13.05.2020 12:15 Vanda Inacio De Carvalho (The University of Edinburgh, UK):
Flexible nonparametric Bayesian density regression via dependent Dirichlet process mixture models and penalised splines(using Zoom, see http://go.tum.de/410163 for more details) (Parkring 11, 85748 Garching)

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 normal 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 normal 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 a study concerning the association of a toxic metabolite on preterm birth.