urhitro: UNU.RAN transformend density rejection generator

Description

UNU.RAN random variate generator for continuous multivariate distributions with given probability density function (PDF). It is based on the Hit-and-Run algorithm in combinaton with the Ratio-of-Uniforms method (HITRO).

Usage

urhitro(n, dim=1, pdf, mode=NULL, thinning=1, burnin = 0, ...)

Arguments

size of required sample.

dim

number of dimensions of the distribution. (integer)

pdf

probability density function. (Rfunction)

mode

location of the mode -- optional. (numeric vector)

thinning

thinning factor. (positive integer)

burnin

lenght of burin-in phase. (positive integer)

...

(optional) arguments for pdf

Details

This is a Markov chain sampler that generates a sequence of continuous random vectors with given probability density function. This function must be provided by pdf, a function which must return non-negative numbers and which need not be normalized (i.e., it can be any multiple of a density function).

Notice that MCMC samplers do not produce a sequence of independent variates. The drawn sample follows the target distribution only appropriately. Beware: MCMC sampling can be dangerous! The algorithm works best with log-concave distributions. Other distributions work as well but convergence can be slower.

References

R. Karawatzki, J. Leydold, and K. P"otzelberger (2005): Automatic Markov Chain Monte Carlo Procedures for Sampling from Multivariate Distributions. Research Report Series / Department of Statistics and Mathematics, Nr. 27, December 2005 Department of Statistics and Mathematics, Wien, Wirtschaftsuniv., 2005. http://epub.wu-wien.ac.at/dyn/virlib/wp/showentry?ID=epub-wu-01_8cb

Examples

Run this code

## Create a sample of size 100 for a 
## Gaussian distribution
mvpdf <- function (x) { exp(-sum(x^2)) }
x <- urhitro(20, dim=2, pdf=mvpdf)
x

## use:
##  mode at (0,0)
##  thinning factor 3
##    (only every 3rd vector in the sequence is returned)
##  burn-in of length 100
##    (the first 1000 vectors in the sequence are discarded)
x <- urhitro(20, dim=2, pdf=mvpdf, mode=c(0,0), thinning=3, burnin=100)
x