Given a mixture of binomial distributions, how do we estimate the unknown mixing distribution? We build on earlier work of Lindsay and further elucidate the geometry underlying this question, exploring the approximating role played by cyclic polytopes. Convergence of a resulting maximum likelihood fitting algorithm is proved and numerical examples given; problems over the lack of identifiability of the mixing distribution in part disappear.
"Binomial mixtures: geometric estimation of the mixing distribution." Ann. Statist. 27 (5) 1706 - 1721, October 1999. https://doi.org/10.1214/aos/1017939148