Bayesian Quantile Matching Estimation

TL;DR

This paper introduces a Bayesian approach for estimating data distributions from quantile information, enabling analysis when only aggregated data like means and quantiles are available, which is common due to privacy restrictions.

Contribution

It presents a novel Bayesian method that accurately models uncertainty in quantile data and provides a practical Python package for implementation.

Findings

Method accurately reflects uncertainty in quantile estimates

Applicable to simulated and real-world data

Provides a Python package for easy use

Abstract

Due to increased awareness of data protection and corresponding laws many data, especially involving sensitive personal information, are not publicly accessible. Accordingly, many data collecting agencies only release aggregated data, e.g. providing the mean and selected quantiles of population distributions. Yet, research and scientific understanding, e.g. for medical diagnostics or policy advice, often relies on data access. To overcome this tension, we propose a Bayesian method for learning from quantile information. Being based on order statistics of finite samples our method adequately and correctly reflects the uncertainty of empirical quantiles. After outlining the theory, we apply our method to simulated as well as real world examples. In addition, we provide a python-based package that implements the proposed model.