## 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.

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### Some articles on dirichlet distribution:

... 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 ...

... 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 ...

... 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 ...

**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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