[Qgis-developer] Kriging interpolation functionality in QGIS?

[Sjur Kolberg]

I'd prefer Kriging to IDW also for simple jobs.

Kriging is (at least) four operations:
0: Know the assumptions and check your data, transform if necessary and possible.
1: Estimate your empirical semivariogram (describing how difference increases with distance).
2: Select a parametric semivariogram model, and adjust parameters to fit the point cloud from 1) 
3: Use the parametric model to calculate a weight matrix between each target location (grid point) and each observation point.

Loosely speaking, the three first operations define the core of Kriging. The last operation answers the same question as IDW, both providing the coefficients (weights) in a linear combination of the input data. 

With Gaussian data, spatial stationarity, well-spread data points and a properly selected/tuned semivariogram model, Kriging can be shown to be 'Best linear unbiased estimator' (BLUE), and provides mathematically correct estimates of the variance at each target location. IDW promises no such thing, hence appears less dependent on assumptions. This does not imply that IDW is more robust or almost-as-good for simple tasks.

For the numbers that both methods do provide, it is possible to evaluate and compare the two using leave-one-out cross validation. 

With just a reasonable a priori judgment for the range parameter, my guess is that Kriging will beat IDW in cross-validation for most problems, including notoriously assumption-breaking daily precipitation data. With some scripting, it is also possible to optimise Kriging's semivariogram parameters by minimising the cross-validation RMSE. This does not qualify for being BLUE or for trusting the variance estimates, though.

All this said, the extra burden of finding Kriging in one of QGIS' plugins, may serve as a warning that there is more to it than just plug-and play.

Sjur  :-)



> -----Original Message-----
> From: qgis-developer-bounces at lists.osgeo.org [mailto:qgis-developer-
> bounces at lists.osgeo.org] On Behalf Of Barry Rowlingson
> Sent: 26. september 2015 19:43
> To: Stefan Keller
> Cc: qgis-developer at lists.osgeo.org
> Subject: Re: [Qgis-developer] Kriging interpolation functionality in QGIS?
> 
> On Fri, Sep 25, 2015 at 6:46 PM, Stefan Keller <sfkeller at gmail.com> wrote:
> > Hi Barry
> >
> > Many thanks for your explanations and hints.
> > So from a pragmatic point-of-view ("80/20 pareto rule"):
> > Do you think Inverse Distance Weighting (IDW) would do the job as
> > well, since Kriging has so many parameters to fiddle around and to
> understand?
> 
>  Depends on what "the job" is. To get an impression of the overall trend of a set
> of samples - IDW is probably fine. But to get a
> *principled* (ie based on a statistical model) set of estimates over a grid *with
> honest estimates of uncertainty* so you can answer probabilistic questions (like
> "what's the chance that the soil over there will contain 1ug gold/tonne?") you
> need something like kriging.
> 
>  Barry
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