nimble (version 1.2.1)

Wishart: The Wishart Distribution

Description

Density and random generation for the Wishart distribution, using the Cholesky factor of either the scale matrix or the rate matrix.

Usage

dwish_chol(x, cholesky, df, scale_param = TRUE, log = FALSE)
rwish_chol(n = 1, cholesky, df, scale_param = TRUE)

Value

dwish_chol gives the density and rwish_chol generates random deviates.

Arguments

x

vector of values.

cholesky

upper-triangular Cholesky factor of either the scale matrix (when scale_param is TRUE) or rate matrix (otherwise).

df

degrees of freedom.

scale_param

logical; if TRUE the Cholesky factor is that of the scale matrix; otherwise, of the rate 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

df <- 40
ch <- chol(matrix(c(1, .7, .7, 1), 2))
x <- rwish_chol(1, ch, df = df)
dwish_chol(x, ch, df = df)