nimble (version 1.2.1)

MultivariateNormal: The Multivariate Normal Distribution

Description

Density and random generation for the multivariate normal distribution, using the Cholesky factor of either the precision matrix or the covariance matrix.

Usage

dmnorm_chol(x, mean, cholesky, prec_param = TRUE, log = FALSE)
rmnorm_chol(n = 1, mean, cholesky, prec_param = TRUE)

Value

dmnorm_chol gives the density and rmnorm_chol generates random deviates.

Arguments

x

vector of values.

mean

vector of values giving the mean of the distribution.

cholesky

upper-triangular Cholesky factor of either the precision matrix (when prec_param is TRUE) or covariance matrix (otherwise).

prec_param

logical; if TRUE the Cholesky factor is that of the precision matrix; otherwise, of the covariance matrix.

log

logical; if TRUE, probability density is returned on the log scale.

n

number of observations (only n=1 is handled currently).

Author

Christopher Paciorek

Details

See Gelman et al., Appendix A or the BUGS manual for mathematical details. The rate matrix as used here is defined as the inverse of the scale matrix, \(S^{-1}\), given in Gelman et al.

References

Gelman, A., Carlin, J.B., Stern, H.S., and Rubin, D.B. (2004) Bayesian Data Analysis, 2nd ed. Chapman and Hall/CRC.

See Also

Distributions for other standard distributions

Examples

mean <- c(-10, 0, 10)
covmat <- matrix(c(1, .9, .3, .9, 1, -0.1, .3, -0.1, 1), 3)
ch <- chol(covmat)
x <- rmnorm_chol(1, mean, ch, prec_param = FALSE)
dmnorm_chol(x, mean, ch, prec_param = FALSE)