{"database":"biostudies-literature","file_versions":[],"scores":null,"additional":{"omics_type":["Unknown"],"volume":["78(4)"],"submitter":["Zhou X"],"pubmed_abstract":["This paper advocates proximal Markov Chain Monte Carlo (ProxMCMC) as a flexible and general Bayesian inference framework for constrained or regularized estimation. Originally introduced in the Bayesian imaging literature, ProxMCMC employs the Moreau-Yosida envelope for a smooth approximation of the total-variation regularization term, fixes variance and regularization strength parameters as constants, and uses the Langevin algorithm for the posterior sampling. We extend ProxMCMC to be fully Bayesian by providing data-adaptive estimation of all parameters including the regularization strength parameter. More powerful sampling algorithms such as Hamiltonian Monte Carlo are employed to scale ProxMCMC to high-dimensional problems. Analogous to the proximal algorithms in optimization, ProxMCMC "],"journal":["The American statistician"],"pagination":["379-390"],"full_dataset_link":["https://www.ebi.ac.uk/biostudies/studies/S-EPMC11670895"],"repository":["biostudies-literature"],"pubmed_title":["Proximal MCMC for Bayesian Inference of Constrained and Regularized Estimation."],"pmcid":["PMC11670895"],"pubmed_authors":["Chi EC","Heng Q","Zhou X","Zhou H"],"additional_accession":[]},"is_claimable":false,"name":"Proximal MCMC for Bayesian Inference of Constrained and Regularized Estimation.","description":"This paper advocates proximal Markov Chain Monte Carlo (ProxMCMC) as a flexible and general Bayesian inference framework for constrained or regularized estimation. Originally introduced in the Bayesian imaging literature, ProxMCMC employs the Moreau-Yosida envelope for a smooth approximation of the total-variation regularization term, fixes variance and regularization strength parameters as constants, and uses the Langevin algorithm for the posterior sampling. We extend ProxMCMC to be fully Bayesian by providing data-adaptive estimation of all parameters including the regularization strength parameter. More powerful sampling algorithms such as Hamiltonian Monte Carlo are employed to scale ProxMCMC to high-dimensional problems. Analogous to the proximal algorithms in optimization, ProxMCMC ","dates":{"release":"2024-01-01T00:00:00Z","publication":"2024","modification":"2025-04-18T22:01:22.822Z","creation":"2025-04-07T09:56:54.291Z"},"accession":"S-EPMC11670895","cross_references":{"pubmed":["39726826"],"doi":["10.1080/00031305.2024.2308821"]}}