sufficientStatistics.GaussianNIG: Sufficient statistics of a "GaussianNIG" object

Description

For following Gaussian-NIG 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. The sufficient statistics of a set of samples (x,X) are:

the effective number of samples N=nrow(X) or length(x)
the covariance of X and x SXx=t(X)
the covariance of X SX=t(X)
the covariance of x Sx=t(x)

Usage

# S3 method for GaussianNIG
sufficientStatistics(obj, x, X, foreach = FALSE, ...)

Arguments

obj

A "GaussianNIG" object.

numeric, must satisfy length(x) = nrow(X)

matrix, must satisfy length(x) = nrow(X)

foreach

logical, if foreach=TRUE, will return a list of sufficient statistics for each (x,X), otherwise will return the sufficient statistics as a whole.

...

Additional arguments to be passed to other inherited types.

Value

If foreach=TRUE, will return a list of sufficient statistics for each row of (x,X), otherwise will return the sufficient statistics of (x,X) as a whole.

References

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

Examples

Run this code

# NOT RUN {
obj <- GaussianNIG(gamma=list(m=0,V=1,a=1,b=0))
X <- 1:20
x <- rnorm(20)+ X*0.3
sufficientStatistics(obj = obj,X=X,x=x)
sufficientStatistics(obj = obj,X=X,x=x,foreach = TRUE)
# }