{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T00:51:50Z","timestamp":1760143910871,"version":"build-2065373602"},"reference-count":11,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2024,3,7]],"date-time":"2024-03-07T00:00:00Z","timestamp":1709769600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Algorithms"],"abstract":"<jats:p>This paper proposes a genetic algorithm-based Markov Chain approach that can be used for non-parametric estimation of regression coefficients and their statistical confidence bounds. The proposed approach can generate samples from an unknown probability density function if a formal functional form of its likelihood is known. The approach is tested in the non-parametric estimation of regression coefficients, where the least-square minimizing function is considered the maximum likelihood of a multivariate distribution. This approach has an advantage over traditional Markov Chain Monte Carlo methods because it is proven to converge and generate unbiased samples computationally efficiently.<\/jats:p>","DOI":"10.3390\/a17030111","type":"journal-article","created":{"date-parts":[[2024,3,7]],"date-time":"2024-03-07T04:19:02Z","timestamp":1709785142000},"page":"111","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["A Markov Chain Genetic Algorithm Approach for Non-Parametric Posterior Distribution Sampling of Regression Parameters"],"prefix":"10.3390","volume":"17","author":[{"given":"Parag C.","family":"Pendharkar","sequence":"first","affiliation":[{"name":"Information Systems School of Business Administration, Pennsylvania State University at Harrisburg, 777 West Harrisburg Pike, Middletown, PA 17057, USA"}]}],"member":"1968","published-online":{"date-parts":[[2024,3,7]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"401","DOI":"10.1214\/aos\/1176345782","article-title":"Nonparametric Maximum Likelihood Estimation by the Method of Sieves","volume":"10","author":"Geman","year":"1982","journal-title":"Ann. 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Res."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"143","DOI":"10.3758\/s13423-016-1015-8","article-title":"A Simple Introduction to Markov Chain Monte-Carlo Sampling","volume":"25","author":"Cassey","year":"2018","journal-title":"Psychon. Bull. Rev."},{"key":"ref_9","doi-asserted-by":"crossref","unstructured":"Ntzoufras, I. (2009). Bayesian Modeling Using WinBUGS, John Wiley and Sons, Inc.","DOI":"10.1002\/9780470434567"},{"key":"ref_10","unstructured":"Goldberg, D.E. (1989). Genetic Algorithms in Search, Optimization & Machine Learning, Addison-Wesley."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"107298","DOI":"10.1016\/j.csda.2021.107298","article-title":"Multimodal Bayesian Registration of Noisy Functions Using Hamiltonian Monte Carlo","volume":"163","author":"Tucker","year":"2021","journal-title":"Comput. Stat. 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