Random irregular histograms

A new method of histogram construction is proposed, providing a fully Bayes-ian approach to irregular histograms. The 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. It is shown 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 Hölder continuous densities. Simulation studies indicate that the new method performs comparably to other histogram procedures in terms of minimizing estimation error, and that it often outperforms other statistical procedures for identifying modes. A software implementation of the proposed method is provided as part of a publicly available Julia package.