Description Usage Arguments Value Author(s) References See Also Examples
A function to determine a Gaussian process fit to a set of
points forming a matrix X
, given a column
of corresponding values of the logdensity
of a target distribution. Returned is a (zero mean)
approximation Ef
of the logdensity and various
components of the Gaussian process fit as used by
hybrid.explore
and hybrid.sample
.
1 
X 
A matrix of at least 2 columns with rows representing the points (nodes) for a Gaussian process fit. 
y 
A column of corresponding values of the logdensity.
Each entry corresponds to the logdensity evaluated
at the respective row in 
params 
Gaussian process parameters as used in 
request.functions 
Optional boolean argument (default TRUE) to request the return of function
approximations 
finetune 
Optional boolean argument (default FALSE) to determine
finetuned optimal values in 
Returned is a list as requested consisting of:
Ef 
The Gaussian process approximation of the logdensity function. 
sigmaf 
Upon request, a function giving the Gaussian process
approximation of the standard deviation with respect to 
Sigma 
Covariance matrix used in the Gaussian process fit. 
Sigma.inv 
The inverse of the Covariance matrix. 
inverseOK 
Boolean flag to indicate successful calculation
of 
X 
The original 
y 

params 
Parameter values for the Gaussian process fit. 
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  mu1 < c(1, 1)
mu2 < c(+1, +1)
sigma.sq < 0.1225
X < matrix(c(2,1,0,2,0,2,0,1,2, 2,1,2,0,0,0,2,1,2), ncol = 2)
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))
}
y < rep(NA, 9)
for(i in 1:9) y[i] < f(X[i,])
Ef < GProcess(X, y, request.functions = TRUE)$Ef
Ey < NA*y
for(i in 1:9) Ey[i] < Ef(X[i,])
data.frame(X, y, Ey)
## Gaussian process close to exact at points supplied.

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