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Title: Flexible nonparametric Bayesian density regression via dependent Dirichlet process mixture models and penalised splines Authors:  Maria Xose Rodriguez-Alvarez - BCAM, Basque Center for Applied Mathematics (Spain) [presenting]
Vanda Inacio - University of Edinburgh (United Kingdom)
Nadja Klein - Humboldt University Berlin (Germany)
Abstract: In many real-life applications, it is of interest to study how the distribution of a (continuous) response variable changes with covariates. Dependent Dirichlet process (DDP) mixture of normals models, a Bayesian nonparametric method, successfully addresses such a goal. The approach of considering covariate independent mixture weights, also known as the single weights dependent Dirichlet process mixture model, is very popular due to its computational convenience, but can have limited flexibility in practice. To overcome the lack of flexibility, but retaining the computational tractability, a single weights DDP mixture of normals model is developed, where the component's means are modelled using Bayesian penalised splines (P-splines). We coin our approach as DDPps. A practically important feature of DDPps models is that all parameters have conjugate full conditional distributions, leading to straightforward Gibbs sampling. In addition, they allow the effect associated with each covariate to be learned automatically from the data. The validity of our approach is supported by simulations and applied to a study concerning the association of a toxic metabolite on preterm birth.