Regularised horse shoe

Global-local shrinkage prior. (Piironen and Vehtari 2017)

$$\begin{array}{rl}{\beta }_i& \sim \text{normal}(0,{\tau }^2{\tilde{\lambda }}_j^2)\\ {\tilde{\lambda }}_j^2& =\frac{c^2{\lambda }_j^2}{c^2+{\tau }^2{\lambda }_j^2}\\ {\lambda }_j& \sim {\text{Cauchy}}^{+}(0,1)\end{array}$$

References

Piironen, Juho, and Aki Vehtari. 2017. “Sparsity Information and Regularization in the Horseshoe and Other Shrinkage Priors.” Electronic Journal of Statistics 11 (2). https://doi.org/10.1214/17-EJS1337SI.