As my series on Expectation Maximisation ("Thoughts on EM") evolved from research, implementations and readings, I will start a new series posting probability functions in their log likelihood form. So in the first post I will post my "log calculations" for the Dirichlet Distribution.

The Dirichlet Distribution is often used as a prior on a multinomial distribution. Using that prior one can estimate Multinomial Distributions more stable, meaning your probability estimates do not go wild. In simple words the Dirichlet Distribution is a distribution over a Multinomial Distribution with parameters

alpha. The alpha parameter is a vector of the same size as the Multinomial Distribution. The probability

density function is:

The scaler can be expressed using the beta function:

Converting the scaler is also straight forwards:

And that is actually all already :D. The log - gamma function can be implemented from the paper :D

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