的背景下，我们重新审视了已被遗忘的最大接受概率概念。 这允许对Metropolis-Hastings算法进行有趣的分类，并提供了更多关于其使用的建议。 对导致上述争议的一些推理错误的回顾总结了本文。 显示英文摘要

摘要： This work is driven by the ubiquitous dissent over the abilities and contributions of the Metropolis-Hastings and reversible jump algorithm within the context of trans dimensional sampling. We demystify this topic by taking a deeper look into the implementation of Metropolis-Hastings acceptance probabilities with regard to general mixture spaces. Whilst unspectacular from a theoretical point of view, mixture spaces gave rise to challenging demands concerning their effective exploration. An often applied but not extensively studied tool for transitioning between distinct spaces are so-called translation functions. We give an enlightening treatment of this topic that yields a generalization of the reversible jump algorithm and unveils another promising translation technique. Furthermore, by reconsidering the well-known Metropolis within Gibbs paradigm, we come across a dual strategy to develop Metropolis-Hastings samplers. We underpin our findings and compare the performance of our approaches by means of a change point example. Thereafter, in a more theoretical context, we revitalize the somewhat forgotten concept of maximal acceptance probabilities. This allows for an interesting classification of Metropolis-Hastings algorithms and gives further advice on their usage. A review of some errors in reasoning that have led to the aforementioned dissent concludes this paper.