# What is dirichlet distribution?

## Dirichlet Distribution

In probability and statistics, the Dirichlet distribution (after Johann Peter Gustav Lejeune Dirichlet), often denoted, is a family of continuous multivariate probability distributions parametrized by a vector of positive reals. It is the multivariate generalization of the beta distribution. Dirichlet distributions are very often used as prior distributions in Bayesian statistics, and in fact the Dirichlet distribution is the conjugate prior of the categorical distribution and multinomial distribution. That is, its probability density function returns the belief that the probabilities of K rival events are given that each event has been observed times.

### Some articles on dirichlet distribution:

Latent Dirichlet Allocation - Inference
... See also Dirichlet-multinomial distribution Learning the various distributions (the set of topics, their associated word probabilities, the topic of each word, and the particular topic mixture of ... The original paper used a variational Bayes approximation of the posterior distribution alternative inference techniques use Gibbs sampling and ... in the above equation by the true distribution expression to write out the explicit equation Let be the number of word tokens in the document with the same word symbol (the word in ...
Rule Of Succession - Generalization To Any Number of Possibilities
... comes from setting a binomial likelihood, and a uniform prior distribution ... is just the multivariate extensions of these two distributions 1)Setting a uniform prior over the initial m categories, and 2) using the multinomial ... It can be shown that the uniform distribution is a special case of the Dirichlet distribution with all of its parameters equal to 1 (just as the uniform is Beta(1,1) in the ...
Hidden Markov Model - Extensions
... discrete (typically generated from a categorical distribution) or continuous (typically from a Gaussian distribution) ... related variables and where all hidden and observed variables follow a Gaussian distribution ... Hidden Markov models are generative models, in which the joint distribution of observations and hidden states, or equivalently both the prior distribution of hidden states (the ...
Dirichlet Distribution - Intuitive Interpretations of The Parameters - Pólya's Urn
... To see that this limiting vector has the above Dirichlet distribution, check that all mixed moments agree ... This "diminishing returns" effect can also help explain how small α values yield Dirichlet distributions with most of the probability mass concentrated ...
Generalized Dirichlet Distribution
... In statistics, the generalized Dirichlet distribution (GD) is a generalization of the Dirichlet distribution with a more general covariance structure and almost twice the ... Random variables with a GD distribution are neutral ... This reduces to the standard Dirichlet distribution if for ( is arbitrary) ...

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