Title: Adapting the horseshoe prior for functional effects in distributional regression models
Authors: Paul Wiemann - University of Goettingen (Germany) [presenting]
Thomas Kneib - University of Goettingen (Germany)
Abstract: A new prior specification based on the horseshoe prior is proposed that allows us to carry the concept of Bayesian global-local shrinkage to functional effect types in the class of distributional regression models. Distributional regression models link structured additive predictors to every distributional parameter via a response function. These predictors can be composed of various effect types, e.g., non-linear effects, varying coefficients random effects, spatial effects and may include hierarchical regression structures. The presented approach adaptively shrinks the estimated effect towards a predefined functional subspace, i.e. a linear function, while keeping desirable properties of the horseshoe prior unchanged, namely, those concerning the handling of sparsity and adaptive shrinkage. A Markov chain Monte Carlo sampling scheme is provided. Using simulated data and real data, empirical experiments show that our approach is applicable in situations with a large number of covariates and non-normal response distributions.