bbricks (version 0.1.1)

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

Description

Generate the marginal likelihood of the following model structure: beta,sigma^2|gamma ~ NIG(gamma) x|beta,sigma^2,X ~ Gaussian(X where gamma = (m,V,a,b) is the Normal-Inverse-Gamma(NIG) parameter, "m" is a numeric "location" parameter; "V" is a symmetric positive definite matrix representing the "scale" parameters; "a" and "b" are the "shape" and "rate" parameter of the Inverse Gamma distribution. The model structure and prior parameters are stored in a "GaussianNIG" object. Marginal likelihood is the likelihood of x|gamma,X.

Usage

# S3 method for 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." Dowloaded from http://www. biostat. umn. edu/~ ph7440 (2008).

See Also

@seealso GaussianNIG, marginalLikelihood_bySufficientStatistics.GaussianNIG

Examples

# NOT RUN {
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)
# }