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Estimation of Discrete Distributions with a Class of Simplex Constraints

Abstract Simplex constraints, such as monotonicity and convexity or concavity on the probabilities of a set of discrete distributions, are useful for modeling and analyzing discrete data. This article considers both maximum likelihood estimation and Bayesian estimation of discrete distribution with a class of simplex constraints using the Expectation-Maximization (EM) algorithm and the data augmentation (DA) algorithm. The formulation and implementation of EM and DA for binomial, Poisson, hierarchical Poisson-binomial, multinomial, and hierarchical multinomial distributions are considered in detail and illustrated with examples.