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).

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)
``` |

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