Normalizing Flows for Bayesian Posteriors: Reproducibility and Deployment

TL;DR

This paper introduces a machine learning framework using normalizing flows to efficiently learn, sample, and deploy complex Bayesian posterior distributions, enhancing reproducibility and scalability in scientific workflows.

Contribution

It presents a novel approach for constructing normalizing flows tailored for Bayesian posteriors, enabling efficient sampling and distribution representation.

Findings

Successfully applied to complex distributions with non-linear correlations and multi-modality.

Demonstrated effectiveness on a realistic Bayesian calibration problem.

Facilitates parallelized, uncorrelated sampling for uncertainty quantification.

Abstract

We present a computational framework for efficient learning, sampling, and distribution of general Bayesian posterior distributions. The framework leverages a machine learning approach for the construction of normalizing flows for the general probability distributions typically encountered in Bayesian uncertainty quantification studies. This normalizing flow can map a trivial distribution to a more complicated one and can be stored more efficiently than the empirical distribution samples themselves. Once the normalized flow is trained, it further enables parallelized and uncorrelated sampling of the learned distribution. We demonstrate our framework with three test distributions with strong non-linear correlations, multi-modality, and heavy tails, as well as with a realistic posterior distribution obtained from a Bayesian calibration of a nuclear relativistic mean-field model. The performance of the framework, as well as its relatively simple implementation, positions it as one fundamental cornerstone in the development and deployment of continuous calibration pipelines of physical models and as a key component of future reproducible science workflows.