QUESTION posted...

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?

ANSWERS:

******

Isobel Clark

drisobelclark@...

http://uk.geocities.com/drisobelclark

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

paulojus@...

http://www.maths.lancs.ac.uk/~ribeiro

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.

********

Gregoire Dubois

gregoire.dubois@...

http://www.ai-geostats.org

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

myers@...

http://www.u.arizona.edu/~donaldm

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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