interpolation, what splines are!

[McCauley Technical Services]

Simon Cox (simon at cerberus.earth.monash.edu.au) writes on 5 Jul 93:
>Kriging, on the other hand, is a purely statistical method, based on

>unknown, and it can also give some statistics about how good the estimate is!

I'm not "in the know," but I thought there was (or is planned) a way
to do cross-validation ("leaving-one-out" in pattern recognition
terms) for s.surf.tps. I believe that the mathematics allow this
to be done without an incredulous amount of computations.

I would tend to value this more than some statistic that tells
me how well I am approximating some unknown process.

>Overall, I think that an adequate toolkit for us all would include both
>thin-plate-splines and kriging, since this would cover both the "integral"
>and "statistical" approaches, each of which are useful in different
>circumstances.

I agree - both are needed.  You could get a lot of mileage out of
these two since these will be the "Crescent wrench" and "Vise-grips"
of our tool box. However, I would not stop here. There may be
situations where other tools are more necessary/sufficient/appropriate.

One concern that I have is the representation of interpolated values.
Putting "floating point now*" aside, I would advocate that any 
ordinary (point) kriging routine produce either a sites list or
vector file with only points. Block kriging is the appropriate
procedure for producing a raster file - where the block sizes
correspond to the current cell size.  

* [a battle cry at the GRASS conference, see the latest GRASSCLIPINGS.]

I do not know enough about splines and Helena's work to comment on the
appropriate spatial representation. (anyone?)
--
James Darrell McCauley                                   phone: 317.497.4757
McCauley Technical Services                      internet: darrellmy at ids.net
P.O. Box 2485                        West Lafayette, Indiana 47906-0485, USA