Bayesian Lasso : Concentration and MCMC Diagnosis

TL;DR

This paper investigates the geometric properties and concentration behavior of the Bayesian LASSO posterior, providing insights into MCMC convergence and the influence of norm ratios on the partition function.

Contribution

It introduces a semi-norm based on the posterior distribution, analyzes the partition function dependence on norm ratios, and offers MCMC convergence diagnostics for Bayesian LASSO.

Findings

Partition function depends on the ratio of l1 and l2 norms.

Identifies three regimes based on norm ratios.

Provides concentration results for Bayesian LASSO.

Abstract

Using posterior distribution of Bayesian LASSO we construct a semi-norm on the parameter space. We show that the partition function depends on the ratio of the l 1 and l 2 norms and present three regimes. We derive the con- centration of Bayesian LASSO, and present MCMC convergence diagnosis. Keywords: LASSO, Bayes, MCMC, log-concave, geometry, incomplete Gamma function