bayesSurv (version 2.4)

rMVNorm: Sample from the multivariate normal distribution

Description

According to the parametrization used, sample from the multivariate normal distribution.

The following parametrization can be specified [object Object],[object Object]

Generation of random numbers is performed by Algorithms 2.3-2.5 in Rue and Held (2005, pp. 34-35).

Usage

rMVNorm(n, mean=0, Sigma=1, Q, param=c("standard", "canonical"))

Arguments

n

number of observations to be sampled.

mean

For param="standard", it is a vector $\mu$ of means. If length(mean) is equal to 1, it is recycled and all components have the same mean. For param="canonical", it is a vector $b$ of canonical mea

Sigma

covariance matrix of the multivariate normal distribution. It is ignored if Q is given at the same time.

Q

precision matrix of the multivariate normal distribution.

It does not have to be supplied provided Sigma is given and param="standard".

It must be supplied if param="canonical".

param

a character which specifies the parametrization.

Value

• Matrix with sampled points in rows.

References

Rue, H. and Held, L. (2005). Gaussian Markov Random Fields: Theory and Applications. Boca Raton: Chapman and Hall/CRC.

See Also

rnorm, Mvnorm.

Examples

### Mean, covariance matrix, its inverse
### and the canonical mean
mu <- c(0, 2, 0.5)
L <- matrix(c(1, 1, 1,  0, 0.5, 0.5,  0, 0, 0.3), ncol=3)
Sigma <- L %*% t(L)
Q <- chol2inv(t(L))
b <- Q %*% mu

print(Sigma)
print(Q)
print(Sigma %*% Q)

### Sample using different parametrizations
set.seed(775988621)
n <- 10000

### Sample from N(mu, Sigma)
xx1 <- rMVNorm(n=n, mean=mu, Sigma=Sigma)
apply(xx1, 2, mean)
var(xx1)

### Sample from N(mu, Q^{-1})
xx2 <- rMVNorm(n=n, mean=mu, Q=Q)
apply(xx2, 2, mean)
var(xx2)

### Sample from N(Q^{-1}*b, Q^{-1})
xx3 <- rMVNorm(n=n, mean=b, Q=Q, param="canonical")
apply(xx3, 2, mean)
var(xx3)