An Alternative Prior for Estimation in High-Dimensional Settings

Abstract

Bayesian estimations of complex regression models with high-dimensional parameter spaces require advanced priors, capable of addressing both sparsity and multicollinearity in the data. The Dirichlet-horseshoe, a new prior distribution that combines and expands on the concepts of the regularized horseshoe and the Dirichlet-Laplace priors, is a novel approach that offers a high degree of flexibility and yields estimates with comparably high accuracy. To evaluate its performance in different frameworks, this study reports on two replicated simulation studies and a real-data example. Across all tested settings, the proposed approach outperforms or achieves similar performance to well-established regularization priors in terms of loss.