StickBreaking function

The Stick Breaking representation of the Dirichlet process.

A Dirichlet process can be represented using a stick breaking construction [REMOVE_ME]$G = \sum _{i=1} ^n pi _i \delta _{\theta _i} [REMOVE_ME_2]$, 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.

Returns

Vector of stick breaking probabilities.

Description

A Dirichlet process can be represented using a stick breaking construction

, 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.

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.