Density estimation on small datasets
Data Analysis, Statistics and Probability
2018-10-24 v4 Numerical Analysis
Computational Physics
Quantitative Methods
Methodology
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.
Cite
@article{arxiv.1804.01932,
title = {Density estimation on small datasets},
author = {Wei-Chia Chen and Ammar Tareen and Justin B. Kinney},
journal= {arXiv preprint arXiv:1804.01932},
year = {2018}
}
Comments
Includes main text (5 pages, 3 figures) and Supplemental Information (10 pages, 4 figures). Same as version 3 but with Feynman diagrams properly rendered