What you call a histogram classifier, is within statistics known as a multinomial classifier. You can include one 'histogram variable', or more histogram variables. Several statisticians have published on this type of classifiers. One classic paper is that of Glick (1973).
A shorter introduction to the histogram classifier is found in the following link Multinomial naive Bayes classifier. When each feature-histogram is treated independently of all the other ones, it is a naive Bayes classifier. For this type a classifier, the assumption of conditional independence applies. This means that all feature outomes are probabilistically independent, given the class label.
In practice, naive Bayes classifiers yield good discriminating performance and should always be used as a comparative benchmark when building a set of classifiers.
N. Glick. "Sample-Based Multinomial Classification," Biometrics,
Vol. 29, No. 2 (Jun., 1973), pp. 241-256.