I was wondering if there any probability distributions over the probability simplex ($p \in \mathbb{R^n_+}:\sum_i^n p_i=1,p_i\geq 0$). In particular, what are the distributions which can be used to model transition probabilities of an MDP?
One of the common distributions is Dirichlet distribution. There is also logit-normal distribution. But, are there any other distributions with simple posterior updates especially for categorical observations.
Any suggestions would be really helpful.
Thanks!