Binomial mixtures: Geometric estimation of the mixing distribution

Given a mixture of binomial distributions, how do we estimate the unknown m ixing distribution? We build on earlier work of Lindsay and further elucida te the geometry underlying this question, exploring the approximating role played by cyclic polytopes. Convergence of a resulting maximum likelihood f itting algorithm is proved and numerical examples given; problems over the lack of identifiability of the mixing distribution in part disappear.