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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Construction of Dirichlet distribution with 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 exactly is the alpha in the Dirichlet distribution?
I'm fairly new to Bayesian statistics and I came across a corrected correlation measure, SparCC, that uses the Dirichlet process in the backend of it's algorithm. I have been trying to go through the ...
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could someone please give a concrete example to illustrate the Dirichlet distribution prior for bag-of-words?
I am aware of the notion of the Dirichlet distribution, a multivariate generalization of the beta distribution.
To get parameters of the Dirichlet distribution prior for bag-of-words, this CMU ...
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What happens when merging random variables in Dirichlet distribution?
Imagine that
$$ X_1,\dots,X_k \sim \mathrm{Dirichlet}(\alpha_1,\dots,\alpha_k) $$
Since $x_i \in (0,1)$ for all $x_i$ and $\sum_{i=1}^k x_i = 1$, then $x_i$'s follow the first two axioms of ...
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Why is the Dirichlet distribution the prior for the multinomial distribution?
In LDA topic model algorithm, I saw this assumption. But I don't know why chose Dirichlet distribution? I don't know if we can use Uniform distribution over Multinomial as a pair?
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The meaning of representing the simplex as a triangle surface in Dirichlet distribution?
I'm reading from a book that introduces the Dirchilet distribution and then presented figures about it. But I was not really able to understand those figures. I attached the figure here at the bottom. ...
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Can a Multinomial(1/n, ..., 1/n) be characterized as a discretized Dirichlet(1, .., 1)?
So this question is slightly messy, but I'll include colourful graphs to make up for that! First the Background then the Question(s).
Background
Say you have a $n$-dimensional multinomial ...
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Distribution of the largest fragment of a broken stick (spacings)
Let a stick of length 1 be broken in $k+1$ fragments uniformly at random. What is the distribution of the length of the longest fragment?
More formally, let $(U_1, \ldots U_k)$ be IID $U(0,1)$, and ...
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Generate a random set of numbers with fixed sum and desired means and variances?
The Dirichlet distribution allows you to generate a sample of numbers $x_i$ with a prescribed sum, say $\sum_i x_i = 1$. Moreover, the parameters $\alpha$ allow some degree of control on the means of ...
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Find marginal distribution of $K$-variate Dirichlet
I've already seen https://math.stackexchange.com/questions/1064995/marginal-of-dirichlet-distribution-is-beta-integral, but need to extend this to the $K$-variate case.
We have $\mathbf{x} = \begin{...
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On posterior in the Bayesian bootstrap
The Bayesian bootstrap was introduced by Rubin (1981) as a Bayesian analog of the original bootstrap. Given dataset $X=\{x_1, \dots, x_N\}$, instead of drawing weights $\pi_{n}$ from the discrete set
$...
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How to use the Dirichlet prior for estimating the multinomial parameters? [closed]
I know that the multinomial distribution gives the likelihood of some vector D of occurrences to happen given a probability vector (parameters) P' i.e. P(D|P'). Now with a Dirichlet prior we are ...
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Multinomial-Dirichlet model with hyperprior distribution on the concentration parameters
I will try to describe the problem at hand as general as possible. I am modeling observations as a categorical distribution with a parameter probability vector theta.
Then, I assume the parameter ...
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What is the expected value of modified Dirichlet distribution? (integration problem)
It is easy to produce a random variable with Dirichlet distribution using Gamma variables with the same scale parameter. If:
$ X_i \sim \text{Gamma}(\alpha_i, \beta) $
Then:
$ \left(\frac{X_1}{\...
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Implementation of Dirichlet cdf?
I need to compute the Dirichlet CDF, but I can only find implementations of the PDF.
Do you guys know of any library (preferably in R) implementing it?
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