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Given an image of a scene comprised of a number of distinct terrain classes, the optimum Bayesian classifier (OBC) provides the highest possible classification accuracy of the imaged scene, provided we have a priori knowledge of the probability density function (pdf) of the sensor's output for each terrain class. If the imaging sensor consists of multiple channels, application of OBC requires knowledge of the joint pdf of the observations made by all the channels. In practice, the volume of data needed in order to generate an accurate multidimensional pdf far exceeds the size of available datasets. The data-size requirement may be relaxed by assuming the pdfs to be Gaussian in form, but such an assumption leads to suboptimum classification performance. This paper addresses the data size issue by (1) taking advantage of the maximum-entropy density estimation (MEDE) technique introduced in a companion paper and (2) using marginal pdfs in a hierarchical approach. Using multidate synthetic aperture radar observations, it was shown that the Bayesian hierarchical classifier introduced in this paper can classify short vegetation classes with an accuracy of 93%, without retraining, compared with an accuracy of 84% for the maximum-likelihood estimator (with Gaussian assumption) and only 74% with ISODATA.