Half-t Horseshoe Prior

Larger finite values of nu produced stronger shrinkage and better empirical behavior while retaining heavy tails. The main BNR analyses use local-shrinkage degrees of freedom nu equal to 1000. Voxel activation coefficients use a half-t horseshoe prior for global-local shrinkage. The half-t horseshoe prior has an infinite spike at zero and tails that allow true signals to escape shrinkage. The degrees of freedom parameter controls the tail behavior of the half-t horseshoe prior.