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How is the mode in Dirichlet-Multinomial calculated?

The mode in Dirichlet-Multinomial is $$ \mathrm{Mode}(\pi_i) = \frac{\alpha_i + x_i - 1}{\sum_{j=1}^k (\alpha_j + x_j -1)} $$ Could you point out how is it calculated please? What is the importance …
Mosab Shaheen's user avatar
1 vote
1 answer
515 views

What are the possible estimates of the parameters of the multinomial distribution?

The expected value of the parameters of the multinomial distribution (taking into account the Dirichlet prior $D(\alpha)$ and the posterior Dirichlet-Multinomial) is: $\pi_i = α_i+ x_i / \sum_{j} α_j …
Mosab Shaheen's user avatar