StickBreaking: The Stick Breaking representation of the Dirichlet process.

In dirichletprocess: Build Dirichlet Process Objects for Bayesian Modelling

The Stick Breaking representation of the Dirichlet process.

Description

A Dirichlet process can be represented using a stick breaking construction

G = \sum _{i=1} ^n pi _i \delta _{\theta _i}

, where \pi _k = \beta _k \prod _{k=1} ^{n-1} (1- \beta _k ) are the stick breaking weights. The atoms \delta _{\theta _i} are drawn from G_0 the base measure of the Dirichlet Process. The \beta _k \sim \mathrm{Beta} (1, \alpha). In theory n should be infinite, but we chose some value of N to truncate the series. For more details see reference.

Usage

StickBreaking(alpha, N)

piDirichlet(betas)

Arguments

alpha	Concentration parameter of the Dirichlet Process.
N	Truncation value.
betas	Draws from the Beta distribution.

Value

Vector of stick breaking probabilities.

Functions

• piDirichlet(): Function for calculating stick lengths.

References

Ishwaran, H., & James, L. F. (2001). Gibbs sampling methods for stick-breaking priors. Journal of the American Statistical Association, 96(453), 161-173.

dirichletprocess documentation built on Aug. 25, 2023, 5:19 p.m.