bbricks (version 0.1.4)

LinearGaussianGaussian: Create objects of type "LinearGaussianGaussian".

Description

Create an object of type "LinearGaussianGaussian", which represents the Linear Gaussian and Gaussian conjugate structure: $$x \sim Gaussian(A z + b, Sigma)$$ $$z \sim Gaussian(m,S)$$ Where Sigma is known. A is a \(m x n\) matrix, x is a \(m x 1\) random vector, z is a \(n x 1\) random vector, b is a \(n x 1\) vector. Gaussian() is the Gaussian distribution. See ?dGaussian for the definition of Gaussian distribution. The created object will be used as a place for recording and accumulating information in the related inference/sampling functions such as posterior(), posteriorDiscard(), MAP(), marginalLikelihood(), dPosteriorPredictive(), rPosteriorPredictive() and so on.

Usage

LinearGaussianGaussian(
  objCopy = NULL,
  ENV = parent.frame(),
  gamma = list(Sigma = 1, m = 0, S = 1)
)

Arguments

objCopy

an object of type "LinearGaussianGaussian". If "objCopy" is not NULL, the function create a new "LinearGaussianGaussian" object by copying the content from objCopy, otherwise this new object will be created by using "ENV" and "gamma". Default NULL.

ENV

environment, specify where the object will be created.

gamma

list, a named list of parameters, gamma=list(Sigma,m,S). Where gamma$Sigma is the known covariance matrix of x, gamma$m and gamma$S are the prior mean and covariance matrix of z.

Value

An object of class "LinearGaussianGaussian".

References

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

See Also

posterior.LinearGaussianGaussian,posteriorDiscard.LinearGaussianGaussian,MAP.LinearGaussianGaussian,MPE.LinearGaussianGaussian,marginalLikelihood.LinearGaussianGaussian,rPosteriorPredictive.LinearGaussianGaussian,dPosteriorPredictive.LinearGaussianGaussian.

Examples

# NOT RUN {
obj <- LinearGaussianGaussian(gamma=list(Sigma=matrix(c(2,1,1,2),2,2),
                              m=c(0.2,0.5,0.3),S=diag(3)))
obj #print the content
# }