dPosteriorPredictive.DP {bbricks} | R Documentation |
Generate the the density value of the posterior predictive distribution of the following structure:
pi|alpha \sim DP(alpha,U)
z|pi \sim Categorical(pi)
theta_z|psi \sim H0(psi)
x|theta_z,z \sim F(theta_z)
where DP(alpha,U) is a Dirichlet Process on positive integers, alpha is the "concentration parameter" of the Dirichlet Process, U is the "base measure" of this Dirichlet process. The choice of F() and H0() can be described by an arbitrary "BasicBayesian" object such as "GaussianGaussian","GaussianInvWishart","GaussianNIW", "GaussianNIG", "CatDirichlet", and "CatDP". See ?BasicBayesian
for definition of "BasicBayesian" objects, and see for example ?GaussianGaussian
for specific "BasicBayesian" instances. As a summary, An "DP" object is simply a combination of a "CatDP" object (see ?CatDP
) and an object of any "BasicBayesian" type.
The model structure and prior parameters are stored in a "DP" object.
Posterior predictive density = p(x,z|alpha,psi).
## S3 method for class 'DP' dPosteriorPredictive(obj, x, z, LOG = TRUE, ...)
obj |
A "DP" object. |
x |
Random samples of the "BasicBayesian" object. |
z |
integer, the partition label of the parameter space where the observation x is drawn from. |
LOG |
Return the log density if set to "TRUE". |
... |
Additional arguments to be passed to other inherited types. |
A numeric vector, the posterior predictive density.
Teh, Yee W., et al. "Sharing clusters among related groups: Hierarchical Dirichlet processes." Advances in neural information processing systems. 2005.
DP
, dPosteriorPredictive.DP
, marginalLikelihood.DP
x <- rnorm(4) z <- sample(1L:10L,size = 4,replace = TRUE) obj <- DP() ss <- sufficientStatistics(obj = obj,x=x,foreach = TRUE) for(i in 1L:length(x)) posterior(obj = obj,ss=ss[[i]],z=z[i]) xnew <- rnorm(10) znew <- sample(1L:10L,size = 10,replace = TRUE) dPosteriorPredictive(obj = obj,x=xnew,z=znew)