All Questions
Tagged with dirichlet-distribution marginal-distribution
9
questions
1
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0
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138
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Marginal density of dirichlet distribution
I'm studying BRML.
In this book, a Dirichlet distribution is defined as
$$
p(\alpha | u) = \frac{\Gamma(\sum_{q=1}^Q u_q)}{\prod_{q=1}^Q \Gamma(u_q)} \delta_0 \left( \sum_{q=1}^{Q} \alpha_q - 1 \right)...
- 11
5
votes
1
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668
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Deriving the marginal multivariate Dirichlet distribution
I am trying to understand how my professor (see derivation below) has derived the multivariate marginal distribution of a subvector of $\theta_j$´s from a Dirichlet distribution. I understand ...
- 83
3
votes
1
answer
1k
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From beta distribution to Dirichlet: Estimation of the concentrantion parameters
Searching at least 3 hours about the connection between beta distribution and dirichlet. My problem is:
I have a collection of random variables $X_i \sim Beta(a_i, b_i)$. The parameters $a_i$ and $...
- 163
1
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0
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113
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Marginal medians of the Dirichlet distribution
I am working with a 3 dimensional Dirichlet distribution with parameters $\alpha_1,\alpha_2,\alpha_3>0$. I have been trying to figure out a useful 'median' concept for this distribution. The vector ...
- 41
2
votes
1
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667
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Why is the mode of the Dirichlet not the same as the modes of its marginals?
The mode of a Dirichlet distribution with parameters $\alpha_1, \alpha_2, \ldots \alpha_N$, $\alpha_i > 1$ is:
$$x_i = \frac{\alpha_i - 1}{\alpha_0 - N}$$.
Where $\alpha_0 = \sum_k{\alpha_k}$. ...
- 85
0
votes
1
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680
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Multivariate marginal Dirichlet distribution
For a vector $X = (x_1, \dots, x_m)$, let $\mathcal{C}(X) = \frac{1}{x_1+\dots+x_m}(x_1, \dots, x_m)$.
If $(X_a, X_b)$ follows a Dirichlet distribution with parameters $(\alpha_{a_1}, \dots, \alpha_{...
- 322
4
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114
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what is this property? $\int p(x,\pi)d\pi=p(x|E[\pi])$?
Sorry if the title does not make sense, from the answer of this question Mistake in derivation about categorical distribution and Dirichlet distribution? it can be shown that
say $p(x|\pi)$ follows ...
- 16.6k
1
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1
answer
380
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Mistake in derivation about categorical distribution and Dirichlet distribution?
$p(x|\pi)$ follows the categorical distribution (the multinomial with one observation), where $\sum\pi_i=1$ and $x$ is a one-hot vector, and $p(\pi|\alpha)$ follows the Dirichlet distribution.
$p(x|\...
- 16.6k
10
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1
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1k
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Marginal probability function of the Dirichlet-Multinomial distribution
I can't seem to find a written out derivation for the marginal probability function of the compound Dirichlet-Multinomial distribution, though the mean and variance/covariance of the margins seem to ...
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