Log-regularly varying scale mixture of asymmetric Laplaces for robust Bayesian quantile regression

2026-08-25

AI Summary

本文针对贝叶斯分位数回归对极端观测值敏感的问题，提出了一种基于非对称拉普拉斯分布和其对数帕累托尺度混合的鲁棒误差分布方法。

Abstract

Bayesian quantile regression based on the asymmetric Laplace (AL) distribution can be sensitive to extreme observations because of its exponentially decaying tails. We propose a robust error distribution constructed as a finite mixture of the AL distribution and a log-Pareto scale mixture of asymmetric Laplace distributions (LPAL). Unlike a direct log-Pareto extension of the normal location-scale representation of the AL distribution, the proposed AL-LPAL mixture preserves the prescribed quantile and exhibits log-regularly varying behavior in both tails. The LPAL component also has an unbounded density at the target quantile, yielding a distribution that combines sharp central concentration with super-heavy tails. We establish posterior robustness under arbitrarily extreme contamination and provide sufficient conditions for the existence of posterior moments of the regression coefficients and scale parameter. For posterior computation, we develop a Gibbs sampler using latent-variable augmentations and a computationally efficient mean-field variational Bayes approximation. Simulation studies show that the proposed method is competitive under moderate contamination and maintains stable point estimation with comparatively concentrated posterior intervals, particularly when severe contamination affects the quantile of interest. Applications to carbon dioxide and Boston housing data, using the same preprocessing as existing robust Bayesian quantile regression analyses, show favorable predictive performance across nearly all quantile levels and loss criteria considered.

Problem

• Bayesian quantile regression
• asymmetric Laplace distribution
• extreme observations
• robust error distribution
• log-regularly varying

Innovation

• log-regularly varying
• asymmetric Laplace distribution
• robust Bayesian quantile regression
• Gibbs sampler
• mean-field variational Bayes