Conditional distribution of a multivariate normal distribution Np

This function can be used to obtain the conditional distribution of any Np.

conditional_np(x, mu, Sigma)

Arguments

x	is a vector with the values that are known. For example, c(3, NA, 5, NA) means that we are interested in the conditional distribution of X2 and X4 when X1=3 and X3=5.
mu	is the mean vector of the Np.
Sigma	is the covariance matrix of the Np.

Value

a list with the mean and covariance matrix of the conditional distribution.

Examples

# Consider a N3 normal distribution
mu <- c(3, -1, 1)
Sigma <- matrix(c(3, -1, 1,
                  -1, 1, 0,
                  1, 0, 2), ncol=3)

# We want the conditional distribution of X2 given X1=2 and X3=0
conditional_np(x=c(2, NA, 0), mu=mu, Sigma=Sigma)
#> $mean
#>      [,1]
#> [1,] -0.8
#> 
#> $sigma
#>      [,1]
#> [1,]  0.6
#> 

# We want the conditional distribution of X1 and X3 given X2=2
conditional_np(x=c(NA, 2, NA), mu=mu, Sigma=Sigma)
#> $mean
#>      [,1]
#> [1,]    0
#> [2,]    1
#> 
#> $sigma
#>      [,1] [,2]
#> [1,]    2    1
#> [2,]    1    2
#>