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We study methods for reconstructing Bayesian uncertainties on dynamical massestimates of galaxy clusters using convolutional neural networks (CNNs). Wediscuss the statistical background of approximate Bayesian neural networks anddemonstrate how variational inference techniques can be used to performcomputationally tractable posterior estimation for a variety of deep neuralarchitectures. We explore how various model designs and statistical assumptionsimpact prediction accuracy and uncertainty reconstruction in the context ofcluster mass estimation. We measure the quality of our model posterior recoveryusing a mock cluster observation catalog derived from the MultiDark simulationand UniverseMachine catalog. We show that approximate Bayesian CNNs producehighly accurate dynamical cluster mass posteriors. These model posteriors arelog-normal in cluster mass and recover $68\%$ and $90\%$ confidence intervalsto within $1\%$ of their measured value. We note how this rigorous modeling ofdynamical mass posteriors is necessary for using cluster abundance measurementsto constrain cosmological parameters.

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