POSTERIOR CONSISTENCY IN CONDITIONAL DENSITY ESTIMATION BY COVARIATE DEPENDENT MIXTURES
POSTERIOR CONSISTENCY IN CONDITIONAL DENSITY ESTIMATION BY COVARIATE DEPENDENT MIXTURES
复制标题
协变量相关混合物条件密度估计的后验一致性
作者：
Andriy Norets;Justinas Pelenis
本文考虑具有协变量依赖混合概率的位置-尺度密度的可数混合的条件密度的贝叶斯非参数估计。混合概率以两种方式建模。首先，我们考虑了有限协变量相依混合模型，其中混合概率与一个常数和一个核的乘积成正比，并且混合分量的个数是先验的。其次，我们考虑了核折断过程来模拟混合概率。我们证明了对于一大类数据生成过程，这两个模型的后验估计是弱一致和强一致的。文中进行的仿真研究表明，该模型在小样本情况下表现良好。
This paper considers Bayesian nonparametric estimation of conditional densities by countable mixtures of location-scale densities with covariate dependent mixing probabilities. The mixing probabilities are modeled in two ways. First, we consider finite covariate dependent mixture models, in which the mixing probabilities are proportional to a product of a constant and a kernel and a prior on the number of mixture components is specified. Second, we consider kernel stick-breaking processes for modeling the mixing probabilities. We show that the posterior in these two models is weakly and strongly consistent for a large class of data-generating processes. A simulation study conducted in the paper demonstrates that the models can perform well in small samples.