Single Factor Transformation Priors for Density Regression

Although discrete mixture modeling has formed the backbone of the literature on Bayesian density estimation incorporating covariates, the use of discrete mixtures leads to some well known disadvantages. Avoiding discrete mixtures, we propose a flexible class of priors based on random nonlinear functions of a uniform latent variable with an additive residual. These priors are related to Gaussian process latent variable models proposed in the machine learning literature. For density regression, we model the response and predictor means as distinct nonlinear functions of the same latent variable, thus inducing dependence through a single factor. The induced prior is shown to have desirable properties including large support and posterior consistency. We demonstrate advantages over Dirichlet process mixture models in a variety of simulations, and apply the approach to an epidemiology application.