Approximate Bayesian Uncertainties on Deep Learning Dynamical Mass Estimates of Galaxy Clusters

TL;DR

This paper develops and evaluates approximate Bayesian neural network methods to accurately estimate uncertainties in galaxy cluster mass predictions, crucial for cosmological studies.

Contribution

It introduces variational inference techniques for Bayesian CNNs applied to galaxy cluster mass estimation, demonstrating high accuracy in posterior recovery.

Findings

Bayesian CNNs produce log-normal mass posteriors.

Confidence intervals are recovered within 1%.

Modeling uncertainties improves cosmological parameter constraints.

Abstract

We study methods for reconstructing Bayesian uncertainties on dynamical mass estimates of galaxy clusters using convolutional neural networks (CNNs). We discuss the statistical background of approximate Bayesian neural networks and demonstrate how variational inference techniques can be used to perform computationally tractable posterior estimation for a variety of deep neural architectures. We explore how various model designs and statistical assumptions impact prediction accuracy and uncertainty reconstruction in the context of cluster mass estimation. We measure the quality of our model posterior recovery using a mock cluster observation catalog derived from the MultiDark simulation and UniverseMachine catalog. We show that approximate Bayesian CNNs produce highly accurate dynamical cluster mass posteriors. These model posteriors are log-normal in cluster mass and recover $68\%$ and $90\%$ confidence intervals to within $1\%$ of their measured value. We note how this rigorous modeling of dynamical mass posteriors is necessary for using cluster abundance measurements to constrain cosmological parameters.