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

## Description

Generate the MAP estimate of (mu,Sigma) in following Gaussian-NIW 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 model structure and prior parameters are stored in a "GaussianNIW" object.
The MAP estimates are:

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

## Usage

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

## Arguments

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

## Value

A named list, the MAP estimate of mu and Sigma.

## 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`
 ```1 2 3 4 5 6 7``` ```## update the piror with new observations then calculate the MAP estimate x <- rGaussian(1000,mu = c(1,1),Sigma = matrix(c(1,0.5,0.5,3),2,2)) w <- runif(1000) obj <- GaussianNIW(gamma=list(m=c(0,0),k=1,v=2,S=diag(2))) ss <- sufficientStatistics_Weighted(obj = obj,x=x,w=w,foreach = TRUE) for(i in 1L:length(ss)) posterior(obj = obj,ss=ss[[i]]) MAP(obj) ```