3:47 AM
Not sure how to ask this, but with the kriging/GPR examples at en.wikipedia.org/wiki/Kriging and scikit-learn.org/stable/auto_examples/gaussian_process/… , the fitted model a) exactly hits each overservation, and b) has zero variance at the observations. This doesn't make much sense to me, since real data almost invariably has some noise in it. Is there a way with these processes to get an estimate that accounts for that?
If I boostrapped the model, removing one data point at a time, and then averaged over those, I would get something approaching what I mean, but it seems like GPR should be able to handle that during fitting.

4:09 AM
Never mind, figured it out. It's the nugget, and in scikit-learn that's been replaced with alpha/WhiteKernel

10 hours later…
1:41 PM
@naught101 It's really the nugget plus an independent noise term. A lot of software doesn't distinguish the two, though.

2 hours later…
3:22 PM
@whuber Wait, there's a difference? Oh.... oh no.

8 hours later…
11:24 PM
@whuber @whuber yeah, I don't yet understand why the sklearn implementation has both alpha and WhiteKernel, but I guess it's to allow that distinction? TBH I'm not sure what that is. geostatisticslessons.com/lessons/nuggeteffect indicates the nugget is related to noise. Is it the difference between natural variability and uncertainty?

@naught101 Basically yes. The nugget captures a low-range component of the variogram--but that's not independent noise; that's spatial variability. Noise can arise, for instance, through independent measurement variability. Sometimes that can be independently estimated, such as through repeated measurements of the value at a given location.

@whuber So variability would be represented by the noise, and uncertainty by the nugget? Or the other way around? And why/when would that distinction matter? (maybe this should be a question for the main site..)