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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Is sparsity of topics a necessary condition for latent Dirichlet allocation (LDA) to work
I have been playing with the hyper-parameters of the latent Dirichlet allocation (LDA) model and am wondering how sparsity of topic priors play a role in inference.
I have not performed these ...
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Statistical test to compare Dirichlet distributions
I want assess if two groups are statistically significantly different. I assume the data points in both groups are generated from a Dirichlet distribution - is there an appropriate test for this?
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Generalization of Dirichlet distribution over matrix
I know there is generalization of normal distribution of matrix-valued random variable, i.e., Matrix normal distribution. I wonder whether there is generalization of Dirichlet distribution that each ...
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Gibbs sampling for LDA -- does a small Dirichlet concentration parameter make a difference?
I'm using a Gibbs sampler for Latent Dirichlet allocation as described by Griffiths and Steyvers (http://www.ncbi.nlm.nih.gov/pmc/articles/PMC387300/). The sampling of a new topic $j$ for word $i$ is ...
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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 ...
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Better prediction models with polling data?
I've been working on a project on measuring polls' accuracy in complex contexts (more than two candidates) where there are a small number of inaccurate polling data points.
I thought it would be the ...
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compute Dirichlet distribution parameter from known mean distribution
For a particular Bayesian study I am going to apply Dirichlet distribution as my proposal random number generator. I am going to update the distribution parameter every trial based on a given ...
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Bounding values of a Dirichlet distribution
Consider $k$ random variables $X_1, X_2, \ldots, X_k$ such that $(X_1, X_2, \ldots, X_k)$ follow a $\text{Dirichlet}(1, 1, \ldots, 1)$ distribution. For a large enough $k$, I am trying to bound/find ...
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A clarification in the original Dirichlet Process paper by Ferguson
I am reading the paper "Bayesian Analysis of Some Nonparametric Problems" by Ferguson where the Dirichlet process is introduced. There is a proposition 5 where the joint distribution of ...
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How to specify a zero-inflated Dirichlet model in JAGS/BUGS
There was a recent publication discussing the advantages of the zero-inflated dirichlet for microbiome count data which is compositional (you are modeling a matrix of species relative abundance data ...
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Sampling from conjugate Dirichlet distribution
Conjugate prior for Dirichlet distribution, as described by Lefkimmiatis, Maragos, and Papandreou (2009; see also here and here), has form
$$
f(\boldsymbol{\alpha}) \propto \frac{1}{B(\boldsymbol{\...
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Help in understanding equation and reference request for multivariate GLM
I am reading page 5 in this document: http://epub.wu.ac.at/4077/1/Report125.pdf
It's about Dirichlet regression in a GLM-like setting. What I don't understand is
each observed $y_c$ (of which there ...
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Categorical Distribution versus Multinomial
In the wikipedia article on Categorical Distribution link under "Terminology" it states that care should be taken between Categorical and Multinomial Distributions, with additionally:
However, ...
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Dirichlet regression with repeated measures
My dependent variable is composition (proportions of a whole object), so I have found that a Dirichlet Regression would be a potential option. However, my study collects repeated measures. Can this ...
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What is the mode of the Dirichlet distribution when some $\alpha_i < 1$
Suppose $X \sim \mathcal D(\alpha_1, \ldots, \alpha_p)$, and suppose $\alpha_i < 1$ for some $\alpha_i$. In this case, the density is unbounded, and so no proper "mode" can exist.
On the other ...
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