# marginalLikelihood.GaussianGaussian: Marginal likelihood of a "GaussianGaussian" object In bbricks: Bayesian Methods and Graphical Model Structures for Statistical Modeling

## Description

Generate the marginal likelihood of the following model structure:

x \sim Gaussian(mu,Sigma)

mu \sim Gaussian(m,S)

Where Sigma is known. Gaussian() is the Gaussian distribution. See `?dGaussian` for the definition of Gaussian distribution.
The model structure and prior parameters are stored in a "GaussianGaussian" object.
Marginal likelihood = p(x|m,S,Sigma)

## Usage

 ```1 2``` ```## S3 method for class 'GaussianGaussian' marginalLikelihood(obj, x, LOG = TRUE, ...) ```

## Arguments

 `obj` A "GaussianGaussian" object. `x` matrix, or the ones that can be converted to matrix, each row of x is an observation. `LOG` Return the log density if set to "TRUE". `...` Additional arguments to be passed to other inherited types.

## Value

numeric, the marginal likelihood.

## References

Gelman, Andrew, et al. Bayesian data analysis. CRC press, 2013.

`GaussianGaussian`, `marginalLikelihood_bySufficientStatistics.GaussianGaussian`
 ```1 2 3 4``` ```obj <- GaussianGaussian(gamma=list(Sigma=matrix(c(2,1,1,2),2,2),m=c(0.2,0.5),S=diag(2))) x <- rGaussian(100,c(0,0),Sigma = matrix(c(2,1,1,2),2,2)) marginalLikelihood(obj = obj,x=x,LOG = TRUE) marginalLikelihood(obj = obj,x=x,LOG = FALSE) ```