Parametric Density Estimation with Uncertainty using Deep Ensembles

In parametric density estimation, the parameters of a known probability density are typically recovered from measurements by maximizing the log-likelihood. Prior knowledge of measurement uncertainties is not included in this method -- potentially producing degraded or even biased parameter estimates. We propose an efficient two-step, general-purpose approach for parametric density estimation using deep ensembles. Feature predictions and their uncertainties are returned by a deep ensemble and then combined in an importance weighted maximum likelihood estimation to recover parameters representing a known density along with their respective errors. To compare the bias-variance tradeoff of different approaches, we define an appropriate figure of merit. We illustrate a number of use cases for our method in the physical sciences and demonstrate state-of-the-art results for X-ray polarimetry that outperform current classical and deep learning methods.