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A1285
Title: Density regression with Bayesian additive regression trees Authors:  Jared Murray - Carnegie Mellon University (United States) [presenting]
Abstract: Modeling how an entire density changes with covariates (``density regression'') is an important but challenging generalization of mean and quantile regression models. We introduce a new continuous latent variable model for density regression. Treating this unobserved variable as the input to a nonparametric regression function induces a flexible model for the conditional density of the response (given the observed covariates) after marginalizing over the latent variable. This model has a natural interpretation in terms of omitted variables, and only requires prior distributions to be specified for one or two regression functions (in contrast to covariate-dependent mixture models). Bayesian additive regression trees (BART) are used as priors over location and scale (or bandwidth) regression functions, yielding attractive invariance properties and computationally efficient posterior inference.