MCMChybridGP-package: Hybrid MCMC for a multimodal density with derivatives...
In MCMChybridGP: Hybrid Markov Chain Monte Carlo using Gaussian Processes

Description Details Author(s) References See Also Examples

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, Nott and Liong (2011).

The authors gratefully acknowledge the support & contributions of the Singapore-Delft Water Alliance. The research presented in this work was carried out as part of the 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 <mark.fielding@gmx.com>

Maintainer: Mark James Fielding <mark.fielding@gmx.com>

"Efficient MCMC Schemes for Computationally Expensive Posterior Distributions", Fielding, Nott and Liong (2011).

hybrid.explore, hybrid.sample

    mu1 <- c(-1, -1)
    mu2 <- c(+1, +1)
    sigma.sq <- 0.1225
    ub <- c(1.5, 3)
    X0 <- generateX0(lb=c(-2,-2), ub=ub)
    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, ub=ub, n=150, 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)