bbricks (version 0.1.1)

linearGaussian: Linear Gaussian systems

Description

For the model structure x1 ~ Gaussian(mu1,Sigma1) x2 ~ Gaussian(Ax1+b,Sigma21) x1|x2,mu1,Sigma1,A,b,Sigma21 ~ Gaussian(mu12,Sigma12)

Usage

linearGaussian(
  x2,
  mu1,
  Sigma1 = NULL,
  Precision1 = NULL,
  A,
  b,
  Sigma21 = NULL,
  Precision21 = NULL
)

Arguments

x2

numberic, an sample of x2, length(x2)=d2.

mu1

numeric, marginal mean of x1, length(m1)=d1.

Sigma1

matrix, marginal covariance matrix of x1. At least one of Sigma1 and Precision1 should be non-NULL.

Precision1

marginal precision matrix of x1,satisfying Precision1 = inverse(Sigma1). At least one of Sigma1 and Precision1 should be non-NULL.

A

matrix, dim(A) = d1 x d2.

b

numeric, length(b)=d1.

Sigma21

matrix, dim(Sigma21) = d1 x d1, either Precision21 or Sigma21 should be non-NULL.

Precision21

matrix, satisfying Precision21 = inverse(Sigma21), either Precision21 or Sigma21 should be non-NULL.

Value

A named list containing the conditional mean and covariance matrix.

See Also

inferenceJointGaussian

Examples

# NOT RUN {
x2 <- rGaussian(1,mu = c(0,0.2),Sigma = diag(2))
mu1 <- c(0,0); Sigma1 <- diag(2); A <- matrix(c(2,1,1,1),2,2); b <- runif(2); Sigma21 <- diag(2)*0.2
linearGaussian(x2=x2,mu1 = mu1,Sigma1 = Sigma1,A=A,b=b,Sigma21 = Sigma21)
# }