skewStudent: Improved and standard Laplace approximations for multivariate...

In erlisR/iLaplaceExamples: Extra Utilities and Examples for iLaplace

Description

These functions give the normalising constant of (skewed) multivariate Student's t densities approximated by the standard and the improved Laplace of Ruli et al. (2015). In particular, iLap_mvt provides the normalising constant of the m-variate Student's t density with df degrees of freedom, centered at zero and indentiy scale matrix. iLap_mvskt provides the normalising constanto of the m-variate t/skew-t density of Jones (2002).

Usage

iLap_mvt(m, df)

iLap_mvskt(a, c, m, df)

Arguments

m	The dimensionality
df	The degrees of freedom
a	The parameter a of the t/skew-t density of Jones(2002)
c	The parameter c of the t/skew-t density of Jones(2002)

Details

These functions use the improved and the standard Laplace approximation for computing the normalising constant of the multivariate t/skew-t density. The functions are similar to iLaplace.

Value

a list with components Lap and iLap

a list with components Lap and iLap

References

Ruli E., Sartori N. & Ventura L. (2015) Improved Laplace approximation for marignal likelihoods. http://arxiv.org/abs/1502.06440

Jones M. C. (2002). Marginal replacement in multivariate densities, with application to skewing spherically symmetric distributions. Journal of Multivariate Analysis 81, 85–99.

See Also

iLaplace

Examples

## Not run: 

library(iLaplaceExamples)

# improved (black) and standard(red) Laplace approximations for the multivariate t
dims = seq(3,100, by = 5)
lap3 = sapply(dims, function(i) iLap_mvt(i, 3))
lap5 = sapply(dims, function(i) iLap_mvt(i, 5))
lap10 = sapply(dims, function(i) iLap_mvt(i, 10))
lap20 = sapply(dims, function(i) iLap_mvt(i, 20))

# improved (black) and standard (red) Laplace approximations for the multivariate t/skewt
# a=4, c=1
lap3s2 = sapply(dims, function(i) iLap_mvskt(a=4, c=1, i, df=3))
lap5s2 = sapply(dims, function(i) iLap_mvskt(a=4, c=1, i, df=5))
lap10s2 = sapply(dims, function(i) iLap_mvskt(a=4, c=1, i, df=10))
lap20s2 = sapply(dims, function(i) iLap_mvskt(a=4, c=1, i, df=20))

postscript("fig1.eps", width=5, height=5)
# red = standard Laplace
# black = improved Laplace
par(par(mai=c(0.85,0.85,0.2,0.03)))
plot(dims, lap3[1,], pch=1, cex=1.2, ylim=c(-55, 0), xlab=NA, main=NA, ylab=NA)
points(dims, lap5[1,], pch=2, cex=1.2, col=1)
points(dims, lap10[1,], pch=3, cex=1.2, col=1)
points(dims, lap20[1,], pch=4, cex=1.2, col=1)
points(dims, lap3[2,], pch=1, cex=1.2, col=2, lwd = 2)
points(dims, lap5[2,], pch=2, cex=1.2, col=2,lwd = 2)
points(dims, lap10[2,], pch=3, cex=1.2, col=2,lwd = 2)
points(dims, lap20[2,], pch=4, cex=1.2, col=2,lwd = 2)
mtext(text="dimension", side=1,line=2.2, cex = 1.3)
mtext(text="log normalising constant", side=2,line=2.5, cex = 1.3)
mtext(text="a=c=3/2", side=3,line=0.4, cex = 1.3)
# points(dims, lap3[2,], pch="°", cex=1.3)
abline(h=0, lwd = 2)
dev.off()

postscript("fig2.eps", width=5, height=5)
# red = standard Laplace
# black = improved Laplace
# par(par(mai=c(0.85,0.85,0.2,0.03)))
plot(dims, lap3s2[1,], pch=1, cex=1.2, ylim=c(-50, 0), xlab=NA, main=NA, ylab=NA)
points(dims, lap5s2[1,], pch=2, cex=1.2, col=1)
points(dims, lap10s2[1,], pch=3, cex=1.2, col=1)
points(dims, lap20s2[1,], pch=4, cex=1.2, col=1)
points(dims, lap3s2[2,], pch=1, cex=1.2, col=2, lwd = 2)
points(dims, lap5s2[2,], pch=2, cex=1.2, col=2,lwd = 2)
points(dims, lap10s2[2,], pch=3, cex=1.2, col=2,lwd = 2)
points(dims, lap20s2[2,], pch=4, cex=1.2, col=2,lwd = 2)
mtext(text="dimension", side=1,line=2.2)
mtext(text="log normalising contant", side=2.5,line=1.7)
mtext(text="a=4, c=1", side=3,line=0.4)
# points(dims, lap3[2,], pch="°", cex=1.3)
abline(h=0, lwd = 2)
dev.off()

## End(Not run)

erlisR/iLaplaceExamples documentation built on May 16, 2019, 8:48 a.m.