Bayesian Skewed-t Multivariate Censored Quantile Regression for Functional Neuroimaging Data

Enas Abid Alhafidh  Mohamed; Saif Hosam  Raheem

Enas Abid Alhafidh Mohamed Department of Statistics, University of Karbala, Collage of Administration and Economics, Karbala, Iraq
Saif Hosam Raheem Department of Statistics, College of Administration and Economics,University of Al-Qadisiyah, Iraq

Keywords: Bayesian Quantile Regression, Skewed-T Distribution, Censored Data, Functional Predictors, Neuroimaging

Abstract

This paper proposes a Bayesian skewed-t multivariate censored quantile regression model tailored for functional neuroimaging data, such as EEG or fMRI signals. The model accommodates functional covariates, multivariate right-censored responses, and asymmetric heavy-tailed error distributions. Functional principal component analysis (FPCA) is employed to reduce dimensionality in the functional inputs, while posterior inference is carried out using Hamiltonian Monte Carlo (HMC). Simulation studies demonstrate the superior performance of the proposed method compared to classical alternatives. Application to real neuroimaging data confirms its robustness and effectiveness in capturing heterogeneous quantile-dependent effects across multiple outcomes.

References

R. Koenker, Quantile Regression. Cambridge, UK: Cambridge University Press, 2005.

J. Yu, L. Wang, and X. Chen, “Inference on linear quantile regression with dyadic data,” J. Multivar. Anal., vol. 195, pp. 105–117, 2023.

Y. Ding, Y. Li, and J. Zhang, “Estimation and testing for varying-coefficient single-index quantile regression models,” Stat. Modelling, vol. 25, no. 1, pp. 89–107, 2025.

S. M. Mousavi, A. Habibi, and H. Sharifian, “Prognostic factors for survival after allogeneic transplantation in acute myeloid leukemia in Iran using censored quantile regression model,” Iran. J. Hematol. Oncol., vol. 15, no. 1, pp. 34–43, 2025.

L. Bonatti, G. Marra, and R. Radice, “Flexible Bayesian functional regression with skewed errors for biomedical applications,” J. Stat. Plan. Inference, vol. 220, p. 104973, 2025.

S. Ghosh, L. Wang, and Y. Tang, “A Bayesian skewed-t process model for quantile regression with censored outcomes,” Bayesian Anal., vol. 19, no. 1, pp. 33–58, 2024.

C. Li, J. Yu, and B. Zhang, “Efficient Hamiltonian Monte Carlo for hierarchical models in high dimensions,” Comput. Stat. Data Anal., vol. 92, pp. 66–78, 2015.

L. Paninski, “Exact Hamiltonian Monte Carlo for truncated distributions,” J. Comput. Graph. Stat., vol. 23, no. 2, pp. 518–539, 2014.

CMStatistics, “Advances in Markov Chain Monte Carlo Methods for Complex Data Structures,” in CMStatistics Conference Proceedings, Lisbon, 2022.