Dear Pierre and Gregorie
Thank you for your help .....
Concluding (considering that natural neighbor method should be a convex and
an exact interpolator) it seems that the approach has not side effects !!!!!!
Sincerely
Sebastiano
At 17.19 05/09/2005, you wrote:
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Hi,
In fact, as long as the weights are all positive and sum up to one, your
interpolated probability
will always be between 0 and 1; so you should be all right..
The approach proposed by Sebastiano is similar to median indicator kriging
in the sense
that the weights assigned to the observations will be the same across all
indicators (here instead of
a single indicator semivariogram used to compute the kriging weights, the
same weighting set
will be applied to all indicators since the data configuration, hence the
size of the Thiessen polygons,
doesn't change among indicators). Because all the weights are positive and
remain the same
for the different indicators, this approach should eliminate all order
relation deviations
(all estimated probabilities will be between 0 and 1, and at each location
their sum will be one).
Pierre
-----Original Message-----
From: Gregoire Dubois [mailto:[EMAIL PROTECTED]
Sent: Mon 9/5/2005 7:00 AM
To: 'seba'; ai-geostats@unil.ch
Cc:
Subject: RE: [ai-geostats] natural neighbor applied to indicator
transforms
Ciao Sebastiano,
I realized nobody replied to your question (sorry for have added
confusion here).
I don't see any objection in applying any interpolator to
probability values.
However, you should better use exact interpolators to avoid
getting probabilities of occurences > 1 (or smaller than 0)
Cheers
Gregoire
-----Original Message-----
From: seba [mailto:[EMAIL PROTECTED]
Sent: 02 September 2005 10:07
To: ai-geostats@unil.ch
Cc: ai-geostats@unil.ch; 'Nicolas Gilardi'
Subject: RE: [ai-geostats] natural neighbor applied to
indicator transforms
I try to reformulate my question.....
When performing direct (i.e. without crossvariogram)
indicator kriging, practically we interpolate probability values by means
of ordinary kriging. These probability values could represent the
probability of occurrence of some category or the probability to overcome
some threshold.
My question is: is there anything wrong to interpolate
these probability values with other interpolating algorithm like, for
example natural neighbor (or triangulation)?
In my opinion is all ok ..... considering also that we
have no problem of order relation violations.
Again, this technique is applied only for a preliminary
data analysis
Then a short consideration directed about the importance
of boundaries:
Quoting Nicolas Gilardi
"My personnal feeling about the distinction between using
a classification algorithm or a regression one is the importance you put
on the boundaries.If you look for smooth boundaries, with uncertainty
estimations, etc., then a regression algorithm (like indicator kriging)
is certainly a good approach."
Well, if you use fuzzy classification the boundaries
become continuos...fuzzy.
Bye
S. Trevisani
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