# dPosteriorPredictive.CatDirichlet: Posterior predictive density function of a "CatDirichlet"... 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 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

 ```1 2``` ```## 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.

`CatDirichlet`, `dPosteriorPredictive.CatDirichlet`, `marginalLikelihood.CatDirichlet`
 ```1 2 3 4 5 6``` ```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) ```