Multilevel Monte Carlo simulation of Bayesian Lasso

Abstract We show that Lasso and Bayesian Lasso are very close when the sparsity is large and the noise is small. We propose to solve Bayesian Lasso using multivalued stochastic differential equation. We derive four discretization algorithms, and present highly efficient multilevel Monte Carlo (MLMC) simulations. Additionally, we perform a numerical comparison of the Monte Carlo (MC), MLMC and proximal Markov chain Monte Carlo algorithm (PMALA).