# Random irregular histograms

arXiv: https://arxiv.org/abs/2505.22034 · HTML: https://mlsanity.com/paper/2505.22034/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 28 May 2025.

## Built on by (most cited first, 1 of 1)

- [Edge Selection for the Effective use of Piecewise-Constant Distributions as Neural Network Outputs for Event Prediction](https://mlsanity.com/paper/2507.21616/) (2025)

## Abstract (arXiv)

We propose a new method of histogram construction, providing a fully Bayesian approach to irregular histograms. Our procedure applies Bayesian model selection to a piecewise constant model of the underlying distribution, resulting in a method that selects both the number of bins as well as their location based on the data in a fully automatic fashion. We show that the histogram estimate is consistent with respect to the Hellinger metric under mild regularity conditions, and that it attains a convergence rate equal to the minimax rate (up to a logarithmic factor) for H"older continuous densities. Simulation studies indicate that the new method performs comparably to other histogram procedures, both for minimizing the estimation error and for identifying modes. A software implementation is included as supplementary material.