MultivariateNormal: The Multivariate Normal Distribution

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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)

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).

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.

Value

dmnorm_chol gives the density and rmnorm_chol generates random deviates.

Author(s)

Christopher Paciorek

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)

nimble documentation built on Sept. 11, 2024, 7:10 p.m.