dPosteriorPredictive.DP: Posterior predictive density function of a Dirichlet Process...

In bbricks: Bayesian Methods and Graphical Model Structures for Statistical Modeling

Description

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).

Usage

## S3 method for class 'DP'
dPosteriorPredictive(obj, x, z, LOG = TRUE, ...)

Arguments

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.

Value

A numeric vector, the posterior predictive density.

References

Teh, Yee W., et al. "Sharing clusters among related groups: Hierarchical Dirichlet processes." Advances in neural information processing systems. 2005.

See Also

DP, dPosteriorPredictive.DP, marginalLikelihood.DP

Examples

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)

bbricks documentation built on July 8, 2020, 7:29 p.m.