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强大的贝叶斯模型对具有重尾误差的线性回归模型的平均值

Shamriddha De¹, Joyee Ghosh²

¹PhD Candidate, Department of Statistics and Actuarial Science, The University of Iowa, Iowa City, USA.

Journal of applied statistics

|February 6, 2026

概括

本研究引入了一种灵活的贝叶斯回归模型,用于改进变量选择. 这种新的方法有效地处理了较重的尾部错误分布,在模拟和现实数据分析中表现优于现有方法.

科学领域:

统计统计统计统计
统计建模统计建模
贝叶斯的推理是贝叶斯的推理.

背景情况:

传统的线性回归假定存在正常分布的误差,但由于异常值,在现实数据中经常存在违规行为.
像贝叶斯的Huberized lasso这样的现有方法在强制执行稀疏性方面存在局限性 (系数完全为零).
超标分布和Student-t分布为模拟较重的尾巴提供了正常分布的替代方案,但它们的形状和尾巴行为不同.

研究的目的:

为线性回归开发贝叶斯模型平均化技术,以适应较重尾错误分布.
提出贝叶斯变量选择方法,使用尖峰和板块先验来更有效地执行稀疏性.
引入一个灵活的错误分布,包括超标和Student-t家族,并估计尾部重度参数.

主要方法:

开发一个贝叶斯变量选择方法,使用尖峰和板块先验.
灵活的错误分布的建议,结合了超标和Student-t特征.
实现一个高效的吉布斯采样器用于后置计算.

主要成果:

提出的方法证明了与最先进的技术相比具有竞争力的性能.
模拟研究和真实数据集分析验证了新贝叶斯方法的有效性.
该模型成功地处理了较重的尾部错误分布,并提高了变量选择的准确性.

结论:

开发的贝叶斯回归模型为具有较重尾误差的变量选择提供了灵活有效的解决方案.
该方法为现有技术提供了可靠的替代方案,特别是在存在异常值的情况下.
该方法增强了在线性回归中建模复杂错误结构的能力.

关键词:

62-08 这是一本书.概括的超模分布概括的超模分布马尔科夫链蒙特卡洛模型组成 (哈伯化的贝叶斯拉索 (Bayesian lasso) 是一个贝叶斯拉索.过度波形分布的分布.尖峰和板块的先行者之前学生-t 分布情况

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