marginalLikelihood.GaussianNIW: Marginal likelihood of a "GaussianNIW" object

In bbricks: Bayesian Methods and Graphical Model Structures for Statistical Modeling

Description

Generate the marginal likelihood of the following model structure:

mu,Sigma|m,k,v,S \sim NIW(m,k,v,S)

x|mu,Sigma \sim Gaussian(mu,Sigma)

Where NIW() is the Normal-Inverse-Wishart distribution, Gaussian() is the Gaussian distribution. See ?dNIW and dGaussian for the definitions of these distribution.
The model structure and prior parameters are stored in a "GaussianNIW" object.
Marginal likelihood = p(x|m,k,v,S)

Usage

## S3 method for class 'GaussianNIW'
marginalLikelihood(obj, x, LOG = TRUE, ...)

Arguments

obj	A "GaussianNIW" 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

Murphy, Kevin P. "Conjugate Bayesian analysis of the Gaussian distribution." def 1.22 (2007): 16.

Gelman, Andrew, et al. "Bayesian Data Analysis Chapman & Hall." CRC Texts in Statistical Science (2004).

See Also

GaussianNIW, marginalLikelihood_bySufficientStatistics.GaussianNIW

Examples

x <- rGaussian(1000,mu = c(1,1),Sigma = matrix(c(1,0.5,0.5,3),2,2))
obj <- GaussianNIW(gamma=list(m=c(0,0),k=1,v=2,S=diag(2)))
marginalLikelihood(obj = obj,x=x)
## or...
ss <- sufficientStatistics(obj=obj,x=x,foreach = FALSE)
marginalLikelihood_bySufficientStatistics(obj = obj,ss=ss)

bbricks documentation built on July 8, 2020, 7:29 p.m.