# marginalLikelihood_bySufficientStatistics.CatDirichlet: Marginal likelihood of a "CatDirichlet" object, using... In bbricks: Bayesian Methods and Graphical Model Structures for Statistical Modeling

## Description

Generate the marginal likelihood of a set of observations of the following model 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.
Marginal likelihood is the likelihood of x|alpha

## Usage

 ```1 2``` ```## S3 method for class 'CatDirichlet' marginalLikelihood_bySufficientStatistics(obj, ss, LOG = TRUE, ...) ```

## Arguments

 `obj` A "CatDirichlet" object. `ss` Sufficient statistics of x. In Categorical-Dirichlet case the sufficient statistic of sample x can be either x itself, of an "ssCat" object generated by the function sufficientStatistics.CatDirichlet(). `LOG` Return the log density if set to "TRUE". `...` Additional arguments to be passed to other inherited types.

## Value

numeric, the marginal likelihood.

## References

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

`CatDirichlet`, `marginalLikelihood.CatDirichlet`
 ```1 2 3 4 5``` ```obj <- CatDirichlet(gamma=list(alpha=runif(26,1,2),uniqueLabels = letters)) x <- sample(letters,size = 20,replace = TRUE) marginalLikelihood(obj=obj,x=x,LOG = TRUE) #marginal likelihood ss <- sufficientStatistics(obj = obj,x=x) marginalLikelihood_bySufficientStatistics(obj=obj,ss = ss,LOG = TRUE) ```