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We present results exploring the role that probabilistic deep learning modelsplay in cosmology from large-scale astronomical surveys through photometricredshift (photo-z) estimation. Photo-z uncertainty estimates are critical forthe science goals of upcoming large-scale surveys such as LSST, however commonmachine learning methods typically provide only point estimates and lackuncertainties on predictions. We turn to Bayesian neural networks (BNNs) as apromising way to provide accurate predictions of redshift values withuncertainty estimates. We have compiled a new galaxy training data set from theHyper Suprime-Cam Survey with grizy photometry, which is designed to be asmaller scale version of large surveys like LSST. We use this data set toinvestigate the performance of a neural network (NN) and a probabilistic BNNfor photo-z estimation and evaluate their performance with respect to LSSTphoto-z science requirements. We also examine the utility of photo-zuncertainties as a means to reduce catastrophic outlier estimates. The BNNmodel outputs the estimate in the form of a Gaussian probability distribution.We use the mean and standard deviation as the redshift estimate anduncertainty, respectively. We find that the BNN can produce accurateuncertainties. Using a coverage test, we find excellent agreement withexpectation -- 67.2% of galaxies between 0 < 2.5 have 1-$\sigma$ uncertaintiesthat cover the spectroscopic value. We find the BNN meets 2/3 of the LSSTphoto-z science requirements in the range 0 < z < 2.5 and generally outperformsthe alternative photo-z methods considered here on the same data.

Photometric Redshifts for Cosmology: Improving Accuracy and Uncertainty Estimates Using Bayesian Neural Networks