Log-regularly varying scale mixture of asymmetric Laplaces for robust Bayesian quantile regression
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.
Related
- Bayesian Quantile Regression for Misclassified Binary Data with an Application to Spousal Violence Reporting
- Quantile-Only Regression: Inference and Partial Identification under Quantile Disclosure
- Clouded Representatives and Score Matching for Distributed Quantile Regression
- A New Framework for Estimation of Unconditional Quantile Treatment Effects: The Residualized Quantile Regression (RQR) Model
- Conformalized Quantile Regression and Minimax Limits of Fixed-Score Calibration under Known Covariate Shift
BibTeX
@misc{han2026logregularly,
title = {{Log-regularly varying scale mixture of asymmetric Laplaces for robust Bayesian quantile regression}},
author = {Dongu Han and Genya Kobayashi and Shonosuke Sugasawa},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2608.25186},
eprint = {2608.25186},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.25186},
note = {CC0},
}
RIS
TY - UNPB
TI - Log-regularly varying scale mixture of asymmetric Laplaces for robust Bayesian quantile regression
AU - Dongu Han
AU - Genya Kobayashi
AU - Shonosuke Sugasawa
PY - 2026
DA - 2026/10/14
PB - arXiv
DO - 10.48550/arxiv.2608.25186
UR - https://arxiv.org/abs/2608.25186
AB - 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.
ER -