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Estimating a Dirichlet distribution
, 2000
"... The Dirichlet distribution and its compound variant, the Dirichletmultinomial, are two of the most basic models for proportional data, such as the mix of vocabulary words in a text document. Yet the maximumlikelihood estimate of these distributions is not available in closedform. This paper descr ..."
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The Dirichlet distribution and its compound variant, the Dirichletmultinomial, are two of the most basic models for proportional data, such as the mix of vocabulary words in a text document. Yet the maximumlikelihood estimate of these distributions is not available in closedform. This paper describes simple and efficient iterative schemes for obtaining parameter estimates in these models. In each case, a fixedpoint iteration and a NewtonRaphson (or generalized NewtonRaphson) iteration is provided. 1 The Dirichlet distribution The Dirichlet distribution is a model of how proportions vary. Let p denote a random vector whose elements sum to 1, so that pk represents the proportion of item k. Under the Dirichlet model with parameter vector α, the probability density at p is p(p) ∼ D(α1,...,αK) = Γ(∑k αk) k Γ(αk)