# marginalLikelihood.GaussianInvWishart: Marginal likelihood of a "GaussianInvWishart" 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)

Sigma \sim InvWishart(v,S)

mu is known. Gaussian() is the Gaussian distribution. See `?dGaussian` and `?dInvWishart` for the definition of the distributions.
The model structure and prior parameters are stored in a "GaussianInvWishart" object.
Marginal likelihood = p(x|v,S,mu)

## Usage

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

## Arguments

 `obj` A "GaussianInvWishart" 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.

MARolA, K. V., JT KBNT, and J. M. Bibly. Multivariate analysis. AcadeInic Press, Londres, 1979.

`GaussianInvWishart`, `marginalLikelihood_bySufficientStatistics.GaussianInvWishart`
 ```1 2 3 4 5 6 7 8``` ```obj <- GaussianInvWishart(gamma=list(mu=c(-1.5,1.5),v=3,S=diag(2))) x <- rGaussian(100,mu = c(-1.5,1.5),Sigma = matrix(c(0.1,0.03,0.03,0.1),2,2)) xNew <- rGaussian(100,mu = c(-1.5,1.5),Sigma = matrix(c(0.1,0.03,0.03,0.1),2,2)) ss <- sufficientStatistics(obj=obj,x=x,foreach = FALSE) ## update piror with x posterior(obj=obj,ss = ss) ## use the posterior to calculate the likelihood of xNew marginalLikelihood(obj = obj,x = xNew,LOG = TRUE) ```