Density estimation on small datasets
For statisticians and practitioners needing reliable density estimates with uncertainty quantification from limited data, this provides a principled nonparametric solution, though it is currently limited to one dimension.
The authors develop a field-theoretic Bayesian method for smooth probability density estimation from small datasets, achieving exact nonparametric posteriors without tunable parameters. The approach demonstrates that non-Gaussian constraints significantly reduce uncertainty in one-dimensional settings.
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.