You may use independent Dirichlet distributions across subjects (i's).

Thank you for answer.

Do I understand your order?

Please see the file and i asked the a question.

Posterior can exhibit any form but the most important is the prior information.Choice of prior is always the issue in Bayesian framework.May you should try possible number of priors;informative, non informative and so on.I think Multivariate gamma prior may be somehow suitable.

Hi.

If your matrix represents a complete set of non-overlapping categories, then Dirichlet is OK.  It does not matter if you represent such categories as a NxM matrix or as a vector of length NxM.

Cheers,

Diego

You might consider a hierarchical model, where you have n independent Dirichlet distributions with common parameter (like in your reply to Hamideh Sadat Fatemi Ghomi), and then put a prior on the common parameter.  This would typically require MCMC to estimate. But you could also use empirical Bayes to come up with a point estimate for the common prior and solve this model exactly.