Density estimation on small datasets
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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.
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