| 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:
pmuSigmadf
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
Nxd) 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 (2009a,b). See also
the package vignette by typing vignette("AdMit") and the
files ‘AdMitJSS.txt’ and ‘AdMitRnews.txt’ in the ‘/doc’ package's folder.
Please cite the package in publications. Use citation("AdMit").
David Ardia <david.ardia@unifr.ch>
Ardia, D., Hoogerheide, L.F., van Dijk, H.K. (2009a). AdMit: Adaptive Mixture of Student-t Distributions. The R Journal 1(1), pp.25–30. http://journal.r-project.org/2009-1/
Ardia, D., Hoogerheide, L.F., van Dijk, H.K. (2009b). Adaptive Mixture of Student-t Distributions as a Flexible Candidate Distribution for Efficient Simulation: The R Package AdMit. Journal of Statistical Software 29(3), pp.1–32. http://www.jstatsoft.org/v29/i03/
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(0.5, 0.5),
mu = matrix(c(-2.0, 0.5), 2, 1, byrow = TRUE),
Sigma = matrix(0.1, 2),
df = 10)
## Generate draws from the mixture
hist(rMit(10000, mit = mit), nclass = 100, freq = FALSE)
x <- seq(from = -5.0, to = 5.0, by = 0.01)
## 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(0.0, 1.0, 2.0),
Sigma = matrix(c(1.0, 0.0, 0.0, 1.0), 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 = -10.0, to = 10.0, by = 0.1)
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 = 0.3,
xlim = thexlim, ylim = theylim, col = "red", las = 1)
## Two dimensional three components mixture of Student-t distributions
mit <- list(p = c(0.2, 0.3, 0.5),
mu = matrix(c(-5.0, -1.0, -3.0, 5.0, 1.0, 2.0), 3, 2, byrow = TRUE),
Sigma = matrix(.5 * c(1.0, 1.0, 1.0, 0.0, 0.0, 0.0,
0.0, 0.0, 0.0, 1.0, 1.0, 1.0), 3, 4),
df = 10)
x1 <- x2 <- seq(from = -10.0, to = 10.0, by = 0.1)
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 = 0.3, xlim = thexlim,
ylim = theylim, col = "red", las = 1)