dist.Stick {LaplacesDemon} | R Documentation |
Truncated Stick-Breaking Prior Distribution
Description
These functions provide the density and random number generation of
the original, truncated stick-breaking (TSB) prior distribution given
\theta
and \gamma
, as per Ishwaran and James
(2001).
Usage
dStick(theta, gamma, log=FALSE)
rStick(M, gamma)
Arguments
M |
This accepts an integer that is equal to one less than the
number of truncated number of possible mixture components
( |
theta |
This is |
gamma |
This is |
log |
Logical. If |
Details
Application: Discrete Multivariate
Density:
p(\pi) = \frac{(1-\theta)^{\beta-1}}{\mathrm{B}(1,\beta)}
Inventor: Sethuraman, J. (1994)
Notation 1:
\pi \sim \mathrm{Stick}(\theta,\gamma)
Notation 2:
\pi \sim \mathrm{GEM}(\theta,\gamma)
Notation 3:
p(\pi) = \mathrm{Stick}(\pi | \theta, \gamma)
Notation 4:
p(\pi) = \mathrm{GEM}(\pi | \theta, \gamma)
Parameter 1: shape parameter
\theta \in (0,1)
Parameter 2: shape parameter
\gamma > 0
Mean:
E(\pi) = \frac{1}{1+\gamma}
Variance:
var(\pi) = \frac{\gamma}{(1+\gamma)^2 (\gamma+2)}
Mode:
mode(\pi) = 0
The original truncated stick-breaking (TSB) prior distribution assigns
each \theta
to be beta-distributed with parameters
\alpha=1
and \beta=\gamma
(Ishwaran and
James, 2001). This distribution is commonly used in truncated Dirichlet
processes (TDPs).
Value
dStick
gives the density and
rStick
generates a random deviate vector of length M
.
References
Ishwaran, H. and James, L. (2001). "Gibbs Sampling Methods for Stick Breaking Priors". Journal of the American Statistical Association, 96(453), p. 161–173.
Sethuraman, J. (1994). "A Constructive Definition of Dirichlet Priors". Statistica Sinica, 4, p. 639–650.
See Also
ddirichlet
,
dmvpolya
, and
Stick
.
Examples
library(LaplacesDemon)
dStick(runif(4), 0.1)
rStick(4, 0.1)