Bayesian Spline Modelling for Nonparametric Quantile Regression

Abstract

This paper proposes a novel Bayesian Spline Quantile Regression (BSQR) model for flexible, nonparametric modeling of conditional quantile functions in economic and demographic data. By combining B-spline basis expansions with a Bayesian hierarchical framework and Reversible Jump Markov Chain Monte Carlo (RJMCMC), the method adaptively selects both the number and locations of knots, enabling it to capture smooth nonlinearities and distributional heterogeneity without manual tuning. The model is built upon the asymmetric Laplace distribution for quantile-specific likelihood specification and employs horseshoe priors and Gaussian random walks to ensure regularization and smoothness. To evaluate the performance of the proposed method, both simulation studies and a real data application using the WHO Child Growth Standards (Height-for-Age) dataset are conducted.