Reviews: Analytic solution and stationary phase approximation for the Bayesian lasso and elastic net

Summary An approximation to the posterior distribution from a Bayesian lasso or Bayesian elastic net prior is developed. The method uses a saddle-point approximation to the partition function. This is developed by writing the posterior distribution in terms of tau n / sigma 2 and uses an approximation for large tau. The results are illustrated on three data sets: diabetes (n 442, p 10), leukaemia (n 72, p 3571) and Cancer Cell Line Encyclopedia (n 474, p 1000). These demonstrate some of the performance characteristics of the approximation.