A Bayesian method for histograms

Abstract

SUMMARY This paper describes a Bayesian procedure for the simultaneous estimation of the probabilities in a histogram. A two-stage prior distribution is constructed which assumes that probabilities corresponding to adjacent intervals are likely to be closely related. The method employs multivariate logit transformations, and a covariance structure similar to that assumed in the first-order autoregressive process. Posterior estimates are obtained which combine information between the intervals and have the practical effect of smoothing the histogram.