best interpolation method for a small sample size

[ScottTweddale]

I have 12 point measurements of noise (decibels) that I need to interpolate over a 100 sq. km area.  Are there any interpolation methods that are well suited for small sample sizes?  Based on some earlier posts to this forum, I saw a suggestion for Kernel Interpolation with Barriers and just don't supply a barrier and IDW.   What about Empirical Bayesian Kriging, or should I eliminate any kind of kriging as a possibility due to the small sample size?  What about machine learning techniques? 

Thanks in advance for any suggestions

[SteveLynch]

Difficult to answer without seeing the data 🙂

Post an image showing the locations and the noise value and, if possible, also attach the data.

-Steve

[ScottTweddale]

Steve,

I have my noise data and an image showing the locations, but I'm not sure how to post them here?  I'll send them as an email attachment to you.   Thanks so much for your response.

Scott

[SteveLynch]

Scott

All I can say is try them all, not really, do ebk, idw, rbf and kernel, and look at the cross validation statistics and pick one that produces what you expect to see and has reasonable cv stats.

[Elijah]

@Scott,

EBK or EBK regression prediction typically outperforms other interpolation techniques, may be, apart from some other ML techniques. However, EBK and EBKRP can't work here using ArcGIS since I guess the minimum number of samples it can handle is 20. If you have covariates with noise, you can try co-kriging since. Adding covariates may help improve the prediction. If not, advise from SteveLynch is most appropriate. Try as many as may appear reasonable, than compare the error stats.