How many bins should be put in a regular histogram

Abstract

Given an n-sample from some unknown density f on [0, 1], it is easy to construct an histogram of the data based on some given partition of [0, 1], but not so much is known about an optimal choice of the partition, especially when the set of data is not large, even if one restricts to partitions into intervals of equal length. Existing methods are either rules of thumbs or based on asymptotic considerations and often involve some smoothness properties of f . Our purpose in this paper is to give a fully automatic and simple method to choose the number of bins of the partition from the data. It is based on a nonasymptotic evaluation of the performances of penalized maximum likelihood estimators in some exponential families due to Castellan and heavy simulations which allowed us to optimize the form of the penalty function. These simulations show that the method works quite well for sample sizes as small as 25.

Adaptive estimation of a quadratic functional of a density by model selection

“…A simulation study would be necessary to know how to calibrate κ 0 in practice. Such a simulation study was carried out by Birgé and Rozenholc [4] in the case of density estimation with histograms.…”

Background subtraction and transient timing with Bayesian Blocks

“…Various estimates for the best bin width have been proposed (see Birgé & Rozenholc 2006 for a discussion), but they often suggest too few bins to perform timing analyses. The commonly used rule of Sturges (1926), taking 1 + log 2 N intervals, gives only 18 or 19 bins for the 154 992 source photons.…”

Uncertainty Assessment and Weight Map Generation for Efficient Fusion of Tandem-X and Cartosat-1 Dems

“…The significant characteristic of this pre-processing step is to bin feature values by a statisticalempirical binning approach. The feature values and their corresponding height residuals are binned by Freedman-Diaconis rule (Birgé and Rozenholc, 2006):…”