A Framework for Obtaining Accurate Posteriors of Strong Gravitational Lensing Parameters with Flexible Priors and Implicit Likelihoods using Density Estimation

TL;DR

This paper introduces a neural network-based Bayesian inference framework for strong gravitational lensing parameters, enabling accurate, scalable posterior estimation with flexible priors and implicit likelihood modeling.

Contribution

It presents a novel implicit likelihood inference method using neural networks and mixture density networks for accurate, scalable Bayesian analysis of strong lensing systems.

Findings

Achieves accurate posteriors with less than 1.4% deviation at 21.8% confidence

Scales efficiently, inferring 100,000 posteriors in one day on a single GPU

Provides a flexible framework for imposing priors and modeling likelihoods in lensing analysis

Abstract

We report the application of implicit likelihood inference to the prediction of the macro-parameters of strong lensing systems with neural networks. This allows us to perform deep learning analysis of lensing systems within a well-defined Bayesian statistical framework to explicitly impose desired priors on lensing variables, to obtain accurate posteriors, and to guarantee convergence to the optimal posterior in the limit of perfect performance. We train neural networks to perform a regression task to produce point estimates of lensing parameters. We then interpret these estimates as compressed statistics in our inference setup and model their likelihood function using mixture density networks. We compare our results with those of approximate Bayesian neural networks, discuss their significance, and point to future directions. Based on a test set of 100,000 strong lensing simulations, our amortized model produces accurate posteriors for any arbitrary confidence interval, with a maximum percentage deviation of $1.4\%$ at $21.8\%$ confidence level, without the need for any added calibration procedure. In total, inferring 100,000 different posteriors takes a day on a single GPU, showing that the method scales well to the thousands of lenses expected to be discovered by upcoming sky surveys.