Regularised horse shoe

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

\[ \begin{align} \beta_i \;&\sim \text{normal}(0, \tau^2\tilde{\lambda}_j^2) \\ \tilde{\lambda}_j^2 \;&= \frac{c^2\lambda_j^2}{c^2 + \tau^2\lambda_j^2} \\ \lambda_j \;&\sim \text{Cauchy}^+(0,1) \\ \end{align} \]

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.