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For our foray into geostatistics we got data that consists of measurements taken from the soil. The dataset has like concentrations of various different minerals.

We were divided into a number of groups that try to explore different types and methods of interpolation. We got saddled with kriging, more specifically something called "5th order kriging". Which for some reason I can't find any documentation or explanation on.

What the heck is 5th order kriging? All I got was simple, ordinary, and universal kriging (or kriging with a trend)... and something or other. Can anybody point me to some resources?

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    $\begingroup$ Without more context it's impossible to tell. The following therefore is pure speculation. It might refer to IRF-k Kriging of fifth order. It could be some form of Universal Kriging with a fifth-degree polynomial drift. Another possibility is a recent proposal to utilize higher-order moments to characterize spatial variability: see Liu et al., "A new approach to spatial data interpolation using higher-order statistics." Perhaps somebody has confused Kriging with some other technique such as fifth-order splines. $\endgroup$ – whuber Apr 27 '17 at 15:53
  • $\begingroup$ Would it help that he gave us 5th order kriging because the measurements are actually far from the area we're supposed to interpolate over? The analogy he gave us was a doughnut, the measurements are located close to the edges of the doughnut, yet the area in question the doughnut's hole. No measurements are taken in that area. $\endgroup$ – ace_01S Apr 28 '17 at 5:22
  • $\begingroup$ When the measurements are located far from the interpolation area, you are performing extrapolation--which is never recommended. When fitting some underlying polynomial trend or "drift," the extrapolation becomes more and more dependent on the degree ("order") of the polynomial. A fifth degree polynomial could introduce huge sensitivity; it's difficult to imagine how such an approach ever could be justified unless enormous amounts of data are available or some well-established theory required such a trend function. I believe there is no such theory of minerals concentrations. $\endgroup$ – whuber Apr 28 '17 at 13:54
  • $\begingroup$ The measurements are surrounding the area though. so it would make sense that interpolation is a suitable method. At least that's what I think, most of the examples I've seen on the web are either close to the area or at least surrounding it. $\endgroup$ – ace_01S Apr 28 '17 at 14:00
  • $\begingroup$ Possibly. It depends on just how correlated the data are, how large that hole is, and how confident you are that the drift and the spatial correlation structure observed among the data persist within the hole. But since we still have little idea what "fifth order kriging" might actually be, I hesitate to speculate any further. $\endgroup$ – whuber Apr 28 '17 at 14:03

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