  We present results exploring the role that probabilistic deep learning models
can play in cosmology from large scale astronomical surveys through estimating
the distances to galaxies (redshifts) from photometry. Due to the massive scale
of data coming from these new and upcoming sky surveys, machine learning
techniques using galaxy photometry are increasingly adopted to predict galactic
redshifts which are important for inferring cosmological parameters such as the
nature of dark energy. Associated uncertainty estimates are also critical
measurements, however, common machine learning methods typically provide only
point estimates and lack uncertainty information as outputs. We turn to
Bayesian neural networks (BNNs) as a promising way to provide accurate
predictions of redshift values. We have compiled a new galaxy training dataset
from the Hyper Suprime-Cam Survey, designed to mimic large surveys, but over a
smaller portion of the sky. We evaluate the performance and accuracy of
photometric redshift (photo-z) predictions from photometry using machine
learning, astronomical and probabilistic metrics. We find that while the
Bayesian neural network did not perform as well as non-Bayesian neural networks
if evaluated solely by point estimate photo-z values, BNNs can provide
uncertainty estimates that are necessary for cosmology
