sufficientStatistics.GaussianNIG {bbricks} | R Documentation |
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)
## S3 method for class 'GaussianNIG' sufficientStatistics(obj, x, X, foreach = FALSE, ...)
obj |
A "GaussianNIG" object. |
x |
numeric, must satisfy length(x) = nrow(X) |
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. |
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.
Banerjee, Sudipto. "Bayesian Linear Model: Gory Details." Downloaded from http://www. biostat. umn. edu/~ph7440 (2008).
GaussianNIG
, sufficientStatistics_Weighted.GaussianNIG
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)