# sufficientStatistics.GaussianInvWishart: Sufficient statistics of a "GaussianInvWishart" object In bbricks: Bayesian Methods and Graphical Model Structures for Statistical Modeling

## Description

For following model structure:

x \sim Gaussian(mu,Sigma)

Sigma \sim InvWishart(v,S)

mu is known. Gaussian() is the Gaussian distribution. See `?dGaussian` and `?dInvWishart` for the definition of the distributions.
The sufficient statistics of a set of samples x (each row of x is a sample) are:

• the effective number of samples N=nrow(x)

• the centered sample scatter matrix S = (t(x)-mu)^T

## Usage

 ```1 2``` ```## S3 method for class 'GaussianInvWishart' sufficientStatistics(obj, x, foreach = FALSE, ...) ```

## Arguments

 `obj` A "GaussianInvWishart" 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. `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.

MARolA, K. V., JT KBNT, and J. M. Bibly. Multivariate analysis. AcadeInic Press, Londres, 1979.

`GaussianInvWishart`, `sufficientStatistics_Weighted.GaussianInvWishart`
 ```1 2 3 4``` ```obj <- GaussianInvWishart(gamma=list(mu=c(-1.5,1.5),v=3,S=diag(2))) x <- rGaussian(10,mu = c(-1.5,1.5),Sigma = matrix(c(0.1,0.03,0.03,0.1),2,2)) sufficientStatistics(obj=obj,x=x,foreach = FALSE) sufficientStatistics(obj=obj,x=x,foreach = TRUE) ```