# MAP.GaussianInvWishart: Maximum A Posteriori (MAP) estimate of a "GaussianInvWishart"... In bbricks: Bayesian Methods and Graphical Model Structures for Statistical Modeling

## Description

Generate the MAP estimate of Sigma in 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 model structure and prior parameters are stored in a "GaussianInvWishart" object.
The MAP estimates are:

• (Sigma_MAP) = argmax p(Sigma|v,S,x,mu)

## Usage

 ```1 2``` ```## S3 method for class 'GaussianInvWishart' MAP(obj, ...) ```

## Arguments

 `obj` A "GaussianInvWishart" object. `...` Additional arguments to be passed to other inherited types.

## Value

matrix, the MAP estimate of "Sigma".

## 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`
 ```1 2 3 4 5``` ```obj <- GaussianInvWishart(gamma=list(mu=c(-1.5,1.5),v=3,S=diag(2))) x <- rGaussian(100,mu = c(-1.5,1.5),Sigma = matrix(c(0.1,0.03,0.03,0.1),2,2)) ss <- sufficientStatistics(obj=obj,x=x,foreach = FALSE) posterior(obj=obj,ss = ss) MAP(obj) ```