  Histograms are convenient non-parametric density estimators, which continue
to be used ubiquitously. Summary quantities estimated from histogram-based
probability density models depend on the choice of the number of bins. We
introduce a straightforward data-based method of determining the optimal number
of bins in a uniform bin-width histogram. By assigning a multinomial likelihood
and a non-informative prior, we derive the posterior probability for the number
of bins in a piecewise-constant density model given the data. In addition, we
estimate the mean and standard deviations of the resulting bin heights, examine
the effects of small sample sizes and digitized data, and demonstrate the
application to multi-dimensional histograms.
