Prior Density of Variance or Standard Deviation

Prior density of variance or standard deviation as specified in a MCMCglmm prior

Usage

dprior(x, prior, sd=FALSE, log=FALSE)

Arguments

x

vector of observations

prior

list: with elements V, nu and (optionally) alpha.mu and alpha.V

sd

logical: if TRUE the density of the standard deviation is returned

log

logical: if TRUE the log density is returned

Value

numeric

Details

If alpha.V is zero (or NULL) the density for the variance is a scalar inverse-Wishart (i.e. inverse-gamma) distribution. If alpha.V is non-zero MCMCglmm uses parameter expansion and the density for the variance is a scaled non-central F distribution with the numerator degrees of freedom equal to one. The density for the standard deviation is a folded scaled non-central t distribution.

Author

Jarrod Hadfield j.hadfield@ed.ac.uk

See also

rIW, rprior

Examples

prior<-list(V=1, nu=1, alpha.mu=0, alpha.V=10)
# parameter expanded prior

x<-seq(1e-6, 10, lenhth=100)
#> Warning: In seq.default(1e-06, 10, lenhth = 100) :
#>  extra argument ‘lenhth’ will be disregarded

plot(dprior(x, prior)~x, type="l", xlab="Variance", ylab="Density")

# Density for variance: central F_{1,1} with scale 10

plot(dprior(sqrt(x), prior, sd=TRUE)~sqrt(x), type="l", xlab="Standard Deviation", ylab="Density")

# Density for standard deviation: half-Cauchy (t_1) with scale sqrt(10)