标题： 具有关于成分数量先验的混合模型的一致性 显示英文标题

标题： Consistency of mixture models with a prior on the number of components

摘要： 本文建立了贝叶斯有限混合模型后验一致性的一般条件，其中在成分数量上赋予先验。也就是说，我们给出了充分条件，使得当数据从假设成分分布族的有限混合生成时，后验集中在真实参数值的邻域内。具体而言，我们证明了成分数量、混合权重以及成分参数（成分标签排列后的）几乎处处一致。这里采用的方法基于杜布定理，其优点是在极其一般的条件下成立，缺点是只能保证在先验概率为一的参数值集合上的一致性。然而，我们表明，实际上对于常用的先验选择，这会导致勒贝格几乎处处的参数值上的一致性——这对于大多数实际应用来说是令人满意的。我们的目标是以最大化清晰度、通用性和易用性的方式陈述这些结果。 显示英文摘要

摘要： 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.