| StickBreaking {dirichletprocess} | R Documentation |
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.