We develop Bayesian models for density regression with emphasis on discrete outcomes. The problem of density regression is approached by considering methods for multivariate density estimation of mixed scale variables, and obtaining conditional densities from the multivariate ones. The approach to multivariate mixed scale outcome density estimation that we describe represents discrete variables, either responses or covariates, as discretised versions of continuous latent variables. We present and compare several models for obtaining these thresholds in the challenging context of count data analysis where the response may be over- and/or under-dispersed in some of the regions of the covariate space. We utilise a nonparametric mixture of multivariate Gaussians to model the directly observed and the latent continuous variables. The paper presents a Markov chain Monte Carlo algorithm for posterior sampling, sufficient conditions for weak consistency, and illustrations on density, mean and quantile regression utilizing simulated and real datasets.

中文翻译：

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离散结果的贝叶斯密度回归

我们开发了密度回归的贝叶斯模型，重点是离散结果。通过考虑混合尺度变量的多元密度估计方法并从多元变量中获得条件密度来解决密度回归问题。我们描述的多元混合尺度结果密度估计方法将离散变量（响应或协变量）表示为连续潜在变量的离散版本。我们提出并比较了几种模型，用于在计数数据分析的挑战性环境中获得这些阈值，其中响应可能在协变量空间的某些区域中过度分散和/或分散不足。我们利用多元高斯的非参数混合来模拟直接观察到的和潜在的连续变量。