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:gregoire.dubois@...]

Sent: Mon 9/5/2005 7:00 AM

To: 'seba'; ai-geostats@...

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:sebastiano.trevisani@...]

Sent: 02 September 2005 10:07

To: ai-geostats@...

Cc: ai-geostats@...; '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