MCMChybridGP-package {MCMChybridGP} | R Documentation |
Hybrid Markov chain Monte Carlo (MCMC) to simulate from
a multimodal target distribution with derivatives unknown.
A Gaussian process fit is used to approximate derivatives.
The Package consists of an Exploratory phase,
with hybrid.explore
, followed by a Sampling
phase, with hybrid.sample
.
The user is to supply the log-density f
of the
target distribution along with a small number of (say 10)
points to get things started.
The Sampling phase allows replacement of the true
target in high temperature chains, or complete replacement
of the target. A full description of the method is given in
Fielding, Mark, Nott, David J. and Liong Shie-Yui (2009).
The authors gratefully acknowledge the support & contributions of the Singapore-Delft Water Alliance (SDWA). The research presented in this work was carried out as part of the SDWA's Multi-Objective Multi-Reservoir Management research programme (R-264-001-272).
Package: | MCMChybridGP |
Type: | Package |
Version: | 1.0 |
Date: | 2009-09-15 |
License: | GPL-2 |
LazyLoad: | yes |
Mark James Fielding <stafmj@nus.edu.sg>
Maintainer: Mark James Fielding <stafmj@nus.edu.sg>
"Efficient MCMC schemes for Bayesian calibration of computer models", Fielding, Mark, Nott, David J. and Liong Shie-Yui (2009), in preparation.
## Not run: mu1 <- c(-1, -1) mu2 <- c(+1, +1) sigma.sq <- 0.1225 X0 <- generateX0(lb=c(-3,-3), ub=c(3,3)) f <- function(x) { px <- 1/4/pi/sqrt(sigma.sq) * exp(-1/2/sigma.sq * sum((x - mu1)^2)) + 1/4/pi/sqrt(sigma.sq) * exp(-1/2/sigma.sq * sum((x - mu2)^2)) return(log(px)) } explore.out <- hybrid.explore(f, X0, n=100, graph=TRUE) sample.out <- hybrid.sample(explore.out, n=500, graph=TRUE) opar <- par(mfrow=c(2,1)) plot(density(sample.out$SAMP[,1]), xlab="x1", ylab="f(x)") plot(density(sample.out$SAMP[,2]), xlab="x2", ylab="f(x)") par(opar) ## End(Not run)