| marginalLikelihood_bySufficientStatistics.GaussianNIG | R Documentation |
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, ...)
obj |
A "GaussianNIG" object. |
ss |
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(). |
LOG |
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).
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)