Consistency of mixture models with a prior on the number of components
Consistency of mixture models with a prior on the number of components
复制标题
混合模型与先验成分数量的一致性
DOI：
10.1515/demo-2022-0150
复制
发表时间：
2022
影响因子：
0.7
通讯作者：
Jeffrey W. Miller
中科院分区：
文献类型：
--
作者：
Jeffrey W. Miller
摘要本文建立了具有先验分量个数的贝叶斯有限混料模型的后验相合性的一般条件。也就是说，我们提供了充分的条件下，后验集中在真正的参数值的邻域时，数据是从一个有限的混合物在假设的家庭的组件分布。具体来说，我们建立几乎肯定的一致性的组件的数量，混合物的权重，和组件的参数，到一个置换的组件标签。这里所采取的方法是基于Doob定理，它具有在非常一般的条件下保持的优点，以及仅在先验下具有概率1的一组参数值处保证一致性的缺点。然而，我们表明，事实上，对于常用的选择之前，这会产生一致性勒贝格几乎所有的参数值，这是令人满意的最实用的目的。我们的目标是以最大限度地提高清晰度，通用性和易用性的方式制定结果。
Abstract This article establishes general conditions for posterior consistency of Bayesian finite mixture models with a prior on the number of components. That is, we provide sufficient conditions under which the posterior concentrates on neighborhoods of the true parameter values when the data are generated from a finite mixture over the assumed family of component distributions. Specifically, we establish almost sure consistency for the number of components, the mixture weights, and the component parameters, up to a permutation of the component labels. The approach taken here is based on Doob’s theorem, which has the advantage of holding under extraordinarily general conditions, and the disadvantage of only guaranteeing consistency at a set of parameter values that has probability one under the prior. However, we show that in fact, for commonly used choices of prior, this yields consistency at Lebesgue-almost all parameter values, which is satisfactory for most practical purposes. We aim to formulate the results in a way that maximizes clarity, generality, and ease of use.