The Stick Breaking representation of the Dirichlet process.

Source: R/stick_breaking.R

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.

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.