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I'm estimating a stationary, spatially random variable over a 2-dimensional domain. I have ground-truth measurements in several locations, over time.

I need some way of spatially-interpolating between the measurements, obviously. I have identified two ways to do this, and I would like to know the trade-offs of each:

1) use a variogram. By dividing the data into training and testing, I can run the variogram on the training data to estimate which variogram is the best fit (gaussian, spherical, etc.), using root-mean square error.

2) use a computational approach. By implementing a gaussian process regression method with an isotropic gaussian covariance function of a given bandwidth. Then, I can loop over bandwidth values, and for each bandwidth value, use a k-folds cross validation to observe the root-mean square error. Then, I would select the bandwidth that yields the smallest root-mean square error.

Which approach is more favorable and why? Of course, I could try both, but I'd like to gain some intuition around this problem since it comes up frequently.

Thank yo.

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Your approaches boil down to one single underlying model: a Gaussian random field with a second order stationary covariance. Bandwidth of 2) corresponds to the range of the variogram model; best fitting variogram model of 1) corresponds to the covariance function type of 2). How you exactly choose and evaluate the models and parameters is a different matter, unrelated to the choice between 1 and 2.

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  • $\begingroup$ Welcome to our site, Edzer! $\endgroup$ – whuber Aug 26 '15 at 13:50

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