sufficientStatistics_Weighted.GaussianNIW: Weighted sufficient statistics for a "GaussianNIW" object

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

Description

For following Gaussian-NIW 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.
The sufficient statistics of a set of samples x (each row of x is a sample) and weights w are:

• the effective number of samples N=sum(w)

• the sample sum xsum = colSums(x*w)

• the uncentered scatter matrix S = t(w*x)

Usage

## S3 method for class 'GaussianNIW'
sufficientStatistics_Weighted(obj, x, w, foreach = FALSE, ...)

Arguments

obj	A "GaussianNIW" object.
x,	matrix, Gaussian samples, when x is a matrix, each row is a sample of dimension ncol(x). when x is a vector, x is length(x) samples of dimension 1.
w	numeric, sample weights.
foreach	logical, if foreach=TRUE, will return a list of sufficient statistics for each row of x, otherwise will return the sufficient statistics of x 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, otherwise will return the sufficient statistics of x as a whole.

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, sufficientStatistics.GaussianNIW

Examples

x <- rGaussian(10,mu = c(-1.5,1.5),Sigma = matrix(c(0.1,0.03,0.03,0.1),2,2))
obj <- GaussianNIW()                    #an GaussianNIW object
w <- runif(10)
sufficientStatistics_Weighted(obj=obj,x=x,w=w,foreach = FALSE)
sufficientStatistics_Weighted(obj=obj,x=x,w=w,foreach = TRUE)

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