Maximum A Posteriori (MAP) estimate of a "GaussianNIG" object

Description

Generate the MAP estimate of (beta,sigma^2) in following Gaussian-NIG structure:

x \sim Gaussian(X beta,sigma^2)

sigma^2 \sim InvGamma(a,b)

beta \sim Gaussian(m,sigma^2 V)

Where X is a row vector, or a design matrix where each row is an obervation. InvGamma() is the Inverse-Gamma distribution, Gaussian() is the Gaussian distribution. See ?dInvGamma and dGaussian for the definitions of these distribution.
The model structure and prior parameters are stored in a "GaussianNIG" object.
The MAP estimates are:

• (beta,sigma^2)_MAP = argmax p(beta,sigma^2|m,V,a,b,x,X)

Usage

## S3 method for class 'GaussianNIG'
MAP(obj, ...)

Arguments

Value

A named list, the MAP estimate of beta and sigma^2.

References

Banerjee, Sudipto. "Bayesian Linear Model: Gory Details." Downloaded from http://www. biostat. umn. edu/~ph7440 (2008).

See Also

GaussianNIG

Examples

obj <- GaussianNIG(gamma=list(m=0,V=1,a=1,b=1))
X <- 1:20
x <- rnorm(20)+ X*0.3
ss <- sufficientStatistics(obj = obj,X=X,x=x)
posterior(obj = obj,ss = ss)
MAP(obj)