Bayesian Non-parametric Quantile Process Regression and Estimation of Marginal Quantile Effects

Flexible estimation of multiple conditional quantiles is of interest in numerous applications, such as studying the effect of pregnancy-related factors on very low or high birth weight. We propose a Bayesian non-parametric method to simultaneously estimate non-crossing, non-linear quantile curves. We expand the conditional distribution function of the response in I-spline basis functions where the covariate-dependent coefficients are modeled using neural networks. By leveraging the approximation power of splines and neural networks, our model can approximate any continuous quantile function. Compared to existing models, our model estimates all rather than a finite subset of quantiles, scales well to high dimensions, and accounts for estimation uncertainty. While the model is arbitrarily flexible, interpretable marginal quantile effects are estimated using accumulative local effect plots and variable importance measures. A simulation study shows that our model can better recover quantiles of the response distribution when the data is sparse, and illustrative applications providing new insights on analyses of birth weight and tropical cyclone intensity are presented.