12.2 Regularization
The linear normal model using the conjugate family is ridge regression (Ishwaran and Rao 2005). We can use empirical Bayes to select the scale parameter of the prior covariance matrix of the location parameters, which is in turn the regularization parameter in ridge regression (see my class notes in MSc in Data Science and Analytics).
12.2.3 Non-local priors
(Johnson and Rossell 2012)
R package: mombf (Model Selection with Bayesian Methods and Information Criteria)
link: https://cran.r-project.org/web/packages/mombf/index.html
References
Ishwaran, H., and J. S. Rao. 2005. “Spike and Slab Variable Selection: Frequentist and Bayesian Strategies.” The Annals of Statistics 33 (2): 730–73.
Johnson, Valen E, and David Rossell. 2012. “Bayesian Model Selection in High-Dimensional Settings.” Journal of the American Statistical Association 107 (498): 649–60.