FINAL: AI-GEOSTATS: Different Spatial Lag tolerance?
- Thanks to all contributors.
I'm using a MATLAB program to plot covariance (and to find a model, as we
usually do for variagrams in Geostatistics).
Till today I've just used lag tolerance as half of the spatial lag, larger
as possible to take account of all possible distances and smaller as
possible to don't take in account the same pairs.
This program allow us to define different lag-tolerance to different lags,
but doing this the mean of pais covariance for each lag, considering each
lag-tolerance, is different, and allow us to choose easilly a model.
Is better than do variograms/covariograms for differents lags to see wich
lag give us a good experimental variogram/cov., even considering the
"physical knowledge" (geology, limits etc.) to choose lags.
My question is: Do we have problems with our var./cov. if we don't
consider some pairs or take in account the same pairs more than one time
(overlaping)? Or we can consider this like a flexibility, depending on the
expert knowledge or judgement?
Using HALF the spatial lag:
1. Maximize information for each point;
2. Do not get "horrendous" inter-relation and smoothing problems from
overlapping distance interval;
3. Need to try several differents lag intervals to get a clear picture
about the behaviour of the phenomenon.
Paulo Justiniano Ribeiro Jr
1. There is not a definitive reason to not to take into account all pairs
or even overlap distance intervals;
2. Overlaping distance intervals can creates a false impression of smooth
behaviour of the variogram, in other words it can overestimate the degree
of spatial structure;
3. Variograms are not the only paradigma to estimate covariance
parameters. Other options includes likelihood based and Bayesian methods.
This leads to the discussion whether models should fit the original data
or the variograms.
4. Models fitted using variograms will always carry subjective decisions,
which are not necessarily a bad thing but should be carefully thought
about and clearly documented.
1. To be really consistent, one should not remove pairs but one should
rather remove a point that creates trouble. Interactive h-scatterplots are
certainly usefull to identify pairs that behave in
an unexpected way but the are even more interesting to find out if these
pairs refer systematically to the same points. Of course, one needs a good
justification to remove a point from a data set.
2. Overlaping distance intervals (as a "moving lag window") could densify
the number of point and get more details (See FLAMM et al., 1994);
Donald E. Myers
1. For more than half of spatial lag or non-uniform distance tolerance we
have more mixing pairs and pairs for more than one distance class,
exacerbating the interdependence between the pairs;
2. There is more advantages potting/modeling variograms than covariances;
3. Fitness of variogram/covariance model to data is not unique,
cross-validation often provides useful information about it.Graphical
"fit" does not tell us much about kriging estimation.
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