Bayesian Lasso : Concentration and MCMC Diagnosis

2018/02/22 by Daoud Ounaissi, Ounaissi, Daoud, Nadji Rahmania +1
Computer Science · Mathematics · #Bayesian Methods and Mixture Models #FOS: Mathematics #Markov Chains and Monte Carlo Methods #Statistical Methods and Inference #Statistics Theory (math.ST)

paper · pdf · doi:10.48550/arxiv.1802.08572

openalex publication_date 2018/02/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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

Citations

• Proximal Markov chain Monte Carlo algorithms
• Values of Mills' Ratio of Area to Bounding Ordinate and of the Normal Probability Integral for Large Values of the Argument
• Atomic Decomposition by Basis Pursuit
• Least angle regression
• Bayesian Lasso Posterior Sampling via Parallelized Measure Transport

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