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

## Description

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

• (mu_MAP) = argmax p(mu|m,S,x,Sigma)

## Usage

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

## Arguments

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

## Value

numeric vector, the MAP estimate of "mu".

## References

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

`GaussianGaussian`
 ```1 2 3 4 5 6 7``` ```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)) ss <- sufficientStatistics(obj=obj,x=x,foreach = FALSE) ## update prior into posterior posterior(obj = obj,ss = ss) ## get the MAP estimate of mu MAP(obj) ```