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Generate the the density value of the posterior predictive distribution of the following structure: pi|alpha ~ DP(alpha,U) z|pi ~ Categorical(pi) theta_z|psi ~ H0(psi) x|theta_z,z ~ 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 arbitrary, they are distributions of x and theta_z correspondingly. The model structure and prior parameters are stored in a "DP" object. Posterior predictive is a distribution of x,z|alpha,psi.
# S3 method for DP
dPosteriorPredictive(obj, x, z, LOG = TRUE, ...)A "DP" object.
Random samples of the "BasicBayesian" object.
integer, the partition label of the parameter space where the observation x is drawn from.
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.
@seealso DP, dPosteriorPredictive.DP, marginalLikelihood.DP
# NOT RUN {
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)
# }
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