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# Questions tagged [multinomial-dirichlet]

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### Multinomial distribution: probability that one outcome is greater than another

Consider a multinomial distribution with three outcomes. Let $x_i$ denote the number of occurences of the $i^{th}$ outcome, and the $i^{th}$ outcome occurs with probability $p_i$, $i=1,2,3$. Let $n$ ...
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### Multinomial-dirichlet with fractional counts

Suppose a lepidopterologist wants to estimate the relative proportions of three different species of butterfly. They go out into the field and count $N$ butterflies and record the number of each ...
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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 ...
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+...