MAP.LinearGaussianGaussian: Maximum A Posteriori (MAP) estimate of a...

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(A z + b, Sigma)

z \sim Gaussian(m,S)

Where Sigma is known. A is a dimx x dimz matrix, x is a dimx x 1 random vector, z is a dimz x 1 random vector, b is a dimm x 1 vector. Gaussian() is the Gaussian distribution. See ?dGaussian for the definition of Gaussian distribution.
The model structure and prior parameters are stored in a "LinearGaussianGaussian" object.
The MAP estimates are:

• z_MAP = argmax p(z|m,S,A,b,x,Sigma)

Usage

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

Arguments

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

Value

numeric vector, the MAP estimate of "z".

References

Murphy, Kevin P. Machine learning: a probabilistic perspective. MIT press, 2012.

See Also

LinearGaussianGaussian

Examples

obj <- LinearGaussianGaussian(gamma=list(Sigma=matrix(c(2,1,1,2),2,2),
                                         m=c(0.2,0.5,0.6),S=diag(3)))
x <- rGaussian(100,mu = runif(2),Sigma = diag(2))
A <- matrix(runif(6),2,3)
b <- runif(2)
ss <- sufficientStatistics(obj,x=x,A=A,b=b)
## update prior into posterior
posterior(obj=obj,ss=ss)
## get the MAP estimate of z
MAP(obj)

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