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

## 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.

See Also

GaussianInvWishart

Examples

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)

bbricks documentation built on July 8, 2020, 7:29 p.m.