# marginalLikelihood.GaussianNIG: Marginal likelihood of a "GaussianNIG" 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(X beta,sigma^2)

sigma^2 \sim InvGamma(a,b)

beta \sim Gaussian(m,sigma^2 V)

Where X is a row vector, or a design matrix where each row is an obervation. InvGamma() is the Inverse-Gamma distribution, Gaussian() is the Gaussian distribution. See `?dInvGamma` and `dGaussian` for the definitions of these distribution.
The model structure and prior parameters are stored in a "GaussianNIG" object.
Marginal likelihood = p(x|m,V,a,b,X).

## Usage

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

## Arguments

 `obj` A "GaussianNIG" object. `x` numeric, must satisfy length(x) = nrow(X). `X` matrix, must satisfy length(x) = nrow(X). `LOG` Return the log density if set to "TRUE". `...` Additional arguments to be passed to other inherited types.

## Value

numeric, the marginal likelihood.

## References

Banerjee, Sudipto. "Bayesian Linear Model: Gory Details." Downloaded from http://www. biostat. umn. edu/~ph7440 (2008).

`GaussianNIG`, `marginalLikelihood_bySufficientStatistics.GaussianNIG`
 ```1 2 3 4 5``` ```obj <- GaussianNIG(gamma=list(m=0,V=1,a=1,b=1)) X <- 1:20 x <- rnorm(20)+ X*0.3 marginalLikelihood(obj = obj,x = x, X = X) marginalLikelihood(obj = obj,x = x, X = X,LOG = FALSE) ```