Re: distribution transformations and Gstat

["Edzer J. Pebesma" <edzer@pangea.Stanford.EDU>]

Ashton Shortridge wrote:
> Normal Score Transform:Clustered 140 primary data
>  4
> Xlocation
> Ylocation
> Primary
> Normal Score value
> 39.5 18.5   .06   -2.525
>  5.5  1.5   .06   -2.112

Your example exactly illustrates the one big problem with normal
scores: tied data. Will backtranforming these data give the original
data? Anyway, in the transformed space, the first .06 is treated
as a lower value than the second .06.

> are then backtransformed; see Deutsch & Journel, 1998, p. 226-7 for a very
> brief discussion of this. GSLIB's program backtr does this using a lookup
> table it created when initially transforming the data.

Not only a lookup table, but also two parameters and two `models' for
extrapolating in both tails.

> I hope this helps either in the development of new code or at least in some
> users' understandings about the model assumptions we make when we use
> geostatistics. From a Gstat development perspective, I understand a line has
> to be walked between usability and multifunctionality. The user has few (if
> any) decisions to make for the transform. The GSLIB code itself is pretty
> short, and mostly consists of data input/output. It is fortran, though! I'd
> think implementation would be pretty straightforward..

I have hardly problems with the normal score transform (although I
would print a BIG warning in case of ties; also you can decide to
make ties come out as ties, or assign arbitrary ranks to them (as
GSLIB does apparently) -- this is also a model decision). I consider
the back-transform as very non-trivial, one that calls for quite
a bit of skill, and knowledge how to do this. (As far as I can see
now, you need to dive into the source code to see what GSLIB really
does here).

Implementing may not be the problem -- documenting may be.
--
Edzer