Beta Cauchy-Cauchy (BECCA)

Global-local shrinkage prior. (Rodrigo et al. 2025)

\[ \begin{align} \beta_j \;&\sim \text{normal}(0, g \sigma^2 \gamma_j^2) \\ \gamma_j \;&\sim \text{Beta}(u, v) \\ g \;&\sim \text{Cauchy}^+(0, 1) \\ u \;&\sim \text{Cauchy}^+(0, 1) \\ v \;&\sim \text{Cauchy}^+(0, 1) \\ \sigma^2 \;&\sim p(\sigma^2) \end{align} \]

References

Rodrigo, Linduni M., Robert Kohn, Hadi M. Afshar, and Sally Cripps. 2025. “A Beta Cauchy-Cauchy (BECCA) Shrinkage Prior for Bayesian Variable Selection.” January 13, 2025. https://doi.org/10.48550/arXiv.2501.07061.