Mean Posterior Estimate (MPE) of a "LinearGaussianGaussian" object

Description

Generate the MPE 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 MPE estimates is:

• z_MPE = E(z|m,S,A,b,x,Sigma)

Usage

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

Arguments

Value

numeric vector, the MPE 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
MPE(obj)