Bayesian Estimation of Simultaneous Regression Quantiles Using Hamiltonian Monte Carlo

Algorithms Pub Date : 2024-05-23 DOI:10.3390/a17060224
Hassan Hachem, Candy Abboud
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Abstract

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 priorwork , 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.
利用哈密尔顿蒙特卡洛对同步回归量进行贝叶斯估计
同时估算多个量化值是一项重要的统计任务,它能让我们透彻地了解数据的分布情况,从而进行稳健的分析和决策。在本研究中,我们采用贝叶斯方法来解决这一关键任务,将非对称拉普拉斯分布(ALD)作为量值建模的灵活框架。我们的方法实施涉及汉密尔顿蒙特卡洛(HMC)算法,该算法建立在先前工作的基础上,其中误差项被假定为遵循 ALD。利用该分布的两个不同量级之间的相互作用,我们认可了一种简单明了的完全贝叶斯方法,该方法坚持量级的非交叉属性。通过模拟场景,我们展示了我们的方法在量值估计中的有效性,并通过 HMC 算法提高了精度。事实证明,所提出的方法用途广泛,可应用于金融、环境科学、医疗保健和制造业,并通过促进创新和加强不同领域的决策,为实现可持续发展目标做出贡献。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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