AutoHist.jl

A pure Julia implementation of automatic regular and irregular histogram methods based on maximizing a goodness-of-fit criterion.

Introduction

Most default histogram plotting software only support a few regular automatic histogram procedures and use very simple plug-in rules by default to compute the the number of bins, frequently leading to poor density estimates for non-normal data [cf. Birgé and Rozenholc (2006), Simensen et al. (2025)]. The purpose of this software package is to offer the user a fast and simple-to-use implementation of more sophisticated regular and irregular histogram procedures. Our package supports a variety of methods including those based on asymptotic risk minimization, leave-one-out cross-validiation, penalized maximum likelihood and fully Bayesian approaches.

Installation

Installing the package is most easily done via Julia's builtin package manager Pkg. This package is part of the Julia general registry, so the installation can be done via the two following lines of code: julia using Pkg Pkg.add("AutoHist")

Quick start

To get started, we illustrate the basic use of the package by fitting histograms to a normal random sample with an automatic selection of the histogram partition.

julia using AutoHist x = randn(10^6) h1 = fit(AutomaticHistogram, x)

Several rules are available to select the histogram partition, and can be controlled through the use of the rule positional argument. For instance, a regular histogram based on maximizing the AIC can be fit as follows: julia h2 = fit(AutomaticHistogram, x, AIC()) Alternatively, we can use the autohist method, which serves as an alias for fit(AutomaticHistogram, ...) julia h2 = autohist(x, AIC())

A detailed exposition of the keyword arguments passed to fit can be found by typing ?fit in the repl or in the API documentation. A detailed description of all methods currently implemented in AutoHist.jl can be found in the methods documentation.

The fitted histograms can be displayed through the Plots.jl or Makie.jl packages as follows:

julia import Plots, CairoMakie, Makie Plots.plot(h1) Makie.plot(h1)

Supported criteria

The argument rule determines the method used to construct the histogram for both of the histogram functions. The rule used to construct the histogram can be changed by setting rule equal to a symbol indicating the method to be used, e.g. BIC() which yields an automatic regular histogram based on the BIC criterion.

The default method is the Bayesian approach of Simensen et al. (2025), corresponding to keyword rule=RIH(). A detailed description of the supported methods can be found in the methods documentation.

Contributing

If you encounter a bug when using this software or have a feature request, then feel free to open a github issue.

Coding contributions are also very much welcome, especially if you are looking to add a new automatic histogram rule or a new algorithm. To make sure that your proposed new feature is a good fit for the AutoHist package, please open a new issue to discuss how your contribution could elevate AutoHist.jl.

References

Simensen, O. H., Christensen, D. & Hjort, N. L. (2025). Random Irregular Histograms. arXiv preprint. doi: 10.48550/ARXIV.2505.22034

Rozenholc, Y., Mildenberger, T., & Gather, U. (2010). Combining regular and irregular histograms by penalized likelihood. Computational Statistics & Data Analysis, 54, 3313–3323. doi: 10.1016/j.csda.2010.04.021

Kanazawa, Y. (1988). An optimal variable cell histogram. Communications in Statistics-Theory and Methods, 17, 1401–1422. doi: 10.1080/03610928808829688

Birgé, L., & Rozenholc, Y. (2006). How many bins should be put in a regular histogram. ESAIM: Probability and Statistics, 10, 24–45. doi: 10.1051/ps:2006001