Dirichlet process

Article summary

view of the Dirichlet process. In probability theory, Dirichlet processes (after the distribution associated with Peter Gustav Lejeune Dirichlet) are a family of stochastic processes whose realizations are probability distributions. In other words, a Dirichlet process is a probability distribution whose range is itself a set of probability distributions. It is often used in Bayesian inference to describe the prior knowledge about the distribution of random variables—how likely it is that the random variables are distributed according to one or another particular distribution. As an example, a single die represents a probability mass function (pmf), so a bag of 100 real-world dice is a collection of random pmfs—when you put your hand in the bag and draw out a die, you draw a single random pmf, thus sampling from that collection of pmfs. A bag of dice manufactured using a crude process 100 years ago will likely contain dice that deviate wildly from the uniform pmf, whereas a bag of state-of-the-art dice used by Las Vegas casinos may have barely perceptible imperfections. Such a collection of pmfs may be modeled by a distribution over pmfs, such as the Dirichlet distribution. The Dirichlet process is specified by a base distribution H and a positive real number \alpha called the concentration parameter (also known as scaling parameter).…

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