R: Posterior predictive density function of a "CatDirichlet"...

dPosteriorPredictive.CatDirichlet

R Documentation

Posterior predictive density function of a "CatDirichlet" object

Description

Generate the the density value of the posterior predictive distribution of the following structure:

pi|alpha \sim Dir(alpha)

x|pi \sim Categorical(pi)

Where Dir() is the Dirichlet distribution, Categorical() is the Categorical distribution. See ?dDir and dCategorical for the definitions of these distribution.
The model structure and prior parameters are stored in a "CatDirichlet" object.
Posterior predictive is a distribution of x|alpha.

Usage

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

Arguments

`obj`	A "CatDirichlet" object.
`x`	numeric/integer/character vector, observed Categorical samples.
`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

Murphy, Kevin P. Machine learning: a probabilistic perspective. MIT press, 2012.

Examples

obj <- CatDirichlet(gamma=list(alpha=runif(26,1,2),uniqueLabels = letters))
x <- sample(letters,size = 20,replace = TRUE)
## res1 and res2 should provide the same result
res1 <- dPosteriorPredictive(obj = obj,x=x,LOG = TRUE)
res2 <- numeric(length(x))
for(i in seq_along(x)) res2[i] <- marginalLikelihood(obj=obj,x=x[i],LOG = TRUE)