Hi Oriol,
 
It is not clear what you want to do with the kriging variance you obtain...
Probably you want to quantify the degree of reliability of the allocation 
of a particular location to a given facies. This could be measured by the 
variance
or entropy of the distribution of probabilities of occurrence of facies at that
location, see my book page 354. This probability distribution is easily computed
by indicator kriging or you can use truncated Gaussian simulation if there is
any physical ordering of your facies.
 
For your last question, look at Journel and Huijbregts "Mining Geostatistics"
page 451 for the "smoothing relations" that link the average kriging variance 
to the
variance of observations and the variance of kriging estimates.
 
Pierre
 
Pierre Goovaerts
Chief Scientist at BioMedware Inc.
Courtesy Associate Professor, University of Florida
President of PGeostat LLC
 
Office address: 
516 North State Street
Ann Arbor, MI 48104
Voice: (734) 913-1098 (ext. 8)
Fax: (734) 913-2201 
http://home.comcast.net/~goovaerts/ 

________________________________

From: [EMAIL PROTECTED] on behalf of Oriol Falivene
Sent: Sat 7/15/2006 7:28 AM
To: [EMAIL PROTECTED]; [EMAIL PROTECTED]; [EMAIL PROTECTED]; [email protected]
Subject: Re: AI-GEOSTATS: Re: generalize kriging variance to 
average-basedestimators different than


Hi all!. 

Isobel, Jan and Adrian, thank you for your useful suggestions. 

I have been studying the information you suggested me to read. Please, correct 
me if I am wrong: 
"It is possible to compute the estimation variance for any weighted average 
estimator. But in order to do this we need to know the semivariogram of the 
property". 

More things regarding estimation variance: 

Actually, I am working in the interpolation/estimation of categorical 
properties (i.e. facies). Categorical properties take discrete values which do 
not need to follow any ordering (i.e. from category A to category C a 
transitional step with category B may not exist). 

1) A possible manner of generating interpolation maps of this type of 
properties would follow this procedure: 1st)  Order categories (this can be 
difficult to justify in some cases). 2nd) Transform the orderd categorical 
property into a continuous property by assigning a numerical value to each 
category. 3rd) Interpolate the numerical values of the continuous property. 4) 
Truncate the results of the interpolation of the continuous property with a 
number of thresholds equals to the number of categories minus one (the 
thresholds should be located between the assigned values), to get the 
interpolated categorical properties (or facies map). 

The estimation variance (or kriging variance) refers to the results of the 
continuous property interpolation (3rd step) and not to the categorical 
property obtained after truncating the continuous property (4th step). And 
therefore I do not know if it would be correct to assign this estimation 
variance to the estimation variance of the categorical property results 
(probably not), any idea on that? 

2) Another option for generating interpolation maps of categorical properties 
is indicator kriging for categorical variables. The following procedure is 
used: 1st) The categorical property is transformes into n new properties (one 
for each category) according to the indicator transform for categorical 
variables, the value of each new property corresponds to the probability of 
finding the related category (or facies) at a given position. 2nd) Each new 
property is interpolated over all the grid and the results correspond to the 
probabilities for each category to be present in a location. 3rd) In each grid 
cell the category with the highest probability is chosen to obtain the 
interpolated categorical properties (or facies map). 

In this case we have a number of estimation variances related to occurrence 
probability at each point (one for each category). It is intuitive to chose the 
one of the selected category, but again I am not sure of how this variances, 
which are originally related to probability of occurrence, can be transported 
into variances of the categorical property, any idea on that? 

And one more question: 
I would like to know if there is any relationship between kriging estimation 
variance and the variance of the actual kriging estimates, any idea? 

Thanks a lot! 
  

Oriol Falivene 
  
  

Isobel Clark wrote: 

        Oriol Download for free, my old book Practical Geostatistics. Chapter 4 
tells you all about calculating the variance for any weighted average 
estimator. Follow links from http://www.kriging.com Isobel 

        Oriol Falivene <[EMAIL PROTECTED]> wrote: 

                Dear Colleagues, 

                I'm a PhD student working on interpolation of categorical 
variables 
                (like facies). 

                I would like to know if it's possible to generalize the kriging 
variance 

                to other average-based estimators different than kriging, such 
as 
                kriging with an areal trend, indicator kriging or inverse 
distance 
                weighting?; if it's possible could you send me some references 
where I 
                can find that?. 

                Thank you. 

                Best regards 

                Oriol 

                -- 
                  
                  

                ______________________________________ 

                Oriol Falivene 
                [EMAIL PROTECTED] 
                http://www.ub.es/ggac 

                tel. (+34) 93 4034028 
                fax (+34) 93 4021340 

                Fac. de Geologia, 
                Univ. de Barcelona 
                  

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______________________________________ 

Oriol Falivene 
[EMAIL PROTECTED] 
http://www.ub.es/ggac 

tel. (+34) 93 4034028 
fax (+34) 93 4021340 

Fac. de Geologia, 
Univ. de Barcelona 
  


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