{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,3]],"date-time":"2026-06-03T04:58:14Z","timestamp":1780462694349,"version":"3.54.1"},"reference-count":47,"publisher":"MDPI AG","issue":"6","license":[{"start":{"date-parts":[[2024,5,23]],"date-time":"2024-05-23T00:00:00Z","timestamp":1716422400000},"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>The simultaneous estimation of multiple quantiles is a crucial statistical task that enables a thorough understanding of data distribution for robust analysis and decision-making. In this study, we adopt a Bayesian approach to tackle this critical task, employing the asymmetric Laplace distribution (ALD) as a flexible framework for quantile modeling. Our methodology implementation involves the Hamiltonian Monte Carlo (HMC) algorithm, building on the foundation laid in prior work, where the error term is assumed to follow an ALD. Capitalizing on the interplay between two distinct quantiles of this distribution, we endorse a straightforward and fully Bayesian method that adheres to the non-crossing property of quantiles. Illustrated through simulated scenarios, we showcase the effectiveness of our approach in quantile estimation, enhancing precision via the HMC algorithm. The proposed method proves versatile, finding application in finance, environmental science, healthcare, and manufacturing, and contributing to sustainable development goals by fostering innovation and enhancing decision-making in diverse fields.<\/jats:p>","DOI":"10.3390\/a17060224","type":"journal-article","created":{"date-parts":[[2024,5,23]],"date-time":"2024-05-23T09:58:47Z","timestamp":1716458327000},"page":"224","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Bayesian Estimation of Simultaneous Regression Quantiles Using Hamiltonian Monte Carlo"],"prefix":"10.3390","volume":"17","author":[{"ORCID":"https:\/\/orcid.org\/0009-0007-5876-853X","authenticated-orcid":false,"given":"Hassan","family":"Hachem","sequence":"first","affiliation":[{"name":"INRAE, UR1204, AgroParisTech, 147 Rue de l\u2019Universit\u00e9, 75338 Paris, France"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5453-2577","authenticated-orcid":false,"given":"Candy","family":"Abboud","sequence":"additional","affiliation":[{"name":"College of Engineering and Technology, American University of the Middle East, Egaila 54200, Kuwait"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2024,5,23]]},"reference":[{"key":"ref_1","first-page":"1","article-title":"Quantile regression: Overview and selected applications","volume":"4","author":"Buhai","year":"2005","journal-title":"Ad Astra"},{"key":"ref_2","first-page":"881","article-title":"Quantile regression for large-scale applications","volume":"28","author":"Yang","year":"2013","journal-title":"Int. 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