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,Im a PhD student working on interpolation of categorical variables
(like facies).I would like to know if its 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 its 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/ggactel. (+34) 93 4034028
fax (+34) 93 4021340Fac. 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
