AI-GEOSTATS: SUM: Sensitivity analysis of automatic variogram fitting
- Dear all,
here is a summary of the two replies I got to my question on robust variograms
and automatic mapping:
1) The following reading was suggested by Victor De Oliveira
Lark, R.M. (2000), A comparison of some robust estimators of the variogram for
use in soil survey, European Journal of Soil Science, 51, 137-157.
2) Dan Cornford made the following comments:
Acronyms used hereafter are:
SVM: Support Vector Machine
GP: Gaussian Processes
SVM are not designed for spatial data. However when treated as
function approximators (i.e. when the process is real and the noise is
IID) they are good. However they are not probabilistic models as
Dan's group (Neural Computing Research Group, http://www.ncrg.aston.ac.uk)
have been doing some work on machine learning algorithms for GP's based on
Bayesian learning algorithms. This allowed them to estimate a GP sequentially
(using one observation at a time) and also estimate the parameters of the
covariance (variogram) function.
It also has a (principled) sparsity heuristic added (which accounts for
first and second moments), so it works on very large data sets, but
gives probabilistic prediction.
However the method is not fully Bayesian in that an approximate MAP
estimate of the covariance function is used. Also the method would not
be robust to outliers, since these are not currently incorporated in the
model. Basically it is very difficult to treat uncertainty in the
covariance parameters analytically (which is necessary for fast
Dan's suggestion has therefore to do with sampling (i.e. Monte Carlo).
This still does not address the functional form, although sampling could
again be used, but would be painfully slow.
Implementing cost functions to cope with kriging with outliers might be a
solution but this would require the use of prior information to set the
PS: For those interested about SVM and geostatistics, I have in my bookmarks
the following reference:
Nicolas Gilardi's publications (as well as his PhD thesis, 2002, which are
available online at http://www.idiap.ch/~gilardi/publi.html and
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