# sufficientStatistics_Weighted.GaussianGaussian: Weighted sufficient statistics of a "GaussianGaussian" object In bbricks: Bayesian Methods and Graphical Model Structures for Statistical Modeling

## Description

For following model structure:

x \sim Gaussian(mu,Sigma)

mu \sim Gaussian(m,S)

Where Sigma is known. Gaussian() is the Gaussian distribution. See `?dGaussian` for the definition of Gaussian 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)

## Usage

 ```1 2``` ```## S3 method for class 'GaussianGaussian' sufficientStatistics_Weighted(obj, x, w, foreach = FALSE, ...) ```

## Arguments

 `obj` A "GaussianGaussian" 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, specifying whether to return the sufficient statistics for each observation. Default FALSE. `...` 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

Gelman, Andrew, et al. Bayesian data analysis. CRC press, 2013.

`GaussianGaussian`, `sufficientStatistics.GaussianGaussian`
 ```1 2 3 4 5``` ```obj <- GaussianGaussian(gamma=list(Sigma=matrix(c(2,1,1,2),2,2),m=c(0.2,0.5),S=diag(2))) x <- rGaussian(100,c(0,0),Sigma = matrix(c(2,1,1,2),2,2)) w <- runif(100) sufficientStatistics_Weighted(obj=obj,x=x,w=w,foreach = FALSE) sufficientStatistics_Weighted(obj=obj,x=x,w=w,foreach = TRUE) ```