Dirichlet depths for point process

The two - parameter Poisson - Dirichlet point process

The two-parameter Poisson-Dirichlet distribution is a probability distribution on the totality of positive decreasing sequences with sum 1 and hence considered to govern masses of a random discrete distribution. A characterization of the associated point process (i.e., the random point process obtained by regarding the masses as points in the positive real line) is given in terms of the correla...

Dirichlet Process

The Dirichlet process is a prior used in nonparametric Bayesian models of data, particularly in Dirichlet process mixture models (also known as infinite mixture models). It is a distribution over distributions, i.e. each draw from a Dirichlet process is itself a distribution. It is called a Dirichlet process because it has Dirichlet distributed finite dimensional marginal distributions, just as...

Lecture 24 : Dirichlet distribution and Dirichlet Process

The local Dirichlet process.

As a generalization of the Dirichlet process (DP) to allow predictor dependence, we propose a local Dirichlet process (lDP). The lDP provides a prior distribution for a collection of random probability measures indexed by predictors. This is accomplished by assigning stick-breaking weights and atoms to random locations in a predictor space. The probability measure at a given predictor value is ...

The Nested Dirichlet Process

In multicenter studies, subjects in different centers may have different outcome distributions. This article is motivated by the problem of nonparametric modeling of these distributions, borrowing information across centers while also allowing centers to be clustered. Starting with a stick-breaking representation of the Dirichlet process (DP), we replace the random atoms with random probability...