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

## Description

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).

## Details

 Package: MCMChybridGP Type: Package Version: 1.0 Date: 2009-09-15 License: GPL-2 LazyLoad: yes

## Author(s)

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

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

## References

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

## See Also

`hybrid.explore`, `hybrid.sample`

## Examples

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20``` ``` 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) ```

MCMChybridGP documentation built on Nov. 13, 2020, 1:13 a.m.