Probabilistic Bayesian Neural Networks and Cluster Stellar Masses*

I discuss the use of Bayesian neural networks in the problem of calculating the stellar masses of clusters of galaxies.  Cluster stellar masses are of interest in cluster cosmology experiments as a measure of the total cluster mass, and thus in comparing the observed cluster mass function with the cosmological parameter sensitive theoretical dark matter halo mass function. I will focus not on the galaxy stellar mass calculation but on the steps necessary to use these for clusters: identification of cluster galaxies with photometric data only and in the presence of large numbers of field galaxies,  choosing a radius within which to sum the galaxy stellar masses, and relating the summed aperture cluster stellar mass with the total cluster stellar mass and the total cluster mass including mean and variance. I work with the public LSST Dark Energy Science Collaboration CosmoDC2 simulations. Neural net classifiers are a natural choice for the cluster galaxy  identification problem, and I find probability threshold maps into an outer cluster radius cutoff. The aperture cluster stellar mass

can be related to the true stellar cluster mass by linear regression with or without a neural net, but a probabilistic neural network allows the characterization of the uncertainty distribution, via  an error model whose parameters are calculated point by point. I then examine the use of Bayesian neural networks in predicting the total cluster mass using the stellar mass of the central galaxy and the aperture some of the satellite cluster galaxies. This report covers the use of new tools in a standard problem in cluster cosmology and elucidates ways to understand uncertainty distributions using machine learning techniques.