# 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

 ```1 2``` ```## 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).

`GaussianNIW`, `sufficientStatistics.GaussianNIW`
 ```1 2 3 4 5``` ```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) ```