A0318
Title: Density regression via Dirichlet process mixtures of normal structured additive regression models
Authors: Vanda Inacio - University of Edinburgh (United Kingdom) [presenting]
Abstract: Within Bayesian nonparametrics, dependent Dirichlet process mixture models provide a flexible approach for conducting inference about the conditional density function. However, several formulations of this class make either restrictive modelling assumptions or involve intricate algorithms for posterior inference. A flexible and computationally tractable approach is presented for density regression based on a single-weights dependent Dirichlet process mixture of normal distributions model for univariate continuous responses. An additive structure is assumed for the mean of each mixture component, and the effects of continuous covariates are incorporated through smooth functions. The key components of the modelling approach are penalised B-splines and their bivariate tensor product extension. The method also seamlessly accommodates categorical covariates, linear effects of continuous covariates, varying coefficient terms, and random effects, which is why the model is referred to as a Dirichlet process mixture of normal structured additive regression models. Results from a simulation study demonstrate that the approach successfully recovers the true conditional densities and other regression functionals in challenging scenarios. Applications to three real datasets further underpin the broad applicability of the method.
