Bayesian density regression for discrete outcomes

TL;DR

This paper introduces Bayesian density regression models for discrete outcomes by modeling discrete variables as discretized latent continuous variables, using nonparametric Gaussian mixtures and MCMC for inference.

Contribution

It proposes a novel Bayesian approach for density regression with discrete data, including methods for threshold estimation and handling over/under-dispersion.

Findings

Effective density, mean, and quantile regression demonstrated on simulated data.

Models handle over- and under-dispersion in count data.

MCMC algorithm ensures reliable posterior sampling.

Abstract

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.