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.