dorsal/arxiv
View SchemaOptimal Data-Based Binning for Histograms
| Authors | Kevin H. Knuth |
|---|---|
| Categories | |
| ArXiv ID | physics/0605197 |
| URL | https://arxiv.org/abs/physics/0605197 |
| License | http://arxiv.org/licenses/nonexclusive-distrib/1.0/ |
Abstract
Histograms are convenient non-parametric density estimators, which continue to be used ubiquitously. Summary quantities estimated from histogram-based probability density models depend on the choice of the number of bins. We introduce a straightforward data-based method of determining the optimal number of bins in a uniform bin-width histogram. By assigning a multinomial likelihood and a non-informative prior, we derive the posterior probability for the number of bins in a piecewise-constant density model given the data. In addition, we estimate the mean and standard deviations of the resulting bin heights, examine the effects of small sample sizes and digitized data, and demonstrate the application to multi-dimensional histograms.
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"date_created": "2026-03-02T18:01:07.419000Z",
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"abstract": "Histograms are convenient non-parametric density estimators, which continue\nto be used ubiquitously. Summary quantities estimated from histogram-based\nprobability density models depend on the choice of the number of bins. We\nintroduce a straightforward data-based method of determining the optimal number\nof bins in a uniform bin-width histogram. By assigning a multinomial likelihood\nand a non-informative prior, we derive the posterior probability for the number\nof bins in a piecewise-constant density model given the data. In addition, we\nestimate the mean and standard deviations of the resulting bin heights, examine\nthe effects of small sample sizes and digitized data, and demonstrate the\napplication to multi-dimensional histograms.",
"arxiv_id": "physics/0605197",
"authors": [
"Kevin H. Knuth"
],
"categories": [
"physics.data-an",
"math.PR",
"math.ST",
"physics.comp-ph",
"stat.TH"
],
"license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
"title": "Optimal Data-Based Binning for Histograms",
"url": "https://arxiv.org/abs/physics/0605197"
},
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