论文标题
混合模型的一致性，与成分数量的先验
Consistency of mixture models with a prior on the number of components
论文作者
论文摘要
本文建立了贝叶斯有限混合模型的后验一致性的一般条件，并且成分数量的先验。也就是说，当数据是从有限混合物在假定的组件分布家族上生成的数据时，我们提供了足够的条件，后验集中于真实参数值的邻域。具体而言，我们建立了几乎确定的组件数量，混合物权重和组件参数的一致性，最高到组件标签的排列。此处采用的方法基于DOOB定理，该定理具有在特殊的一般条件下持有的优势，并且仅保证在一组参数值下保证一组概率下的参数值的缺点。但是，我们表明，实际上，对于普遍使用的先验选择，这在lebesgue-几乎所有参数值中都产生了一致性 - 对于大多数实际目的而言，这是令人满意的。我们旨在以最大化的清晰度，一般性和易用性来制定结果。
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.
