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In Peter Alfred's article on multivariative scattered data interpolation he mentioned, that from a variety of schemes only few are really popular among practitioners. He named for instance Shepard's method and Hardy Multiquadrics. But that article is almost 20 years old by now, and what is really interesting, is what methods are widely used nowadays.
If you have any experience of using some of spatial interpolation schemes, please tell about it.
UPD: To make this question more competitive, I've restated it. It was "What methods of multivariate interpolation have you ever used?"
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Radial Basis Function interpolation is a diverse group of data interpolation methods. In terms of the ability to fit your data and produce a smooth surface, the Multiquadric method is considered by many to be the best.
The uses of interpolation include: Help users to determine what data might exist outside of their collected data. Similarly, for scientists, engineers, photographers and mathematicians to fit the data for analysing the trend and so on.
While the best geostatistical interpolation method is the EBK and the best overall interpolation method is the IDW.
A good starting point is to use a linear interpolation. This draws a straight line between available data, in this case on the first of the month, and fills in values at the chosen frequency from this line. Running this example, we can see interpolated values.
I've used Kriging in the past, with scattered data which came with estimates of accuracy at each sample. Seemed like a powerful technique which deserved to be more widely used outside the geostatistics world.
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(A year later) see inverse-distance-weighted-idw-interpolation-with-python, a combination of inverse-distance weighting and scipy.spatial.KDTree.
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