Questions tagged [dirichlet-distribution]
The Dirichlet distribution refers to a family of multivariate distributions, which are the generalization of the univariate beta distribution.
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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 ...
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Parametrization of Dirichlet distribution
Hej!
Consider I have a Dirichlet distribution with 4 variables, where the mean (u) values of these are known. $(u1+u2+u3+u4=1)$
Now, I want to obtain the parameters of the Dirichlet distribution ($\...
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Calculate log likelihood of Dirichlet distribution using Gamma distribution
Let $X_1,\dots,X_{k+1}$ be mutually independent random variables, each having a gamma distribution with parameters $\alpha_i,i=1,2,\dots,k+1$ show that $Y_i=\frac{X_i}{X_1+\cdots+X_{k+1}},i=1,\dots,k$,...
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What Distribution Do I need?
Suppose I am drawing coloured balls from a bag.
The ball can be red, green or blue.
The probabilities of drawing a red, green or blue bag are uncertain, but I have confidence bounds for the ...
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Is there a statistical distribution whose values are bounded $[-1,1]$ and sum to 1?
The Dirichlet distribution contains values that are bounded $[0,1]\in \mathbb{R}$ and sum to $1$. Is there a parametric distribution or similar method whose values do the same but reach as low as $-1$?...
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Probability that a Linear Combination of Dirichlet Random Variables is a Distribution
I've been putting a lot of thought on this problem, but it seems I ran out of ideas. Any help would be appreciated! Suppose we generate two probability vectors $\boldsymbol{\theta}_1, \boldsymbol{\...
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Restriction and dependence in the Dirichlet distributon
The Dirichlet distribution is sometimes said that it is "too restrictive and imposes strong conditions on the dependence between components". What is the reason?
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Overall variance of a Dirichlet distribution
I have observations on proportion of individuals at different age groups. I'm doing some simulation experiments, and I need to introduce error in the observed data. For that, I'm simulating data from ...
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Marginal Cluster assignments for Dirichlet Process mixture model
I am watching Tamara' Broderick video on Dirichlet Process mixture models where she talks about computing $p(z_n = k | z_1,z_2,..z_{n-1})$ at ardoun 16:06. The z's are drawn from $$\rho_1 \sim beta(...
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How to derive the expectation of $\ln \mu_j$ in Dirichlet distribution
I have derived the mean and variance of $\mu_j$ in Dirichlet distribution $\text{Dir}(\mu_1, \cdots, \mu_K|\alpha_1, \cdots, \alpha_k)$.
On https://en.wikipedia.org/wiki/Dirichlet_distribution, it ...
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What is a non-informative choice of parameters for a Dirichlet distribution?
Dirichlet distribution is a conjugate prior for multinomial distribution. I want to impose a non-informative prior over sampling weights $\pi$ for a draw $x=(x_1,…,x_N)$ from a multinomial ...
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Uniform posterior on bounded space [duplicate]
In a particular Bayesian problem, I have encountered a choice of parameters that leads to a uniform posterior distribution. Given prior
\begin{equation}
p(\boldsymbol{\pi}) =Dirichlet(\boldsymbol{\...
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How to model proportions with a hierarchical structure?
I have thinking about how to model proportions for a problem with hierarchical structure.
In the problem, I have observations of users over multiple days, where each observation is a proportion of ...
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Softmax vs the Dirichlet distribution
As far as I understand one can in principle model the distribution over a set of $k$ categories using e.g.:
the Dirichlet distribution
A softmax model.
As far as I can tell, both use $k$ parameters ...
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How does the uniform Dirichlet PDF integrate to 1?
For the uninformative 3-dimensional Dirichlet prior ${\rm Dir}(1, 1, 1)$, I understand that the probability density function (PDF) evaluates uniformly to 2, and the support are all three-dimensional ...
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