point; Fig. 3, middle panel), along with heavy, Cauchy-like tails (Fig. 3, lower panel). This prior is known as the horseshoe prior50, due to the horseshoe-shaped prior density on the shrinkage factor τj. As a increases, the prior on βj becomes less peaked at zero but the tails remain heavy. Finally, for fixed a and b, decreasing the global shrinkage parameter ϕ shifts the TPB prior from left to right, which imposes stronger shrinkage on the regression coefficients βj.
