posterior.GaussianNIW: Update a "GaussianNIW" object with sample sufficient...

In bbricks: Bayesian Methods and Graphical Model Structures for Statistical Modeling

Description

For the model structure:

mu,Sigma|m,k,v,S \sim NIW(m,k,v,S)

x|mu,Sigma \sim Gaussian(mu,Sigma)

Where NIW() is the Normal-Inverse-Wishart distribution, Gaussian() is the Gaussian distribution. See ?dNIW and dGaussian for the definitions of these distribution.
Update (m,k,v,S) by adding the information of newly observed samples x. The model structure and prior parameters are stored in a "GaussianNIW" object, the prior parameters in this object will be updated after running this function.

Usage

## S3 method for class 'GaussianNIW'
posterior(obj, ss, ...)

Arguments

obj	A "GaussianNIW" object.
ss	Sufficient statistics of x. In Gaussian-NIW case the sufficient statistic of sample x is a object of type "ssGaussian", it can be generated by the function sufficientStatistics().
...	Additional arguments to be passed to other inherited types.

Value

None. the gamma stored in "obj" will be updated based on "ss".

References

Murphy, Kevin P. "Conjugate Bayesian analysis of the Gaussian distribution." def 1.22 (2007): 16.

Gelman, Andrew, et al. "Bayesian Data Analysis Chapman & Hall." CRC Texts in Statistical Science (2004).

See Also

GaussianNIW,posteriorDiscard.GaussianNIW,sufficientStatistics.GaussianNIW

Examples

x <- rGaussian(1000,mu = c(1,1),Sigma = matrix(c(1,0.5,0.5,3),2,2))
w <- runif(1000)
obj <- GaussianNIW(gamma=list(m=c(0,0),k=1,v=2,S=diag(2)))
obj
ss <- sufficientStatistics_Weighted(obj = obj,x=x,w=w,foreach = TRUE)
for(i in 1L:length(ss)) posterior(obj = obj,ss = ss[[i]])
obj

bbricks documentation built on July 8, 2020, 7:29 p.m.