Density Estimation via Bayesian Inference Engines

TL;DR

This paper introduces a Bayesian inference-based method for density estimation that leverages modern inference engines, demonstrating strong performance and scalability, with practical implementation in R.

Contribution

It presents a novel Bayesian density estimation approach using contemporary inference engines, with scalable binning and credible intervals, and provides an R package for easy application.

Findings

Excellent comparative performance in simulations

Scales well to large sample sizes

Provides credible intervals for estimates

Abstract

We explain how effective automatic probability density function estimates can be constructed using contemporary Bayesian inference engines such as those based on no-U-turn sampling and expectation propagation. Extensive simulation studies demonstrate that the proposed density estimates have excellent comparative performance and scale well to very large sample sizes due to a binning strategy. Moreover, the approach is fully Bayesian and all estimates are accompanied by pointwise credible intervals. An accompanying package in the R language facilitates easy use of the new density estimates.