Thus p(d|α) (using the standard α notation for Dirichlet parameters) has distribution: Maximum likelihood estimates for the α are difficult to obtain, since the likelihood for α is a function which must be maximised for all components simultaneously, leading some authors to use approximate distributions to improve the tractability of maximum likelihood estimation (Elkan, 2006).
we reparameterise the Dirichlet compound multinomial, and estimate some of the parameters in closed form.