marginalLikelihood_bySufficientStatistics.GaussianNIG {bbricks}R Documentation

Marginal likelihood of a "GaussianNIG" object, using sufficient statistics


Generate the marginal likelihood of a set of observations 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)


## S3 method for class 'GaussianNIG'
marginalLikelihood_bySufficientStatistics(obj, ss, LOG = TRUE, ...)



A "GaussianNIG" object.


Sufficient statistics of (x,X). In Gaussian-NIG case the sufficient statistic of sample (x,X) is a object of type "ssGaussianLinear", it can be generated by the function sufficientStatistics().


Return the log density if set to "TRUE".


Additional arguments to be passed to other inherited types.


numeric, the marginal likelihood.


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

See Also

GaussianNIG, marginalLikelihood.GaussianNIG


obj <- GaussianNIG(gamma=list(m=0,V=1,a=1,b=1))
X <- 1:20
x <- rnorm(20)+ X*0.3
ss <- sufficientStatistics(obj=obj,x=x,X=X,foreach=FALSE)
marginalLikelihood_bySufficientStatistics(obj = obj,ss = ss)
marginalLikelihood_bySufficientStatistics(obj = obj,ss = ss,LOG = FALSE)

[Package bbricks version 0.1.4 Index]