MCMC convergence diagnosis using geometry of Bayesian LASSO

TL;DR

This paper introduces a geometric approach to diagnose MCMC convergence in Bayesian LASSO by analyzing the posterior distribution's semi-norm and the partition function's dependence on norms.

Contribution

It develops a novel geometric framework for MCMC convergence diagnosis in Bayesian LASSO based on the semi-norm and partition function analysis.

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 l1 and l2 norms and present three regimes. We derive the concentration of Bayesian LASSO, and present MCMC convergence diagnosis.