Bayesian structured additive quantile regression for inflated bounded data

2026-03-04

AI Summary

This study addresses the challenge of modeling bounded continuous data on the unit interval that exhibit a high frequency of boundary values (0 and/or 1). The authors propose the first Bayesian structured additive quantile regression model that jointly models the conditional quantiles of the continuous component and the probability of observing boundary points. By integrating nonlinear, spatial, random, and varying-coefficient effects, this approach uniquely combines Bayesian structured additive modeling with quantile regression to provide a unified and flexible characterization of both the bulk and the inflated boundary parts of the data. Posterior inference is carried out via Markov chain Monte Carlo within the Liesel probabilistic programming framework. The model’s robustness and practical utility are demonstrated through simulations and real-world applications to Brazilian traffic fatality rates and speech intelligibility scores among cochlear implant users.

Technology Category

• Reasoning under Uncertainty: Relational Probabilistic Models
• Machine Learning: Bayesian Learning
• Knowledge Representation and Reasoning: Qualitative Reasoning

Application Category

• Graph Algorithms and Modeling for the Web: Querying, indexing, and retrieval in Web-related graphs
• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

Bounded continuous data on the unit interval frequently arise in applied fields and often exhibit a non-negligible proportion of observations at the boundaries. Inflated regression models address this feature by combining a continuous distribution on the unit interval with a discrete component to account for zero- and/or one-inflation. In this paper, we propose a class of Bayesian structured additive quantile regression models for inflated bounded continuous data that accommodates zero- and/or one-inflation. The proposed approach enables direct modeling of both the conditional quantiles of the continuous component and the probabilities of observing zeros and/or ones, with structured additive predictors incorporated in both parts, including nonlinear effects, spatial effects, random effects, and varying-coefficient terms. Posterior inference is carried out using Markov chain Monte Carlo algorithms implemented through the software Liesel, a probabilistic programming framework for semiparametric regression. The practical performance of the proposed models is illustrated through simulation studies and two real-data applications: one analyzing the proportion of traffic-related fatalities across Brazilian municipal districts, and another evaluating speech intelligibility in cochlear implant recipients under different experimental conditions.

Problem

• inflated bounded data
• quantile regression
• zero-inflation
• one-inflation
• Bayesian regression

Innovation

• Bayesian quantile regression
• inflated bounded data
• structured additive predictors
• zero-and-one inflation
• probabilistic programming