posterior.GaussianNIG {bbricks} | R Documentation |
For the 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.
Update (m,V,a,b) by adding the information of newly observed samples (x,X). The model structure and prior parameters are stored in a "GaussianNIG" object, the prior parameters in this object will be updated after running this function.
## S3 method for class 'GaussianNIG' posterior(obj, ss, ...)
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(). |
... |
Additional arguments to be passed to other inherited types. |
None. the gamma stored in "obj" will be updated based on "ss".
Banerjee, Sudipto. "Bayesian Linear Model: Gory Details." Downloaded from http://www. biostat. umn. edu/~ph7440 (2008).
GaussianNIG
,posteriorDiscard.GaussianNIG
,sufficientStatistics.GaussianNIG
obj <- GaussianNIG(gamma=list(m=0,V=1,a=1,b=0)) X <- 1:20 x <- rnorm(20)+ X*0.3 ss <- sufficientStatistics(obj = obj,X=X,x=x) posterior(obj = obj,ss = ss) obj