Data analysis recipes: Choosing the binning for a histogram

Abstract

Data points are placed in bins when a histogram is created, but there is always a decision to be made about the number or width of the bins. This decision is often made arbitrarily or subjectively, but it need not be. A jackknife or leave-one-out cross-validation likelihood is defined and employed as a scalar objective function for optimization of the locations and widths of the bins. The objective is justified as being related to the histogram's usefulness for predicting future data. The method works for data or histograms of any dimensionality.