  We present a novel population-based Bayesian inference approach to model the
average and population variance of spatial distribution of a set of observables
from ensemble analysis of low signal-to-noise ratio measurements. The method
consists of (1) inferring the average profile using Gaussian Processes and (2)
computing the covariance of the profile observables given a set of independent
variables. Our model is computationally efficient and capable of inferring
average profiles of a large population size from noisy measurements, without
stacking and binning data nor parameterizing the shape of the mean profile. We
demonstrate the performance of our method using dark matter, gas and stellar
profiles extracted from hydrodynamical cosmological simulations of galaxy
formation. Population Profile Estimator (PoPE) is publicly available in a
GitHub repository. Our new method should be useful for measuring the spatial
distribution and internal structure of a variety of astrophysical systems using
large astronomical surveys.
