ABSTRACT
Structured additive distributional regression provides a general framework for semiparametric regression where effects are assumed for all parameters characterizing the distribution of the response. This allows the analyst to focus on distributional aspects beyond the mean such as variability, skewness or other shape features. The predictors assigned to the parameters comprise structured additive combinations of various effect types such as nonlinear effects of continuous covariates, spatial effects, random effects, varying coefficient terms, interaction surfaces, or high-dimensional vectors of linear effects. However, the resulting flexibility makes effect selection and regularization a challenge that can be conveniently tackled in a Bayesian framework by placing prior structures on blocks of regression coefficients relating to the different effects. We will review both effect selection priors based on spike-and-slab structures and regularization priors enforcing shrinkage and smoothness of effect estimates from a conceptual as well as a computational point of view.
