 EM for merged multinomial cells

For a multinomial distribution with two unobserved cells merged into one observed count, the conditional allocation is a binomial distribution with probabilities proportional to the two cell probabilities. The expectation-maximization algorithm replaces the missing counts by their conditional expectations in the parameter-dependent part of the complete-data log-likelihood. The expectation of a log-factorial normalization generally differs from its value at the expected count, but this difference is independent of the candidate parameter and does not affect the maximization step.