Title: Density estimation on small datasets,
Abstract: How might a smooth probability distribution be estimated, with accurately
quantified uncertainty, from a limited amount of sampled data? Here we describe
a field-theoretic approach that addresses this problem remarkably well in one
dimension, providing an exact nonparametric Bayesian posterior without relying
on tunable parameters or large-data approximations. Strong non-Gaussian
constraints, which require a non-perturbative treatment, are found to play a
major role in reducing distribution uncertainty. A software implementation of
this method is provided.