A while back, I asked a question regarding the fitting of Gaussian Process (GP) smooths within a GAM framework that garnered some interest:
A very recent article (published yesterday on BioRxiv) by @GavinSimpson expands on general ideas mentioned in the response to the above post through application to paleoecological and paleolimnological climate data.
In fitting GPs within the R package 'mgcv', it is best to specify the estimated range parameter ($\rho$), above which observations are no longer correlated with one another. 'mgcv' uses a default for $\rho$ equal to the maximum distance between pairs of observations, which may be adequate for some purposes (i.e., smooth, non-stochastic trends = non-time series).
The most straightforward method to go about selecting the optimal $\rho$ is to compare against some model selection criterion (AIC/UBRE/ML/REML) to see where a global minimum occurs.
My question is: how should one go about selecting a suitable interval of values to test for the range parameter? @GavinSimpson tested $\rho \in$ [15, 500] in his recent work, whereas Simon Wood uses 1:10*10 (10, 20, 30, ...) in his book (2nd ed. p. 362).
Any thoughts are greatly appreciated and welcomed.