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Thank you very much to Jim Garrett, Patrick Bélisle and David Spiegelhalter for their answers. I'll resume their suggestions. First, it is not possible to have uncertainty on the parameters of the Dirichlet distribution and learn about them. It's just not a facility within BUGS at the moment and it is not a priority. 1/ first suggestion : The Dirichlet distribution is the distribution of independent, equally-scaled gamma variates divided by their sum, perhaps you could work with gamma variables instead. For example, if z_1 ~ gamma(alpha_1, 1), z_2 ~ gamma(alpha_2, 1), and z_3 ~ gamma(alpha_3, 1), and they are independent, and K = z_1 + z_2 + z_3, then z_1/K, z_2/K, and z_3/K are jointly Dirichlet. 2/ second suggestion : logistic-normal models. Having said this, I read an excellent book on compositional data "Analysis of Compositional Data" by Aitchison, from Chapman and Hall publishers. The author points out several limitations to the Dirichlet stemming from the independence assumption, and recommends an alternative in which P variables that sum to one are transformed to P-1 variables that are unconstrained, so that the (P-1)-vector may reasonably be modeled by a multivariate normal. This allows for correlations among the proportions in addition to the correlations implied by the unit-sum constraint. If I recall correctly, the author refers to the generalized logistic transformation, which would be (following the example above) s_1 = log(z_1 / z_3) s_2 = log(z_2 / z_3) s_3 = 0 (i.e., = log(z_3 / z_3) ) The choice of which component will be in the denominator is completely arbitrary. This transformation has the inverse z_1 = exp(s_1) / (exp(s_1) + exp(s_2) + exp(s_3) ), z_2 = exp(s_2) / (exp(s_1) + exp(s_2) + exp(s_3) ), and z_3 = exp(s_3) / (exp(s_1) + exp(s_2) + exp(s_3) ). You could then suppose that (s_1, s_2) ~ bivariate normal and estimate both the mean and variance matrix. It seems to me likely to be straightforward. It is a richer model for the data. (but it cannot handle zero compositions). Claire Chabanet INRA - Laboratoire de Recherches sur les Aromes 17 rue SULLY, BV1540 21034 DIJON cedex FRANCE e-mail : [log in to unmask] %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%