María Xosé Rodríguez Álvarez, Universidade de Vigo and Basque Center for Applied Mathematics (BCAM)
Density regression via dependent Dirichlet process mixtures and penalised splines
Joint work with:Vanda Inácio (University of Edimburgh)
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 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, this work develops a single-weights DDP mixture of normals model, where the components’ means are modelled using Bayesian penalised splines (P-splines). We coin our approach as psDDP. A practically important feature of psDDP models is that all parameters have conjugate full conditional distributions thus 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 two real datasets, one concerning the study of the association of a toxic metabolite on preterm birth, and the other one in the context of field trials experiments.