2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/84251We study properties of popular near-uniform (Dirichlet) priors for learning undersampled probability distributions on discrete nonmetric spaces and show that they lead to disastrous results. However, an Occam-style phase space argument expands the priors into their infinite mixture and resolves most of the observed problems. This leads to a surprisingly good estimator of entropies of discrete distributions.LaTex2e, 9 pages, 5 figures; references added, minor revisions introduced, formatting errors correctedData Analysis, Statistics and Probabilitytext