Dirichlet distribution

(45 minutes to learn)


The Dirichlet distribution specifies a distribution on a n-dimensional vector and can be viewed as a probability distribution on a n-1 dimensional simplex (a simplex is an n-dimensional generalization of a triangle). Its parameters determine the distribution of mass on this simplex. The Dirichlet distribution is a conjugate prior to the categorigal and multinomial distributions, and for this reason, it is common in Bayesian statistics. Also, the Dirichlet distribution is a generalization of the beta distribution to higher dimensions (for n=2 it is the beta distribution).


This concept has the prerequisites:

Core resources (read/watch one of the following)


Introduction to the Dirichlet Distribution and Related Processes
Location: Ch 1 provides core information while Ch 2 focuses on sampling
Authors: Bela A. Frigyik,Amon Kapila,Maya R. Gupta
Mathematical Monk: Machine Learning (2011)
Online videos on machine learning.

Supplemental resources (the following are optional, but you may find them useful)


See also

  • We can define the Dirichlet distribution in terms of the gamma distribution .
  • The Dirichlet process is a generalization of the Dirichlet distribution to possibly infinite spaces, and is useful in mixture modeling.
  • The Dirichlet distribution is a conjugate prior to the categorical and multinomial distribution.