Bayesian structured additive quantile regression for inflated bounded data
Fuente:
arXiv
Saved in:
| Main Authors: | , , , |
|---|---|
| Format: | Preprint |
| Published: |
2026
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866911484236267520 |
|---|---|
| author | Queiroz, Francisco F. Brachem, Johannes Wiemann, Paul F. V. Kneib, Thomas |
| author_facet | Queiroz, Francisco F. Brachem, Johannes Wiemann, Paul F. V. Kneib, Thomas |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_03987 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Bayesian structured additive quantile regression for inflated bounded data Queiroz, Francisco F. Brachem, Johannes Wiemann, Paul F. V. Kneib, Thomas Methodology 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. |
| title | Bayesian structured additive quantile regression for inflated bounded data |
| topic | Methodology |
| url | https://arxiv.org/abs/2603.03987 |