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kriging and the nugget? 
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Joined: Mon Feb 21, 2011 1:35 pm
Posts: 1
Post kriging and the nugget?
Can anybody explain or give good resources on the basics of kriging (and nuggets etc...).

Any help is very welcome

Mon Feb 21, 2011 1:48 pm

Joined: Thu Sep 16, 2010 8:38 pm
Posts: 14
Post Re: krigging and the nugget?
Hope this explains your question. It's pretty basic inofrmation but explains all you need to know to do further web and resource research....

Kriging derives from the ubiquitous eponym that recognizes Professor D G Krige’s contribution to geostatistics. Krige was the pioneering plotter of distance-weighted averages at the Witwatersrand gold complex in South Africa where he found the infinite set of distance-weighted averages but lost the correspondingly infinite set of variances. Professor Dr G Matheron was so mesmerized by the infinite set of distance-weighted average that he, too, failed to notice that the correspondingly infinite set of variances was lost. Krige’s honorific eponym inspired a cult like lingo of neologisms such as kriged estimate, kriged estimator, kriging variance, kriging covariance, zero kriging variance, kriging matrix, kriging method, kriging model, kriging plan, kriging process, kriging system, block kriging, co-kriging, disjunctive kriging, linear kriging, ordinary kriging, point kriging, random kriging, regular grid kriging, simple kriging and universal kriging. Geostatisticians refuse to explain why the variance of the distance-weighted average vanished before it turned into a kriged estimate.

Kriging (or Gaussian process regression for statisticians) can be understood as linear prediction or a form of Bayesian inference. Kriging starts with a prior distribution over functions. This prior takes the form of a Gaussian process: N samples from a function will be normally distributed, where the covariance between any two samples is the covariance function (or kernel) of the Gaussian process evaluated at the spatial location of two points.

A set of values are then observed, each value associated with a spatial location. Now, a new value can be predicted at any new spatial location, by combining the Gaussian prior with a Gaussian likelihood function for each of the observed values. The resulting posterior distribution is also a Gaussian, with a mean and covariance that can be simply computed from the observed values, their variance, and the kernel matrix derived from the prior.

From the geological point of view, Kriging uses prior knowledge about the spatial distribution of a mineral: this prior knowledge encapsulates how minerals co-occur as a function of space. Then, given a series of measurements of mineral concentrations, Kriging can predict mineral concentrations at unobserved points.

Kriging is a family of linear least squares estimation algorithms. The end result of Kriging is to obtain the conditional expectation as a best estimate for all unsampled locations in a field and consequently, a minimized error variance at each location. The conditional expectation minimizes the error variance when the optimality criterion is based on least squares residuals. The Kriging estimate is a weighted linear combination of the data. The weights that are assigned to each known datum are determined by solving the Kriging system of linear equations, where the weights are the unknown regression parameters. The optimality criterion used to arrive at the Kriging system, as mentioned above, is a minimization of the error variance in the least-squares sense.

Please feel free to ask questions!



Mon Feb 21, 2011 7:47 pm

Joined: Fri Feb 15, 2013 10:36 pm
Posts: 1
Post Re: kriging and the nugget?
Do you know if anyone has addressed "why the variance of the distance-weighted average vanished" and what to do about that? I have read this sort of criticism of kriging before elsewhere, but don't know how to resolve the problem or proceed.

I have noticed, however, some programs that do kriging report a variance for each kriged value. And one can plot a map of this variance to give an indication of confidence that can be attributed to a map of the kriged variable. Is this reported variance different from the one you mention above that vanished?

thanks, Dave

Tue Feb 19, 2013 5:19 pm
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