Hi! Thanks for the reply …
Well, to my mind the mean of the lower level category rates lam_j would not be on the same order of magnitdude as the parent rate, lam and this is really the crux of the issue to my mind … Let’s say lam was around 3, and there were 6 sub-categories lam_1 … lam_6 then each lam_j would each be in the ball park of 0.5, as a naive estimate, since we require lam_1 + … + lam_6 = lam … But this does give me the simple idea of centering each lam_j around lam/n where n is the number of categories …
—> Would estimating each lam_j ~ N(lam/n, sigma) make sense? where n = number of sub-categories … [or replace N(lam/n, sigma) by some more appropriate distribution]
… or to put it in terms of Dirichlet distribution, this would be (p1, … pn) ~ Dirichlet(alpha_1, … alpha_n) where all alpha_j are approximately equal and therefore pj is approx 1/n
and lam_j = pj lam