Nonparametric hierarchical Bayesian quantiles

TL;DR

This paper introduces a nonparametric Bayesian method for quantile inference using geometric measure theory, enabling hierarchical modeling of subpopulation quantiles with straightforward computation, applicable to censored and noisy data.

Contribution

It develops a novel nonparametric Bayesian approach for quantiles based on Hausdorff measures, extending to hierarchical models for subpopulations, with practical computational advantages.

Findings

Method stabilizes and improves inference in simulated data.

Effective in handling censored and noisy data.

Applied successfully to sports statistics data.

Abstract

Here we develop a method for performing nonparametric Bayesian inference on quantiles. Relying on geometric measure theory and employing a Hausdorff base measure, we are able to specify meaningful priors for the quantile while treating the distribution of the data otherwise nonparametrically. We further extend the method to a hierarchical model for quantiles of subpopulations, linking subgroups together solely through their quantiles. Our approach is computationally straightforward, allowing for censored and noisy data. We demonstrate the proposed methodology on simulated data and an applied problem from sports statistics, where it is observed to stabilize and improve inference and prediction.