An Elliptical Slice Sampler for the Beta Prime prior

Abstract

Global-local type priors are theoretically ideal for variable selection. However, they suffer from difficulty to implement computationally. Since these distributions usually have sharp spikes and heavy tails, then standard sampling methods often struggle from their complex geometry. The beta prime slice sampler is introduced to solve some of these problems by solving for the lower bound to demonstrate how the prior is highly concentrated, with elliptical arcs restricted to a small region near the origin. An efficient algorithm is introduced by combining the Elliptical Slice Sampling. Simulations tests are to compare the new sampler with other established methods. It is shown that the new sampler reduces the Mean Squared Error by half compared to the Lasso. Furthermore, it offers greater stability than the Elastic Net and standard Horseshoe implementations. These results prove that the proposed method is a practical and robust solution for high-dimensional data.