标题： 关于在混合空间中采样的Metropolis-Hasting的注记 显示英文标题

标题： A note on Metropolis-Hasting for sampling across mixed spaces

摘要： 我们关注的是在所谓的混合空间中进行采样的Metropolis-Hastings算法。 混合空间最重要的例子是一个由不同长度的实向量组成的空间。 在这个空间内的采样被称为跨维度采样，并在许多统计学领域中非常流行。 然而，现有的文献在Metropolis-Hastings算法在这些情况下的能力方面存在完全的分歧。 这导致了可逆跳跃算法作为准黄金标准的成功。 不幸的是，可逆跳跃的实际贡献一直被误解。 因此，本文对构建混合空间内采样的数学基础的理论进行了详尽的概述，讨论了一个变化点示例，并最终澄清了所有误解。 显示英文摘要

摘要： We are concerned with the Metropolis-Hastings algorithm for sampling across so-called mixed spaces. The most important example of a mixed space is a space that consists of real vectors of different lengths. Sampling within this space is called trans dimensional sampling and enjoys an enormous popularity across many statistical communities. However, the ubiquitous literature is completely divided over the abilities of the Metropolis-Hastings algorithm in these scenarios. This lead to the success of the reversible jump algorithm as the quasi gold standard. Unfortunately, the actual contribution of reversible jump is consistently misunderstood. Thus, this paper gives a dense overview of the theory that builds the mathematical foundations of sampling within mixed spaces, discusses a changepoint example and finally clears up any misunderstandings.