Mit {AdMit} | R Documentation |
Density function or random generation for an adaptive mixture of Student-t distributions
dMit(theta, mit=list(), log=TRUE) rMit(N=1, mit=list())
theta |
matrix (of size Nxd, where N,d>=1) of real values. |
mit |
list containing information on the mixture approximation (see *Details*). |
log |
logical; if log=TRUE , returns (natural) logarithm
values of the density. Default: log=TRUE . |
N |
number of draws (positive integer number). |
dMit
returns the density values while rMit
generates
draws from a mixture of Student-t distributions.
The argument mit
is a list containing information on the
adaptive mixture of Student-t distributions. The following components must
be provided:
p
mu
Sigma
df
where H (>=1) is the number of components and
d (>=1) is
the dimension of the mixture approximation. Typically,
mit
is estimated by the function AdMit
. If the
mit=list()
, a Student-t distribution located
at rep(0,d)
with scale matrix diag(d)
and one
degree of freedom parameter is used.
Vector (of length N of density values, or matrix (of size
N
xd) of random draws, where d (>=1) is the
dimension of the mixture approximation.
Further details and examples of the R package AdMit
can be found in Ardia, Hoogerheide, van Dijk (2008).
David Ardia <david.ardia@unifr.ch>
Ardia, D., Hoogerheide, L.F., van Dijk, H.K. (2008) `Adaptive mixture of Student-t distributions as a flexible candidate distribution for efficient simulation: The R package AdMit', Working paper, Econometric Institute, Erasmus University Rotterdam (NL). http://www.tinbergen.nl/
AdMit
for fitting an adaptive mixture of
Student-t distributions to a given function KERNEL
,
AdMitIS
for importance sampling using an adaptive
mixture of Student-t distributions as the importance density,
AdMitMH
for the independence chain Metropolis-Hastings
using an adaptive mixture of Student-t distributions as the
candidate density.
## One dimensional two components mixture of Student-t distributions mit <- list(p=c(.5,.5), mu=matrix(c(-2,.5), 2, 1, byrow=TRUE), Sigma=matrix(.1,2), df=10) ## Generate draws from the mixture hist(rMit(10000, mit=mit), nclass=100, freq=FALSE) x <- seq(from=-5, to=5, by=.01) ## Add the density to the histogram lines(x, dMit(x, mit=mit, log=FALSE), col='red', lwd=2) ## Two dimensional (one component mixture) Student-t distribution mit <- list(p=1, mu=matrix(0,1,2), Sigma=matrix(c(1,0,0,1),1,4), df=10) ## Function used to plot the mixture in two dimensions 'dMitPlot' <- function(x1, x2, mit=mit) { dMit(cbind(x1, x2), mit=mit, log=FALSE) } x1 <- x2 <- seq(from=-10, to=10, by=.1) thexlim <- theylim <- range(x1) z <- outer(x1, x2, FUN=dMitPlot, mit=mit) ## Contour plot of the mixture contour(x1, x2, z, nlevel=20, las=1, col=rainbow(20), xlim=thexlim, ylim=theylim) par(new=TRUE) ## Generate draws from the mixture plot(rMit(10000, mit=mit), pch=20, cex=.3, xlim=thexlim, ylim=theylim, col="red", las=1) ## Two dimensional three components mixture of Student-t distributions mit <- list(p=c(.2,.3,.5), mu=matrix(c(-5,-1,-3,5,1,2),3,2,byrow=TRUE), Sigma=matrix(.5*c(1,1,1,0,0,0,0,0,0,1,1,1),3,4), df=10) x1 <- x2 <- seq(from=-10, to=10, by=.1) thexlim <- theylim <- range(x1) z <- outer(x1, x2, FUN=dMitPlot, mit=mit) ## Contour plot of the mixture contour(x1, x2, z, nlevel=20, las=1, col=rainbow(20), xlim=thexlim, ylim=theylim) par(new=TRUE) ## Generate random draws from the mixture plot(rMit(10000, mit=mit), pch=20, cex=.3, xlim=thexlim, ylim=theylim, col="red", las=1)