Thank you Gregoire for your input. As far as I understand there is various
types of Bayesian kriging, within a general framework, according to how
you specify the prior distributions of your model parameters, i.e. the
parameters describing your mean field as well as your covariance
structure. For example you can chose uniform priors for the parameters
describing your mean field, and assume that the parameters used to
characterise your covariance structure are well-known. This corresponds to
the classical universal or ordinary kriging model, depending on how you
specify your mean field.

From my point of view a highly relevant question regarding sample size
is: How many data points do we need before predictions, computed by
Bayesian kriging, are no longer influenced by our choice of
priors. And, how does this depend on the design ??


On Tue, 31 Aug 2004, Gregoire Dubois wrote:

> Hello everyone,
>
> I'm profiting from the discussion about Bayesian kriging to update my
> knowledge. Are there not various types of Bayesian kriging?
>
> I remember having applied in 1998 methodologies and codes (in C)
> developed in Klagenfurt, by the team of the Juergen Pilz (see
> http://www.math.uni-klu.ac.at/?language=en ). If I remember well, I have
> used functions like
>
> - Subjective Bayesian kriging (SBK) is a scenario that is between Simple
> Kriging (mean is known) and Ordinary kriging (mean unknown). In the case
> of SBK, one has some knowledge about the min and max values taken by the
> mean value of the variable that is analysed. In other words, the values
> of the mean values are constrained. Various scenarios were implemented
> in the code depending on the shape of the probability distribution
> function. For what concerns the kriging variance, the theory predicts a
> lower kriging variance for SBK only if the experimental semivariogram is
> the true one. A case study I did in my PhD was to improve estimations of
> radioactivity in Switzerland, using information provided by measurements
> made in a neighbouring country. Although the statistical distribution of
> these two datasets were very different but with similar mean values,
> this information could be efficiently used to improve to clearly reduce
> estimation errors. On the other hand, I often got a higher kriging
> variance with SBK than with OK.
>
> - Empirical Bayesian kriging (EBK): one has a much better knowledge of
> the pdf of the analysed dataset than in SBK. I did apply it to
> investigate two contaminated regions with similar distributions. Mean
> errors were lower for EBK than for Ordinary kriging. However, I also
> encountered many cases in which I got terrible results with EBK.
>
> Are other versions of Bayesian kriging not those with known
> semivariograms (Cui & Stein?) or those for which some knowledge about a
> number of parameters of the semivariogram is known, etc. Thus, going
> back to my first question, is there not a standard vocabulary that would
> allow readers to distinguish the type of prior knowledge used when one
> is talking about Bayesian kriging?
>
> For what concerns the number of points to be used etc... I don't
> understand the discussion. Should the correct question not be "how far
> does the number of samples used reflect the prior knowledge?".
>
> I hope I did not add too much confusion here :((
>
> Cheers,
>
> Gregoire
>
> PS: useful resources about the above described methods:
>
> Practically, the codes I used were written by Albrecht Gebhard( I think
> they are still available from his web site)and had a number of bugs at
> that time (in 1998-1999). The codes may have been updated since.
>
> For what concerns the mathematical developments, I used papers from
> Klagenfurt (all of them are in German, sorry). I enjoyed reading Pilz &
> Knospe (1997): Eine Anwendung des Bayes Kriging in der
> Lagerstaettentmodellierung. Glueckauf-Forschungshefte, 58(4): 670-677. I
> also recommend the master's thesis of Gerhard Buchacher: Bayes'sche und
> Empirisch Bayes'sche Methoden in der Geostatistik.
>
> More recent codes and papers should be available from Juergen Pilz's and
> Albrecht Gebhardt's homepages (again, see
> http://www.math.uni-klu.ac.at/?language=en )
>
> Hope this helps a bit.
>
> __________________________________________
> Gregoire Dubois (Ph.D.)
> JRC - European Commission
> IES - Emissions and Health Unit
> Radioactivity Environmental Monitoring group
> TP 441, Via Fermi 1
> 21020 Ispra (VA)
> ITALY
>
> Tel. +39 (0)332 78 6360
> Fax. +39 (0)332 78 5466
> Email: gregoire.dubois@...
> WWW: http://www.ai-geostats.org
> WWW: http://rem.jrc.cec.eu.int
>
> "The views expressed are purely those of the writer and may not in any
> circumstances be regarded as stating an official position of the
> European Commission."
>
>
>
>
>
> -----Original Message-----
> From: Soeren Nymand Lophaven [mailto:snl@...]
> Sent: 30 August 2004 22:13
> To: Edzer J. Pebesma
> Cc: Monica Palaseanu-Lovejoy; kai.zosseder@...;
> ai-geostats@...
> Subject: Re: [ai-geostats] extreme values
>
>
>
> Based on my relatively limited knowledge on Bayesian kriging I have a
> few comments to the current discussion:
>
> - Bayesian kriging gives better predictions than the classical approach
> if you have relatively few data points and at the same time is able to
> come up with good prior distributions for your model parameters.
>
> - The two approaches gives similar predictions if you have many data
> points.
>
> - The Bayesian approach always results in higher prediction variances,
> i.e. the classical kriging approach under estimates the prediction
> variances, because it is assumed that the parameters are known, which in
> practice they are not.
>
> - I chapter 2 in the reference below there is a figure showing
> predictions computed by the two approaches. Predictions were computed
> from a subset of the Swiss rainfall dataset (SIC97) consisting of 100
> data values. It is seen that the predictions are very close to being
> exactly equal. This means that if you are interested in prediction and
> have more than 100 data values it does not matter which approach you
> use. If you for some reason are interested in prediction variance, e.g.
> for comparing the efficiency of different designs, then Bayesian kriging
> gives you the best answer.
>
> Best regards / Venlig hilsen
>
> Søren Lophaven
> ************************************************************************
> ******
> Master of Science in Engineering        |  Ph.D. student
> Informatics and Mathematical Modelling  |  Building 321, Room 011
> Technical University of Denmark         |  2800 kgs. Lyngby, Denmark
> E-mail: snl@...                  |  http://www.imm.dtu.dk/~snl
> Telephone: +45 45253419                 |
> ************************************************************************
> ******
>
> On Mon, 30 Aug 2004, Edzer J. Pebesma wrote:
>
> >
> >
> > Monica Palaseanu-Lovejoy wrote:
> > ....
> >
> > >If you are still interested in predicting values, a better solution,
> > >in
> > >my experience, is to use a bayesian kriging method. Such
> > >methods are implemented in the package R (which is free) with the
> > >geoR routine (http://cran.r-project.org/)({ HYPERLINK
> "http://cran.r-project.org/" }. Using this method i
> > >always had smaller error standard deviations, and the precision and
> > >accuracy are better than the "normal" kriging method.
> > >
> > Thanks for sharing your experiences with us, Monica. I wondered if you
> > published
> > your results somewhere, because there is, AFAIK, little published
> > material on
> > comparisons of the "traditional" and the "model based" geostatistical
> > approaches.
> >
> > You mention smaller error standard deviations -- I assume that you
> > refer to cross validation error standard deviations, and not kriging
> > prediction standard errors? How did you calculate precision and
> > accuracy? In addition to specifying
> > a variogram model, you also need to specify prior distribution on all
> > variogram
> > parameters in the model-based approach, how did you choose these?
> >
> > One paper that does the comparison is Moyeed and Papritz, Math Geol
> > 34(4), 365-386 but they found little improvement in using model-based
> > as opposed to regular kriging; in their comparison case they used a
> > large (n>2500) data set
> > though.
> >
> > Anyone else who wants to shed light on this issue? Is there e.g. a
> > minimum sample size above which both approaches become hard to
> > distinguish?
> > --
> > Edzer
> >
> >
> >
>
>
>
>

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Signoff ai-geostats

Hello everyone,

I'm profiting from the discussion about Bayesian kriging to update my
knowledge. Are there not various types of Bayesian kriging?

I remember having applied in 1998 methodologies and codes (in C)
developed in Klagenfurt, by the team of the Juergen Pilz (see
http://www.math.uni-klu.ac.at/?language=en ). If I remember well, I have
used functions like

- Subjective Bayesian kriging (SBK) is a scenario that is between Simple
Kriging (mean is known) and Ordinary kriging (mean unknown). In the case
of SBK, one has some knowledge about the min and max values taken by the
mean value of the variable that is analysed. In other words, the values
of the mean values are constrained. Various scenarios were implemented
in the code depending on the shape of the probability distribution
function. For what concerns the kriging variance, the theory predicts a
lower kriging variance for SBK only if the experimental semivariogram is
the true one. A case study I did in my PhD was to improve estimations of
radioactivity in Switzerland, using information provided by measurements
made in a neighbouring country. Although the statistical distribution of
these two datasets were very different but with similar mean values,
this information could be efficiently used to improve to clearly reduce
estimation errors. On the other hand, I often got a higher kriging
variance with SBK than with OK.

- Empirical Bayesian kriging (EBK): one has a much better knowledge of
the pdf of the analysed dataset than in SBK. I did apply it to
investigate two contaminated regions with similar distributions. Mean
errors were lower for EBK than for Ordinary kriging. However, I also
encountered many cases in which I got terrible results with EBK.

Are other versions of Bayesian kriging not those with known
semivariograms (Cui & Stein?) or those for which some knowledge about a
number of parameters of the semivariogram is known, etc. Thus, going
back to my first question, is there not a standard vocabulary that would
allow readers to distinguish the type of prior knowledge used when one
is talking about Bayesian kriging?

For what concerns the number of points to be used etc... I don't
understand the discussion. Should the correct question not be "how far
does the number of samples used reflect the prior knowledge?".

I hope I did not add too much confusion here :((

Cheers,

Gregoire

PS: useful resources about the above described methods:

Practically, the codes I used were written by Albrecht Gebhard( I think
they are still available from his web site)and had a number of bugs at
that time (in 1998-1999). The codes may have been updated since.

For what concerns the mathematical developments, I used papers from
Klagenfurt (all of them are in German, sorry). I enjoyed reading Pilz &
Knospe (1997): Eine Anwendung des Bayes Kriging in der
Lagerstaettentmodellierung. Glueckauf-Forschungshefte, 58(4): 670-677. I
also recommend the master's thesis of Gerhard Buchacher: Bayes'sche und
Empirisch Bayes'sche Methoden in der Geostatistik.

More recent codes and papers should be available from Juergen Pilz's and
Albrecht Gebhardt's homepages (again, see
http://www.math.uni-klu.ac.at/?language=en )

Hope this helps a bit.

__________________________________________
Gregoire Dubois (Ph.D.)
JRC - European Commission
IES - Emissions and Health Unit
Radioactivity Environmental Monitoring group
TP 441, Via Fermi 1
21020 Ispra (VA)
ITALY

Tel. +39 (0)332 78 6360
Fax. +39 (0)332 78 5466
Email: gregoire.dubois@...
WWW: http://www.ai-geostats.org
WWW: http://rem.jrc.cec.eu.int

"The views expressed are purely those of the writer and may not in any
circumstances be regarded as stating an official position of the
European Commission."





-----Original Message-----
From: Soeren Nymand Lophaven [mailto:snl@...]
Sent: 30 August 2004 22:13
To: Edzer J. Pebesma
Cc: Monica Palaseanu-Lovejoy; kai.zosseder@...;
ai-geostats@...
Subject: Re: [ai-geostats] extreme values



Based on my relatively limited knowledge on Bayesian kriging I have a
few comments to the current discussion:

- Bayesian kriging gives better predictions than the classical approach
if you have relatively few data points and at the same time is able to
come up with good prior distributions for your model parameters.

- The two approaches gives similar predictions if you have many data
points.

- The Bayesian approach always results in higher prediction variances,
i.e. the classical kriging approach under estimates the prediction
variances, because it is assumed that the parameters are known, which in
practice they are not.

- I chapter 2 in the reference below there is a figure showing
predictions computed by the two approaches. Predictions were computed
from a subset of the Swiss rainfall dataset (SIC97) consisting of 100
data values. It is seen that the predictions are very close to being
exactly equal. This means that if you are interested in prediction and
have more than 100 data values it does not matter which approach you
use. If you for some reason are interested in prediction variance, e.g.
for comparing the efficiency of different designs, then Bayesian kriging
gives you the best answer.

Best regards / Venlig hilsen

Søren Lophaven
************************************************************************
******
Master of Science in Engineering        |  Ph.D. student
Informatics and Mathematical Modelling  |  Building 321, Room 011
Technical University of Denmark         |  2800 kgs. Lyngby, Denmark
E-mail: snl@...                  |  http://www.imm.dtu.dk/~snl
Telephone: +45 45253419                 |
************************************************************************
******

On Mon, 30 Aug 2004, Edzer J. Pebesma wrote:

>
>
> Monica Palaseanu-Lovejoy wrote:
> ....
>
> >If you are still interested in predicting values, a better solution,
> >in
> >my experience, is to use a bayesian kriging method. Such
> >methods are implemented in the package R (which is free) with the
> >geoR routine (http://cran.r-project.org/)({ HYPERLINK
"http://cran.r-project.org/" }. Using this method i
> >always had smaller error standard deviations, and the precision and
> >accuracy are better than the "normal" kriging method.
> >
> Thanks for sharing your experiences with us, Monica. I wondered if you
> published
> your results somewhere, because there is, AFAIK, little published
> material on
> comparisons of the "traditional" and the "model based" geostatistical
> approaches.
>
> You mention smaller error standard deviations -- I assume that you
> refer to cross validation error standard deviations, and not kriging
> prediction standard errors? How did you calculate precision and
> accuracy? In addition to specifying
> a variogram model, you also need to specify prior distribution on all
> variogram
> parameters in the model-based approach, how did you choose these?
>
> One paper that does the comparison is Moyeed and Papritz, Math Geol
> 34(4), 365-386 but they found little improvement in using model-based
> as opposed to regular kriging; in their comparison case they used a
> large (n>2500) data set
> though.
>
> Anyone else who wants to shed light on this issue? Is there e.g. a
> minimum sample size above which both approaches become hard to
> distinguish?
> --
> Edzer
>
>
>

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Hi,

Well, the bayesian kriging methods you are describing are
somewhat different than what i am using. I am using R and geoR
by Ribeiro and Diggle (2001).

Web pages for R:{ HYPERLINK "http://cran.r-project.org/"
}http://cran.r-project.org/

Web page for geoR: www.est.ufpr.br/geoR

Usually with Bayesian kriging you will have higher variance just
because the uncertainty is incorporated in all (some) parameters,
while for the geostatistical kriging (or the "other kriging") there is no
uncertainty assumed for the semi-variogram model. So, in a way
kriging is a particular case of bayesian kriging as it is described by
Ribeiro and Diggle.

Uncertainty can be assumed for nugget, variance, mean and range,
or only for one parameter, or a combination of parameters. Usually
everything is depending on how well one is understanding the data,
or at least so i think. Citing from Ribeiro the inference is done by
Monte Carlo simulations, and samples are taken from the posterior
and predictive distributions and used for inference and predictions.
One of his algorithms looks like that:

1. Choose a range of values for phi (range parameter in
geostatistical kriging) which is sensible for the given data, and
assign a discrete uniform prior for phi on a set of values spanning
the chosen range;

2. compute the posterior probabilities on this discrete support set,
defining a discrete posterior distribution with probability mass
function pr(phi | y);

3. sample a value of phi from this discrete distribution pr(phi | y);

4. attach the sampled value phi to the distribution [beta, sigma
square |y, phi] and sample from this distribution (beta = mean
param., sigma square = variance, phi = range)

5. repeat steps 3 and 4 as many times as required / desired. the
resulting sample of the triplets (beta, sigma square, phi) is a
sample from the joint posterior distribution.

In my experience, if the data set is highly skewed and the spatial
autocorrelation is weak, bayesian kriging does a better job than
geostatistical kriging, even if the data is transformed to approach
normality. From literature (see the paper mentioned by Edzer
Pebesma - Moyeed and Papritz, Math Geol 34(4), 365-386) it
seems that for very large sets of data (n > 2500) the advantage
Bayesian kriging has over geostatistical kriging is minimal, while
with the data sets i am using (random locations, weak spatial
autocorrelation, areas of spatial heterogeneity, n in between  200 to
350 points), Bayesian kriging seems to be superior.

I hope this helps a little,

Monica


Monica Palaseanu-Lovejoy
University of Manchester
School of Geography
Mansfield Cooper Bld. 3.21
Oxford Road
Manchester M13 9PL
England, UK
Tel: +44 (0) 275 8689
Email: monica.palaseanu-lovejoy@...

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Signoff ai-geostats

Mark

I could not agree more with Gregoire (with one
proviso, see below).

Both geostatistics and any weighted average estimators
are based on the same assumptions -- that relationship
between values at two locations depends on the
distance between them and (possibly) their relative
orientation. If you cannot get a decent semi-variogram
after trying every type of graph [normal, robust,
relative] and every transformation and/or
interpretation of your data [logarithm, indicator,
rank transforms, Normal scores, mixed populations],
you do not have a distance-based relationship. This
conclusion also rules out: inverse distance weighting
of any kind; Delaunay triangles; Thiessen polygons and
so on.

My proviso: there are other forms of spatial
relationship than pure distance/direction types. The
simplest example of this is data with a trend, where
the value at a specified point will depend on its
absolute position. There may be an added component for
the 'residuals' which turns out to be
distance/direction based. There are also many examples
where, for example, flow characteristics, connectivity
and so on play a large part in the structure of your
variable.

In short: no decent semi-variogram does NOT mean no
spatial relationship. It means no simple second-order
stationary geostatistical type spatial relationship.

Isobel
http://geoecosse.bizland.com/whatsnew.htm





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Hi Mark,

1) At

http://www.ai-geostats.org/software/Codes_Softfaq.htm

you will find a few codes for Surfer. I have just added
crossvalidation.bas , a code I derived from Aleksey Amantov's
jacknife.bas
You will need to code a bit yourself to select the correct interpolation
function (Inverse Distance Weighted is the default) as well as the
proper parameters. Surfers manual is sufficient to learn to program with
Scripter (quick basic). Sorry, but I will not provide any support. Note
that crossvalidations are implemented in Surfer 8.

2) In short: Geostatistics are not appropriate when you don't have a
spatial correlation (even this is questionable :) ).
Frequently, people who do not find any spatial correlation in their data
apply other functions like Inverse Weighted Distance. I believe such a
solution is completelt wrong. Either you have a spatial correlation and
you can interpolate/predict values, or you don't and only models based
on sound physics (e.g. Temperature T decreases with latitude and
altitude, thus you can predict T) can be used. Outside of these two
solutions, I would recommend only to use Thiessen polygons for
displaying purposes (not for real estimations!): they do not look
"natural" when applied to continuous variables and can thus not fool the
persoon looking at the output. Moreover, Thiessen polygons provides
useful information on the weight of each sample. Maps of proportional
symbols would also do.

Cheers,

Gregoire

-----Original Message-----
From: Mark Dowdall [mailto:mark.dowdall@...]
Sent: 01 September 2004 10:02
To: ai-geostats@...
Subject: [ai-geostats] XValid script




Hello

It may be cheeky, but I have two questions:

1. Where can I get I get the Surfer v7.0 script for crossvalidation? I
have been through the archives and although its mentioned I cannot find
a download site. Nor could I find it and the site of Aleksey Amantov.
Some emails mentioned it is in the samples folder of the surfer install
but I could not find it. I know its in Surfer 8 as standard but thats
not available to me at the moment.

2. I have been following the discussion on extreme values in a data set.
And my question is: is there any context in which geostatistical methods
are absolutely not appropriate? If so, how can this appropriateness be
tested? Is there a point at which a user should know that it would be
better to try something else?

Any help with these two is very much welcome

mdowdall

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Signoff ai-geostats

Hello

It may be cheeky, but I have two questions:

1. Where can I get I get the Surfer v7.0 script for crossvalidation? I
have been through the archives and although its mentioned I cannot find
a download site. Nor could I find it and the site of Aleksey Amantov.
Some emails mentioned it is in the samples folder of the surfer install
but I could not find it. I know its in Surfer 8 as standard but thats
not available to me at the moment.

2. I have been following the discussion on extreme values in a data set.
And my question is: is there any context in which geostatistical methods
are absolutely not appropriate? If so, how can this appropriateness be
tested? Is there a point at which a user should know that it would be
better to try something else?

Any help with these two is very much welcome

mdowdall

* By using the ai-geostats mailing list you agree to follow its rules
( see http://www.ai-geostats.org/help_ai-geostats.htm )

* To unsubscribe to ai-geostats, send the following in the subject or in the
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Signoff ai-geostats

Hi Mark,

re-reading Isobel's mail, I thought about a proviso on the proviso. I personally do consider that a semivariogram showing a pure trend is decent. Not in a geostatistical point of view, but it does provide you with some useful information. If you have a trend, the variogram becomes incompatible with the intrinsic hypothesis… but you still have a slope in the experimental correlation functions (semivariograms, correlograms, madogram, etc.). Thus you have a structure, that is you "have something" there that may provide you with some useful information about your data set that can be used for estimating values of your variable at unsampled locations. If you have a flat correlation function, that is a pure nugget effect, then certainly you are in troubles.

Regards,

Gregoire

Isobel Clark <drisobelclark@...> wrote:

> Mark
>
> I could not agree more with Gregoire (with one
> proviso, see below).
>
> Both geostatistics and any weighted average estimators
> are based on the same assumptions -- that relationship
> between values at two locations depends on the
> distance between them and (possibly) their relative
> orientation. If you cannot get a decent semi-variogram
> after trying every type of graph [normal, robust,
> relative] and every transformation and/or
> interpretation of your data [logarithm, indicator,
> rank transforms, Normal scores, mixed populations],
> you do not have a distance-based relationship. This
> conclusion also rules out: inverse distance weighting
> of any kind; Delaunay triangles; Thiessen polygons and
> so on.
>
> My proviso: there are other forms of spatial
> relationship than pure distance/direction types. The
> simplest example of this is data with a trend, where
> the value at a specified point will depend on its
> absolute position. There may be an added component for
> the 'residuals' which turns out to be
> distance/direction based. There are also many examples
> where, for example, flow characteristics, connectivity
> and so on play a large part in the structure of your
> variable.
>
> In short: no decent semi-variogram does NOT mean no
> spatial relationship. It means no simple second-order
> stationary geostatistical type spatial relationship.
>
> Isobel
> http://geoecosse.bizland.com/whatsnew.htm
>
>
>      
>      
>              
> ___________________________________________________________ALL-NEW Yahoo! Messenger - all new features - even more fun!  http://uk.messenger.yahoo.com

>
>

> ---------------------------------------------
>       Attachment: message-footer.txt
>       MIME Type: text/plain
> ---------------------------------------------

__________________________________________
Gregoire Dubois (Ph.D.)
JRC - European Commission
IES - Emissions and Health Unit
Radioactivity Environmental Monitoring group
TP 441, Via Fermi 1
21020 Ispra (VA)
ITALY
 
Tel. +39 (0)332 78 6360
Fax. +39 (0)332 78 5466
Email: gregoire.dubois@...
WWW: http://www.ai-geostats.org
WWW: http://rem.jrc.cec.eu.int
 
"The views expressed are purely those of the writer and may not in any circumstances be regarded as stating an official position of the European Commission."

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( see http://www.ai-geostats.org/help_ai-geostats.htm )

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Signoff ai-geostats

Gregoire/Mark

Yes, a trend is a spatial structure and can be used
for prediction purposes. It just isn't suitable for
'stationary' geostatistical analysis.

I have seen cases where the semi-variogram was almost
pure nugget effect, but there was a spatial structure.
Again, just not a straight-forward 'stationary'
geostatistical analysis. Need to look at all the
possibilities and at other forms of spatial
relationship.

Do not despair, there is a pattern!
Isobel
http://www.geostatistics.info





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Thisa reminds me of a site where the "failure" of variogram modeling actually
told me quite a bit about the problem at hand.  It was a large field where
dumptruck loads of soil with a contaminant had been dumped randomly and spread. 
This was unknown until after a gridded set of samples had been taken and a
bizarre spotted pattern emerged.  The directional variogram showed an unusual
hump - increasing variance with distance, then decreasing variance with even
more distance.  This was the clue that some sort of "spot" activity had
occurred. We finally tracked down a retired ex-employee who remembered the
dumping activity.

Sometimes a failed model tells more than one that fits!

Tim Glover
Senior Environmental Scientist - Geochemistry
Geoenvironmental Department
MACTEC Engineering and Consulting, Inc.
Kennesaw, Georgia, USA
Office 770-421-3310
Fax 770-421-3486
Email ntglover@...
Web www.mactec.com
-----Original Message-----
From: Gregoire Dubois [mailto:gregoire.dubois@...]
Sent: Thursday, September 02, 2004 3:53 AM
To: ai-geostats@...
Subject: [ai-geostats] FW: spatial relationships

 
-----Original Message-----
From: Gregoire Dubois [mailto:gregoire.dubois@...]
Sent: 02 September 2004 09:42
To: mark.dowdall@...
Cc: drisobelclark@...
Subject: Re: spatial relationships
Hi Mark,
re-reading Isobel's mail, I thought about a proviso on the proviso. I personally
do consider that a semivariogram showing a pure trend is decent. Not in a
geostatistical point of view, but it does provide you with some useful
information. If you have a trend, the variogram becomes incompatible with the
intrinsic hypothesis... but you still have a slope in the experimental
correlation functions (semivariograms, correlograms, madogram, etc.). Thus you
have a structure, that is you "have something" there that may provide you with
some useful information about your data set that can be used for estimating
values of your variable at unsampled locations. If you have a flat correlation
function, that is a pure nugget effect, then certainly you are in troubles.
Regards,
Gregoire

Isobel Clark <drisobelclark@...> wrote:
> Mark
>
> I could not agree more with Gregoire (with one
> proviso, see below).
>
> Both geostatistics and any weighted average estimators
> are based on the same assumptions -- that relationship
> between values at two locations depends on the
> distance between them and (possibly) their relative
> orientation. If you cannot get a decent semi-variogram
> after trying every type of graph [normal, robust,
> relative] and every transformation and/or
> interpretation of your data [logarithm, indicator,
> rank transforms, Normal scores, mixed populations],
> you do not have a distance-based relationship. This
> conclusion also rules out: inverse distance weighting
> of any kind; Delaunay triangles; Thiessen polygons and
> so on.
>
> My proviso: there are other forms of spatial
> relationship than pure distance/direction types. The
> simplest example of this is data with a trend, where
> the value at a specified point will depend on its
> absolute position. There may be an added component for
> the 'residuals' which turns out to be
> distance/direction based. There are also many examples
> where, for example, flow characteristics, connectivity
> and so on play a large part in the structure of your
> variable.
>
> In short: no decent semi-variogram does NOT mean no
> spatial relationship. It means no simple second-order
> stationary geostatistical type spatial relationship.
>
> Isobel
> http://geoecosse.bizland.com/whatsnew.htm
>
>
>      
>      
>              
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__________________________________________
Gregoire Dubois (Ph.D.)
JRC - European Commission
IES - Emissions and Health Unit
Radioactivity Environmental Monitoring group
TP 441, Via Fermi 1
21020 Ispra (VA)
ITALY
 
Tel. +39 (0)332 78 6360
Fax. +39 (0)332 78 5466
Email: gregoire.dubois@...
WWW: http://www.ai-geostats.org
WWW: http://rem.jrc.cec.eu.int
 
"The views expressed are purely those of the writer and may not in any
circumstances be regarded as stating an official position of the European
Commission."

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On 02-Sep-04 Glover, Tim wrote:
> Thisa reminds me of a site where the "failure" of variogram modeling
> actually told me quite a bit about the problem at hand.  It was a large
> field where dumptruck loads of soil with a contaminant had been dumped
> randomly and spread.  This was unknown until after a gridded set of
> samples had been taken and a bizarre spotted pattern emerged.  The
> directional variogram showed an unusual hump - increasing variance with
> distance, then decreasing variance with even more distance.  This was
> the clue that some sort of "spot" activity had occurred. We finally
> tracked down a retired ex-employee who remembered the dumping activity.
>
> Sometimes a failed model tells more than one that fits!

Indeed! It's the difference between discovery and measurement.

Best wishes,
Ted.


--------------------------------------------------------------------
E-Mail: (Ted Harding) <Ted.Harding@...>
Fax-to-email: +44 (0)870 167 1972
Date: 02-Sep-04                                       Time: 14:19:37
------------------------------ XFMail ------------------------------

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Dear oh Dear, I am failing to communicate (again).

As far as I know, I didn't say you could not use
geostatistics when a trend is present! I regularly use
Universal Kriging for data with a trend and kriging
with an external drift when the trend is governed by
an outside factor (see free tutorial at website).

The question originally posed what how does one decide
that geostatistics is not appriate. The answer
Gregoire and myself gave was "when you cannot get a
semi-variogam graph" after trying all possible
variations of transforms, interpretation and
de-trending.

I recently worked with an orange grove in Florida
(bugs on oranges) which showed no decent
semi-variogram even though rough inverse distance maps
looked reasonable. It turned out they had two
different kinds of tree in the orchard. Separating the
'rootstocks' yielded a vastly improved semi-variogram
and decent geostatistical analysis.

My additional point was that failure to obtain a
semi-variogram model simply means that there is no
'distance related' structure. It does NOT mean there
is NO spatial structure.

Isobel
http://geoecosse.bizland.com/softwares





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I would agree with Gregoire's assessment.
The presence of a global trend does not prohibit the use of geostatistics.
As illustrated in the following paper by Journel and Rossi:
Journel, A.G. and M.E. Rossi. 1989. When do we need a trend model
in kriging? Mathematical Geology, 21(7):715--739.
global trends can be easily handled by the use of local search
windows in kriging, which allows us to rely on the assumption of
quasi-stationarity.

Of course if the trend is complex and can be described using
process-based models (e.g. urban pollution), it is better to use
this physical model for the trend and use geostatistics to
interpolate the residuals, provided there is some spatial
correlation left.

Cheers,

Pierre
<><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><>

Dr. Pierre Goovaerts
President of PGeostat, LLC
Chief Scientist with Biomedware Inc.
710 Ridgemont Lane
Ann Arbor, Michigan, 48103-1535, U.S.A.

E-mail:  goovaert@...
Phone:   (734) 668-9900
Fax:     (734) 668-7788
http://alumni.engin.umich.edu/~goovaert/

<><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><>

On Thu, 2 Sep 2004, Gregoire Dubois wrote:

>
> -----Original Message-----
> From: Gregoire Dubois [mailto:gregoire.dubois@...]
> Sent: 02 September 2004 09:42
> To: mark.dowdall@...
> Cc: drisobelclark@...
> Subject: Re: spatial relationships
>
>
>
> Hi Mark,
>
> re-reading Isobel's mail, I thought about a proviso on the proviso. I
> personally do consider that a semivariogram showing a pure trend is
> decent. Not in a geostatistical point of view, but it does provide you
> with some useful information. If you have a trend, the variogram becomes
> incompatible with the intrinsic hypothesis. but you still have a slope
> in the experimental correlation functions (semivariograms, correlograms,
> madogram, etc.). Thus you have a structure, that is you "have something"
> there that may provide you with some useful information about your data
> set that can be used for estimating values of your variable at unsampled
> locations. If you have a flat correlation function, that is a pure
> nugget effect, then certainly you are in troubles.
>
> Regards,
>
> Gregoire
>
>
> Isobel Clark <drisobelclark@...> wrote:
>
> > Mark
> >
> > I could not agree more with Gregoire (with one
> > proviso, see below).
> >
> > Both geostatistics and any weighted average estimators
> > are based on the same assumptions -- that relationship
> > between values at two locations depends on the
> > distance between them and (possibly) their relative
> > orientation. If you cannot get a decent semi-variogram
> > after trying every type of graph [normal, robust,
> > relative] and every transformation and/or
> > interpretation of your data [logarithm, indicator,
> > rank transforms, Normal scores, mixed populations],
> > you do not have a distance-based relationship. This
> > conclusion also rules out: inverse distance weighting
> > of any kind; Delaunay triangles; Thiessen polygons and
> > so on.
> >
> > My proviso: there are other forms of spatial
> > relationship than pure distance/direction types. The
> > simplest example of this is data with a trend, where
> > the value at a specified point will depend on its
> > absolute position. There may be an added component for
> > the 'residuals' which turns out to be
> > distance/direction based. There are also many examples
> > where, for example, flow characteristics, connectivity
> > and so on play a large part in the structure of your
> > variable.
> >
> > In short: no decent semi-variogram does NOT mean no
> > spatial relationship. It means no simple second-order
> > stationary geostatistical type spatial relationship.
> >
> > Isobel
> >  <http://geoecosse.bizland.com/whatsnew.htm>
> http://geoecosse.bizland.com/whatsnew.htm
> >
> >
> >
> >
> >
> > ___________________________________________________________ALL-NEW
> Yahoo! Messenger - all new features - even more fun!
> <http://uk.messenger.yahoo.com> http://uk.messenger.yahoo.com
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> >
> >
>
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> >       MIME Type: text/plain
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>
> __________________________________________
> Gregoire Dubois (Ph.D.)
> JRC - European Commission
> IES - Emissions and Health Unit
> Radioactivity Environmental Monitoring group
> TP 441, Via Fermi 1
> 21020 Ispra (VA)
> ITALY
>
> Tel. +39 (0)332 78 6360
> Fax. +39 (0)332 78 5466
> Email:  <mailto:gregoire.dubois@...> gregoire.dubois@...
> WWW:  <http://www.ai-geostats.org> http://www.ai-geostats.org
> WWW:  <http://rem.jrc.cec.eu.int> http://rem.jrc.cec.eu.int
>
> "The views expressed are purely those of the writer and may not in any
> circumstances be regarded as stating an official position of the
> European Commission."
>
>

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Kevin

Sounds like an ideal case for Geographically Weighted
Regression.

You could use semi-variograms or spatial
auto-correlation to determine exactly how proximity
defines relationship. My only current beef with GWR is
the seemingly pre-defined distance weighting
functions. Not had much time to get into this yet, so
don't dump on me all you experts out there.

I would be interested in any published results on this
as one of my business partners is doing similar work
on bronze age denmark.

Isobel
http://uk.geocities.com/drisobelclark





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Some random remarks that went through my single braincell:

I would focus on the physical environment to predict the locations, but
it depends on what you call an archeological site.

A part of the place where a settlement would be created, could be
explained by the distance from the surrounding sites. But I would think
of it as a marginal effect until pretty recent times.

Why do I think this:

- If you go way back, people where selfsubstaining living communities.
So, if commerce wasn't that big a part of their life the distance to
other villages wouldn't matter and the choices for starting a village
would only be dominated by physical factors.

- In recent times the distances could become more important because of
trade and the fact that their were more people around, that would spread
across the land to claim their part of a living community where there
would be some "breathing" space. That "breathing" space could be your
clue to finding more sites. But again only if the combination of the
social factors (preventing overcrowding and the urge to claim your patch
of land) and the biophysical ones were in favour of the people.

No social pressure on a community = no need to resettle, bad land = no
way someone is going to settle there (until recent times with better
agricultural techniques).

A case where your technique would work is a uniform type of soil and
topography, where the (re-)settlement of people would only be dominated
by social factors and not so much by biophysical ones. Look at maps of
the champagne area in France (sorry, only example I could think of).

So, depending on the timeframe your looking at my strategy would differ.
On old settlements I wouldn't include the distance and focus more on
detailed biophysical data like pollen data. For recent times the SA
approach could be interesting, because of the social aspect, but I
wouldn't let it dominate a prediction model. You could cross check it
with a model without the distances and known sites with a leave one out
methode to see how good it behaves. Anyway... have fun with it...

Cheers,
Koen.



On Thu, 2004-09-02 at 21:43, Kevin M. Curtin wrote:
> Hello All,
>
> I’m not sure if this is the correct forum for this…but a colleague has
> asked a question I’d like to address.
>
>
>
> This fellow wants to predict the location of archaeological sites
> based on factors such as soil type, proximity to a water source,
> slope, AND proximity to other archaeological sites.
>
>
>
> On proposing such a predictive model he has been challenged with, “How
> are you going to deal with Spatial Autocorrelation�. We’re not sure
> why SA should be a problem since we are suggesting that spatial
> proximity is a factor in settlement location.
>
>
>
> So, do we need to test for SA and why?
>
>
>
> Thanks in advance,
>
> Kevin
>
>
>
>
>
> ______________________________________________________________________
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Hello Kevin

You may like to speak to David Hansen a GIS Specialist/ Soil Scientist at
the USGS in Sacramento - dhansen@...

He has a good paper "Describing GIS Applications: Spatial Statistics and
Weights of Evidence Extension to ArcView in the Analysis of the
distribution of Archaeological Sites in Landscape. You may know this one -
if not you can view it at www.goscafe.com?technical_papers/Papers/paper054

Kind regards


Beatrice





"Kevin M. Curtin" <curtin@...>
03/09/2004 07:43


         To:     <ai-geostats@...>
         cc:
         Subject:        [ai-geostats] Frightened of Spatial Autocorrelation


Hello All,
I'm not sure if this is the correct forum for this?but a colleague has
asked a question I'd like to address.

This fellow wants to predict the location of archaeological sites based on
factors such as soil type, proximity to a water source, slope, AND
proximity to other archaeological sites.

On proposing such a predictive model he has been challenged with, "How are
you going to deal with Spatial Autocorrelation". We're not sure why SA
should be a problem since we are suggesting that spatial proximity is a
factor in settlement location.

So, do we need to test for SA and why?

Thanks in advance,
Kevin
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Hello All,
I’m not sure if this is the correct forum for this…but a colleague has asked a question I’d like to address.
 
This fellow wants to predict the location of archaeological sites based on factors such as soil type, proximity to a water source, slope, AND proximity to other archaeological sites.
 
On proposing such a predictive model he has been challenged with, “How are you going to deal with Spatial Autocorrelation”. We’re not sure why SA should be a problem since we are suggesting that spatial proximity is a factor in settlement location.
 
So, do we need to test for SA and why?
 
Thanks in advance,
Kevin
 
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You might look at the following series of papers:
http://www.nceas.ucsb.edu/~liebhold/ecography/
While the papers are written with an ecological focus, settling is
settling is settling.
Hope they help...
Steve

Isobel Clark wrote:

>Kevin
>
>Sounds like an ideal case for Geographically Weighted
>Regression.
>
>You could use semi-variograms or spatial
>auto-correlation to determine exactly how proximity
>defines relationship. My only current beef with GWR is
>the seemingly pre-defined distance weighting
>functions. Not had much time to get into this yet, so
>don't dump on me all you experts out there.
>
>I would be interested in any published results on this
>as one of my business partners is doing similar work
>on bronze age denmark.
>
>Isobel
>http://uk.geocities.com/drisobelclark
>
>
>
>
>
>___________________________________________________________ALL-NEW Yahoo!
Messenger - all new features - even more fun!  http://uk.messenger.yahoo.com
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>
>
>------------------------------------------------------------------------
>
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Hello, Kevin !

Predictive interpolation is a very interesting field.

You may be interested in  GIS applications based on Dempster-Shafer Theory.
There are some online material also linked to archeology and prediction of
archaeological sites at  http://gis.esri
com/library/userconf/proc99/proceed/papers/pap295/p295.htm
and  http://websrv5.sdu.dk/ejstrud/forskning.html

Also IDRISI GIS has a collection of useful modeling tools for multicriteria
analysis. It is described in manual which can be downloaded from IDRISI web
site...

Another subject of interest might be various AI techniques. I personally am
experimenting with Case Based Reasoning (spatial predictions of community
structure). There are some references and an experimental module online at
http://www.alleco.fi/allmaps
Currently I am rewriting the code (for the third time already :)). Still, at
least for me it looks promising. Although currently I came to a decision
that these 'explicit' GIS modeling techniques must be suplemented with the
implicit' ones based on cellular automation, nearest neighbourhood or
variograms and krigging. The reason to think so is that those 'inteligent'
methods predict ecological niches. But in real world those niches may remain
unoccupied. So we need an interaction of explicit top-down influence in form
of 'niches' and implicit bottom-up influence in the form of 'growth from a
seed'.

Best regards
Viktoras

-------Original Message-------

From: Kevin M. Curtin
Date: 2004 m. rugsëjis 02 d. 12:44:03
To: ai-geostats@...
Subject: [ai-geostats] Frightened of Spatial Autocorrelation

Hello All,
I’m not sure if this is the correct forum for this…but a colleague has asked
a question I’d like to address.

This fellow wants to predict the location of archaeological sites based on
factors such as soil type, proximity to a water source, slope, AND proximity
to other archaeological sites.

On proposing such a predictive model he has been challenged with, “How are
you going to deal with Spatial Autocorrelation”. We’re not sure why SA
should be a problem since we are suggesting that spatial proximity is a
factor in settlement location.

So, do we need to test for SA and why?

Thanks in advance,
Kevin

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With ref. to the posting below (AI techniques and predictive work), we
have recently done a lot of work comparing kriging and neural network
performance.  As an example, one of those papers (soon to show up in
Jo. Exp. Geol) is posted at
http://www.faculty.uaf.edu/ffrg/papers/nomepap_modi_revise.zip.

To summarize our findings, I would say there hasn't been much
difference in prediction performance.  One or the other is marginally
better on any given case.  An indication of the absolute performance
of either methods can be easily obtained from the semi-variogram:
lower the nugget, better both methods perform, while higher the nugget
the worse they both perform.

In the paper that is posted, both methods performed very well with NN
having a prediction performance (R_sq) upwards of 0.98 with very low
bias and kriging being 0.95.

Thanks,


Rajive Ganguli, Ph.D., P.E., C.O.I
Associate Professor of Mining Engineering
University of Alaska Fairbanks
================================
Office: 317 Duckering Building
Mailing Add: Box 755800, Fairbanks, AK 99775
ph: 907-474-7631, fax: 907-474-6635
web: http://www.faculty.uaf.edu/ffrg/
-------------------------------------------
"He uses statistics as a drunken man uses lamp-posts... for support rather
than illumination."  - Andrew Lang (1844-1912)




-----Original Message-----
From: Viktoras Didziulis [mailto:viktoras.didziulis@...]
Sent: Friday, September 03, 2004 12:12 AM
To: ai-geostats@...
Subject: Re: [ai-geostats] Frightened of Spatial Autocorrelation

Hello, Kevin !   Predictive interpolation is a very interesting field.   You
may be interested in  GIS applications based on Dempster-Shafer Theory.
There are some online material also linked to archeology and prediction of
archaeological sites at  http://gis.esri
com/library/userconf/proc99/proceed/papers/pap295/p295.htm and
http://websrv5.sdu.dk/ejstrud/forskning.html   Also IDRISI GIS has a
collection of useful modeling tools for multicriteria
analysis. It is described in manual which can be downloaded from IDRISI web
site...   Another subject of interest might be various AI techniques. I
personally am
experimenting with Case Based Reasoning (spatial predictions of community
structure). There are some references and an experimental module online at
http://www.alleco.fi/allmaps Currently I am rewriting the code (for the
third time already :)). Still, at
least for me it looks promising. Although currently I came to a decision
that these 'explicit' GIS modeling techniques must be suplemented with the
implicit' ones based on cellular automation, nearest neighbourhood or
variograms and krigging. The reason to think so is that those 'inteligent'
methods predict ecological niches. But in real world those niches may remain
unoccupied. So we need an interaction of explicit top-down influence in form
of 'niches' and implicit bottom-up influence in the form of 'growth from a
seed'.   Best regards Viktoras   -------Original Message-------   From:
Kevin M. Curtin Date: 2004 m. rugsëjis 02 d. 12:44:03 To:
ai-geostats@... Subject: [ai-geostats] Frightened of Spatial
Autocorrelation   Hello All, I'm not sure if this is the correct forum for
this…but a colleague has asked
a question I'd like to address.   This fellow wants to predict the location
of archaeological sites based on
factors such as soil type, proximity to a water source, slope, AND proximity
to other archaeological sites.   On proposing such a predictive model he has
been challenged with, "How are
you going to deal with Spatial Autocorrelation". We're not sure why SA
should be a problem since we are suggesting that spatial proximity is a
factor in settlement location.   So, do we need to test for SA and why?
Thanks in advance, Kevin

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Kevin
Sounds like an ideal case for Geographically Weighted
Regression. You could use semi-variograms or spatial
auto-correlation to determine exactly how proximity
defines relationship. My only current beef with GWR is
the seemingly pre-defined distance weighting
functions. Not had much time to get into this yet, so
don't dump on me all you experts out there.
I would be interested in any published results on this
as one of my business partners is doing similar work
on bronze age denmark.
Isobel
http://uk.geocities.com/drisobelclark
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-- Niels Chr. Nielsen, M.Sc.
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DK-6720 Fanø
Tlf. (+45)76121216(evening),(+45)65504152(during day)
mobile (+45)20878568
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Please find hereafter the last call for a scientific exercise dedicated to spatial statistics called SIC2004.
SIC2004 stands for Spatial Interpolation Comparison 2004. It is the second edition of a scientific exercise of this type that is dedicated to Decision Support Systems and Spatial Statistics.

This year's issue is about AUTOMATIC INTERPOLATION.
Participants will receive a subset of an environmental data set (typically measurements of an environmental variable + spatial coordinates of the sampling places) and will have to estimate the values taken by the variable at the remaining locations of the full data set. The true values found at these locations will be made public only at the end of the exercise. Various criteria will be used to assess the performances of the interpolation algorithms (time of calculation, minimum errors, etc.).

This edition will focus on automatic mapping algorithms: participants to SIC2004 will have to prepare their algorithms before receiving the data (only sampling locations + prior information are available at the moment from the web site) and no interaction with the algorithm will be allowed during the exercise.

As for SIC97, participants to SIC2004 are invited to submit a manuscript at the end of the exercise for publication in the online journal GIDA (Geographic Information and Decision Analysis) as well as in a European Report (hardcopy).

For more information, please visit the web site http://www.ai-geostats.org/events/sic2004/index.htm
Deadline for participation (free of charge) is Monday the 13th of September 2004.
Best regards,
Gregoire

Keywords: Decision Support Systems, spatial statistics, geostatistics, neural networks, spatial interpolation

PS: I would very much appreciate if you could help to further distribute this information

__________________________________________
Gregoire Dubois (Ph.D.)
JRC - European Commission
IES - Emissions and Health Unit
Radioactivity Environmental Monitoring group
TP 441, Via Fermi 1
21020 Ispra (VA)
ITALY
 
Tel. +39 (0)332 78 6360
Fax. +39 (0)332 78 5466
Email: gregoire.dubois@...
WWW: http://www.ai-geostats.org
WWW: http://rem.jrc.cec.eu.int
 
"The views expressed are purely those of the writer and may not in any circumstances be regarded as stating an official position of the European Commission."

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Hi Kevin,

I work in the field of distribution modeling of birds and somewhat come from
the other direction than most geostatistics people here on the list. In
ecology, we first only predicted by local conditions and habitat, then were
pointed to the problems of spatial autocorrelation in such an approach, then
tried to compensate for autocorrelation problems in statistics and only
lately recognized that autocorrelation is actually additional information
that could improve prediction. Steve already posted the most current papers
regarding this issue in Ecography, which helped me much
(http://www.nceas.ucsb.edu/~liebhold/ecography/). I would add the following
paper to the list:

Lichstein J. W., T. R. Simons, S. A. Shriner, and K. E. Franzreb. 2002.
Spatial autocorrelation and autoregressive models in ecology. Ecological
Monographs 72(3):445-463.

For birds it has been well documented that autocorrelation in distributions
are caused by autocorrelation in underlying resources. Thus, in theory, if
you cover ALL important predictors in your model (let's say a regular
regression or any other "non-spatial" method), the spatial structure in the
distribution is modeled implicitly by being contained in the predictors.
However, if you miss a predictor (which in practice will always be the
case), you will miss its spatial structure and the residuals of your
analysis will reflect this structure rendering these approaches ineffective
and statistically flawed. In addition, I'm trying to show in my research
that dispersal of individuals (meaning leaving either the birthplace or the
last breeding place permanently to breed elsewhere) also leads to
autocorrelation in distributions. This could also be the case for
archeological sites as there was undoubtedly some contact and exchange among
neighbors and this contact would have been more intense with close neighbors
as travel comes at a cost. Thus I would expect autocorrelation in the
spatial distribution of archeological sites above and beyond the
autocorrelation in the underlying conditions predicting archeological sites.
I use conditional autoregressive regression models (CAR) in Splus to model
bird distributions.

I hope this helps

Volker
_______________________________
Volker Bahn
Dept. of Wildlife Ecology - Rm. 210
University of Maine
5755 Nutting Hall
Orono, Maine
04469-5755, USA
Tel. (207) 581 2799
Fax: (207) 581 2858
volker.bahn@...
http://www.wle.umaine.edu/used_text%20files/Volker%20Bahn/home.htm


----- Original Message -----
From: Kevin M. Curtin
To: ai-geostats@...
Sent: Thursday, September 02, 2004 15:43
Subject: [ai-geostats] Frightened of Spatial Autocorrelation


Hello All,
I'm not sure if this is the correct forum for this.but a colleague has asked
a question I'd like to address.

This fellow wants to predict the location of archaeological sites based on
factors such as soil type, proximity to a water source, slope, AND proximity
to other archaeological sites.

On proposing such a predictive model he has been challenged with, "How are
you going to deal with Spatial Autocorrelation". We're not sure why SA
should be a problem since we are suggesting that spatial proximity is a
factor in settlement location.

So, do we need to test for SA and why?

Thanks in advance,
Kevin




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Hello list,

First of all, thanks for the many replies to my last question. That was really
helpful. Thanks !!

Now I have an additional question (and hope it is not too naively):

In my dataset exist a clustering structure. I declustered my dataset by
seperating a part of it and get a diffuse spherical structure in the remaining
dataset.
So far so good. But by ignoring the clustering structure there is a quite clear
power function structure in the dataset. So my question: is that typical for
clustered data ?? Or is there more behind ?

Kai Zoßeder

Department of Geo- and Environmental Science
Ludwig-Maximilians University Munich

P.S.: Sorry for sending an empty message before.

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Dear everyone,

I'm new to this mailing list and the field of geostatistics, so my question
might be too obvious, but I don't have anyone around to get some help.

I'm trying to analyze potential factors influencing soil microbes. For those
soil characteristics, some of them were anisotropic and some not. I modeled
and ran sgsim for stochastic simulation maps to get qualitative comparison
among variables. It looked fine for those isotropic variables but there were
lines in anistropic variables. Those lines aligned along the major axes, so
I guess they might be generated from search radii. However, maps I've seen
didn't have those features in them and I'm not comfortable with that. I
would like to get some opinions and if possible solution to get rid of them.
You can see the maps by clicking the link.
http://www.people.virginia.edu/~sk7k/Material/maps.pdf

Any general advice or guidelines would be helpful as well.

Thanks.

-----------------------------------------------------

  Sanghoon Kang
  Lab. Microbial Ecology
  Dept. Environmental Sciences, UVa
  434-924-0537 (T)  434-982-2137 (F)

  http://www.people.virginia.edu/~sk7k
  http://janicekang.net
-----------------------------------------------------


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Hi Sanghoon,

Your maps look fine and would reflect a strong anisotropy.
What is the anisotropy ratio for your variables and did you
select a circular or ellptical search window?

Pierre

<><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><>

Dr. Pierre Goovaerts
President of PGeostat, LLC
Chief Scientist with Biomedware Inc.
710 Ridgemont Lane
Ann Arbor, Michigan, 48103-1535, U.S.A.

E-mail:  goovaert@...
Phone:   (734) 668-9900
Fax:     (734) 668-7788
http://alumni.engin.umich.edu/~goovaert/


<><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><>

On Fri, 10 Sep 2004, Sanghoon Kang wrote:

> Dear everyone,
>
> I'm new to this mailing list and the field of geostatistics, so my question
> might be too obvious, but I don't have anyone around to get some help.
>
> I'm trying to analyze potential factors influencing soil microbes. For those
> soil characteristics, some of them were anisotropic and some not. I modeled
> and ran sgsim for stochastic simulation maps to get qualitative comparison
> among variables. It looked fine for those isotropic variables but there were
> lines in anistropic variables. Those lines aligned along the major axes, so
> I guess they might be generated from search radii. However, maps I've seen
> didn't have those features in them and I'm not comfortable with that. I
> would like to get some opinions and if possible solution to get rid of them.
> You can see the maps by clicking the link.
> http://www.people.virginia.edu/~sk7k/Material/maps.pdf
>
> Any general advice or guidelines would be helpful as well.
>
> Thanks.
>
> -----------------------------------------------------
>
>  Sanghoon Kang
>  Lab. Microbial Ecology
>  Dept. Environmental Sciences, UVa
>  434-924-0537 (T)  434-982-2137 (F)
>
>  http://www.people.virginia.edu/~sk7k
>  http://janicekang.net
> -----------------------------------------------------
>
>
> ----------------------------------------
> My Inbox is protected by SPAMfighter
> 3995 spam mails have been blocked so far.
> Download free www.spamfighter.com today!
>
>
>

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Mark -

you'll find a list of free GIS packages on this website:

http://freegis.org/

One of the most comprehensive free and open source GIS is GRASS, which
is also available for Mac OS X:

http://grass.itc.it/

You can download the binaries or source code for version 5.3 or 5.7.

Christof

On 29.09.2004, at 20:11, Mark Coleman wrote:

> Greetings,
>
> I am interested in getting a basic GIS package that runs on Mac OSX.
> I'd very much appreciate suggestions.
>
> Thanks,
>
> -Mark

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Greetings,

I am interested in getting a basic GIS package that runs on Mac OSX.
I'd very much appreciate suggestions.

Thanks,

-Mark

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