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I have a set of 5 data points (x=10,20,30,40,50 and its corresponding response values y and noise as s.d. of y). These data are obtained from stochastic computer experiments.

How can I use DiceKriging in R to fit a kriging model for these data?

x <- seq(from=10, to=50, length=5)
y <- c(-0.071476,0.17683,0.19758,0.2642,0.4962)
noise <- c(0.009725,0.01432,0.03284, 0.1038, 0.1887)

Examples online with heterogeneous noise are pre-specified with coef.var, coef.trend and coef.theta. It is unlikely that I can have a priori on these.

I have referred to the answer here. However, other references suggest adding the nugget parameter lambda is similar to adding homogeneous noise, which is not likely "individual errors".

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  • Is that really noise if it is so correlated with x and y? I may not understand heterogeneous noise completely. If not, perhaps add the noise as an independent effect in the model? – cgage1 Jun 09 '16 at 16:44
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    @cgage I have changed the wordings in case I used the wrong word to make myself clear. Yes, these data are highly linearly correlated (just to test, the actual data are much more nonlinear). But being able to tell the model "there are individual errors" but not same sd for everyone" makes it a better estimation of confidence intervals (and thus EI, expected improvements). – user2513881 Jun 09 '16 at 16:48

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The use of km with noise is quite simple:

model <- km(~1, data.frame(x=x), y, noise.var = noise, covtype = "matern3_2")

However, your noise term make the line search part of L-BFGS algorithm fail. It may be due to the fact that is is strongly correlated with y, because when I run the following lines, it works:

noice <- c(0.009725,0.01432,0.03284, 0.001, 0.1887)
model <- km(~1, data.frame(x=x), y, noise.var = noise, covtype = "matern3_2")
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