Harland,

You could use the exact form of the Wilcoxon Rank Sum test, which is
appropriate for sample sizes of 10 or less per group.  Computational details
are shown on p. 120 of "Statistical Methods in Water Resources," Helsel and
Hirsch, 1992, Elsevier.  The test is commonly used to determine whether two
groups are from the same population (i.e. have the same median and other
percentiles), or alternatively whether the medians are different.

Tom Nolan

> -----Original Message-----
> From: ai-geostats-list@... [mailto:ai-geostats-list@...]On
> Behalf Of mercury1@...
> Sent: Tuesday, December 19, 2000 12:08 PM
> To: ai-geostats@...
> Subject: AI-GEOSTATS: In need of some help.
>
>
>
> Hi Folks!
> This is my first post to this list.  Hope it is not out of place.
>  I need a
> way to compare two small populations (very small sample sizes..5
> and 6....both
> of which lack normality).  I would like to compare them based on
> 3-5 parameters.
>  Because of the above limitations I have given up on the validity
> of a t-test
> (which assumes a normal distribution and larger sample sizes).
> My basic question
> is this: are these two small populations statistically different
> or do they
> belong to the same population?  I have asked many elementary
> level stats folks
> and have not been entirely satisfied with their solutions.  So, I
> pose this
> 'problem' to you.
> Thanks for your time.
> Happy Holidays!
>      -Harland
>
> --
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With  five to six samples per population, concluding
anything from the tests would really be pushing it.
Complementing the results with any deterministic
knowledge of the underlying population (genesis,
noteworthy features, prior experience, etc) could lend
some measure of validity to what you will eventually
conclude from such tests (i.e. do they make sense).

Unfortunately, doing that often leaves one in the
unsavory position of realizing that there is more
uncertainty than first thought of. Somewhat counter-intuitive,
but so true in my personal experience.

Syed

-----Original Message-----
From: Tom Nolan <btnolan@...>
To: <ai-geostats@...>
Date: Thursday, December 28, 2000 10:41 PM
Subject: RE: AI-GEOSTATS: In need of some help.


>Harland,
>
>You could use the exact form of the Wilcoxon Rank Sum test, which is
>appropriate for sample sizes of 10 or less per group.  Computational
details
>are shown on p. 120 of "Statistical Methods in Water Resources," Helsel and
>Hirsch, 1992, Elsevier.  The test is commonly used to determine whether two
>groups are from the same population (i.e. have the same median and other
>percentiles), or alternatively whether the medians are different.
>
>Tom Nolan
>
>> -----Original Message-----
>> From: ai-geostats-list@... [mailto:ai-geostats-list@...]On
>> Behalf Of mercury1@...
>> Sent: Tuesday, December 19, 2000 12:08 PM
>> To: ai-geostats@...
>> Subject: AI-GEOSTATS: In need of some help.
>>
>>
>>
>> Hi Folks!
>> This is my first post to this list.  Hope it is not out of place.
>>  I need a
>> way to compare two small populations (very small sample sizes..5
>> and 6....both
>> of which lack normality).  I would like to compare them based on
>> 3-5 parameters.
>>  Because of the above limitations I have given up on the validity
>> of a t-test
>> (which assumes a normal distribution and larger sample sizes).
>> My basic question
>> is this: are these two small populations statistically different
>> or do they
>> belong to the same population?  I have asked many elementary
>> level stats folks
>> and have not been entirely satisfied with their solutions.  So, I
>> pose this
>> 'problem' to you.
>> Thanks for your time.
>> Happy Holidays!
>>      -Harland
>>
>> --
>> * To post a message to the list, send it to ai-geostats@...
>> * As a general service to the users, please remember to post a
>> summary of any useful responses to your questions.
>> * To unsubscribe, send an email to majordomo@... with no
>> subject and "unsubscribe ai-geostats" followed by "end" on the
>> next line in the message body. DO NOT SEND Subscribe/Unsubscribe
>> requests to the list
>> * Support to the list is provided at http://www.ai-geostats.org
>
>
>--
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Greetings!

At the suggestion of Isobel Clark, I have just joined this list.
Below is a message I already posted to the allstat mailing list,
and Isobel has suggested I might get good responses from ai-geostats.

Clearly, I have asked my question somewhat informally, but I think
the intention is clear. I would be most obliged to hear of
work directed towards a relative evaluation of two such hypotheses.

With thank, and best wishes to all for the New Year.
Ted.

=======================================

I would be interested to learn of references to _data_ and to
good discussions of such data which are relevant to a hypothesis
of true global warming.

By "true global warming" I mean in effect a sustained positive
trend in the total heat content of the Earth's air and water
(including major ice and snow masses and no doubt some allowance
for the surface of the Earth itself).

No doubt a good statement of what I mean would have to be more
sophisticated, but you get the idea.

The idea specifically being to consider also an alternative
hypothesis whereby currently reported climatic changes, described
as "global warming", may be manifestations of a redistribution of
heat that is there already.

A nice question in spatial statistics, I feel.

With thanks in advance; interesting contributions will be
summarised to the list.

And, from globally warmed Manchester (-10 deg. C last night,
allegedly), a Happy New Year to all.

Ted.

--------------End of forwarded message-------------------------


--------------------------------------------------------------------
E-Mail: (Ted Harding) <Ted.Harding@...>
Fax-to-email: +44 (0)870 284 7749
Date: 31-Dec-00                                       Time: 12:06:22
------------------------------ XFMail ------------------------------

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Is anybody interested in 25 years worth of the Journal
of the International Association of Mathematical
Geology and/or Computers and Geosciences?

I have decided to clear my library for the new
millenium. There are also 20 years of so of Mining
Engineering, Mining Magazine for the 1980's, IMM
Transactions and some odd Engineering and Mining
Journals.

You'd have to pay freight, but otherwise free gift.
Isobel Clark
drisobelclark@...
http://uk.geocities.com/drisobelclark

____________________________________________________________
Do You Yahoo!?
Get your free @yahoo.co.uk address at http://mail.yahoo.co.uk
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I would like to thank Benjamin Warr for his siggestion about doing
difference images instead of global measures as MSE.

I'm confused because crossvalidation MSE (taking one sample out and
recalculating) and validation MSE (taking 15 percent of the samples out and
recalculating) are giving me opposite results. The validation method would
allows me to compare kriging vs cokriging vs Kriging with an external drift
vs regression , but I don't know if I can trust the results at this point.

Does anybody have any input about this?
Thanks in advance,
Mercedes Berterretche

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"(Ted Harding)" wrote:

> I would be interested to learn of references to _data_ and to
> good discussions of such data which are relevant to a hypothesis
> of true global warming.

If you are interested in RAW data (that is, globally exhaustive observations
which are usually compiled into low-level products: radiation budget, clouds,
precipitation, etc; at medium spatial (1km ~ 300km) and
temporal (1h ~ 1 mo) scales) there is no better place to start searching than
http://eosweb.larc.nasa.gov/.

>
>
> By "true global warming" I mean in effect a sustained positive
> trend in the total heat content of the Earth's air and water
> (including major ice and snow masses and no doubt some allowance
> for the surface of the Earth itself).
>
> No doubt a good statement of what I mean would have to be more
> sophisticated, but you get the idea.
>
> The idea specifically being to consider also an alternative
> hypothesis whereby currently reported climatic changes, described
> as "global warming", may be manifestations of a redistribution of
> heat that is there already.

The above site being run by the most powerful government in the World, expect
stated hypotheses to be politically coloured. No doubt many people would like an
"alternative" hypothesis to be validated
(particularly their new oil-sheikh cum president-elect).

>
>
> A nice question in spatial statistics, I feel.
>
> With thanks in advance; interesting contributions will be
> summarised to the list.
>
> And, from globally warmed Manchester (-10 deg. C last night,
> allegedly), a Happy New Year to all.
>
> Ted.
>

Likewise from globally warmed Edmonton, where once the dinosaurs roamed.

Patrick


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Dear Mercedes,

doing k fold cross validation (taking out X % of the samples) will not give
you any reliable results unless you repeat the operation several times. Taking
out 15% of the samples one time only will give you an MSE that will depend
strongly on the data you have removed. Has the selection of the 15% been made
randomly? You may get a strong bias if the 15% of the samples have been taken
in one region in particular or if you have taken out extreme values only. At
this stage, I would trust more the results obtained by standard cross
validation (leave one out method).

I didn’t check your previous mail but if you have few samples only,
k-fold cross validation won’t help you much.

If you have many samples, then you should repeat the procedure at least 10
times to be sure that the way you  have extracted the data has not influenced
too much the results.
Also, if you have a phenomenon that fluctuates at different scales, you may
have removed the short scale effect by taking out only few samples (15% is not
much).

My suggestion is the following: it is time consuming but might be worth the
effort. The idea is to take out an increasing number of samples (10, 20, 30,
40, 50, 60, ...,X%) of samples, this 10 times, and see how the average MSE
evolves. You may find out that methods A & B work better than C & D when only
few samples are removed and that C & D give better results than A & B when
more than 40% of the samples have been removed. This would mean that C & D
describe better the general trend of the  phenomenon while A & B are more
sensitive to the local structures (since you have more dense data).

If you don’t have the time to proceed in such a way, you should use standard
cross validation only and investigate the regions/samples where you have the
highest errors.

Just few thoughts.

Gregoire

"Berterretche, Mercedes" <Mercedes.Berterretche@...> wrote:
>
> I would like to thank Benjamin Warr for his siggestion about doing
> difference images instead of global measures as MSE.
>
> I'm confused because crossvalidation MSE (taking one sample out and
> recalculating) and validation MSE (taking 15 percent of the samples out and
> recalculating) are giving me opposite results. The validation method would
> allows me to compare kriging vs cokriging vs Kriging with an external drift
> vs regression , but I don't know if I can trust the results at this point.
>
> Does anybody have any input about this?
> Thanks in advance,
> Mercedes Berterretche
>
> --
> * To post a message to the list, send it to ai-geostats@...
> * As a general service to the users, please remember to post a summary of
any useful responses to your questions.
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Gregoire Dubois (Ph.D.)
Institute of Mineralogy and Petrography
Dept. of Earth Sciences
University of Lausanne
Switzerland

http://www.ai-geostats.org

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Hi Mercedes,

I fully agree with Gregoire's suggestions of performing
a series of jackknifes over a range of sampling densities.
In this way, you account for both the impact of sampling
density and sampling fluctuations in the comparison.
An example of this approach can be found in:
Saito, H. and P. Goovaerts. 2000.
Geostatistical interpolation of positively skewed and censored data
in a dioxin contaminated site.
Environmental Science & Technology, vol.34, No.19: 4228-4235.

I can e-mail you a PDF copy of the paper if you like.

Cheers,

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

   ________      ________
  |        \    /        |    Pierre Goovaerts
  |_        \  /        _|    Assistant professor
  __|________\/________|__    Dept of Civil & Environmental Engineering
|                        |   The University of Michigan
|     M I C H I G A N    |   EWRE Building, Room 117
|________________________|   Ann Arbor, Michigan, 48109-2125, U.S.A
   _|    |_\    /_|    |_
  |        |\  /|        |    E-mail:  goovaert@...
  |________| \/ |________|    Phone:   (734) 936-0141
                              Fax:     (734) 763-2275
                              http://www-personal.engin.umich.edu/~goovaert/

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


On 7 Jan 2001, Gregoire Dubois wrote:

> Dear Mercedes,
>
> doing k fold cross validation (taking out X % of the samples) will not give
> you any reliable results unless you repeat the operation several times. Taking
> out 15% of the samples one time only will give you an MSE that will depend
> strongly on the data you have removed. Has the selection of the 15% been made
> randomly? You may get a strong bias if the 15% of the samples have been taken
> in one region in particular or if you have taken out extreme values only. At
> this stage, I would trust more the results obtained by standard cross
> validation (leave one out method).
>
> I didn’t check your previous mail but if you have few samples only,
> k-fold cross validation won’t help you much.
>
> If you have many samples, then you should repeat the procedure at least 10
> times to be sure that the way you  have extracted the data has not influenced
> too much the results.
> Also, if you have a phenomenon that fluctuates at different scales, you may
> have removed the short scale effect by taking out only few samples (15% is not
> much).
>
> My suggestion is the following: it is time consuming but might be worth the
> effort. The idea is to take out an increasing number of samples (10, 20, 30,
> 40, 50, 60, ...,X%) of samples, this 10 times, and see how the average MSE
> evolves. You may find out that methods A & B work better than C & D when only
> few samples are removed and that C & D give better results than A & B when
> more than 40% of the samples have been removed. This would mean that C & D
> describe better the general trend of the  phenomenon while A & B are more
> sensitive to the local structures (since you have more dense data).
>
> If you don’t have the time to proceed in such a way, you should use standard
> cross validation only and investigate the regions/samples where you have the
> highest errors.
>
> Just few thoughts.
>
> Gregoire
>
> "Berterretche, Mercedes" <Mercedes.Berterretche@...> wrote:
> >
> > I would like to thank Benjamin Warr for his siggestion about doing
> > difference images instead of global measures as MSE.
> >
> > I'm confused because crossvalidation MSE (taking one sample out and
> > recalculating) and validation MSE (taking 15 percent of the samples out and
> > recalculating) are giving me opposite results. The validation method would
> > allows me to compare kriging vs cokriging vs Kriging with an external drift
> > vs regression , but I don't know if I can trust the results at this point.
> >
> > Does anybody have any input about this?
> > Thanks in advance,
> > Mercedes Berterretche
> >
> > --
> > * To post a message to the list, send it to ai-geostats@...
> > * As a general service to the users, please remember to post a summary of
> any useful responses to your questions.
> > * To unsubscribe, send an email to majordomo@... with no subject and
> "unsubscribe ai-geostats" followed by "end" on the next line in the message
> body. DO NOT SEND Subscribe/Unsubscribe requests to the list
> > * Support to the list is provided at http://www.ai-geostats.org
>
>
> Gregoire Dubois (Ph.D.)
> Institute of Mineralogy and Petrography
> Dept. of Earth Sciences
> University of Lausanne
> Switzerland
>
> http://www.ai-geostats.org
>
> ____________________________________________________________________
> Get free email and a permanent address at http://www.netaddress.com/?N=1
>
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>


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Aargh!

Stop stop. They are gone! I have a waiting list of 10
for my IAMG and C&G and am getting repetitive strain
injury from typing apologies.

If anyone else out there wants to clear their
libraries or studies, please let me know. I would be
more than happy to co-ordinate a clearing house
between wants and haves.

Happy New Year to everyone
Isobel Clark


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Get your free @yahoo.co.uk address at http://mail.yahoo.co.uk
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d. 06/01/01 21:33 skrev Berterretche, Mercedes på
Mercedes.Berterretche@...:

> I'm confused because crossvalidation MSE (taking one sample out and
> recalculating) and validation MSE (taking 15 percent of the samples out and
> recalculating) are giving me opposite results. The validation method would
> allows me to compare kriging vs cokriging vs Kriging with an external drift
> vs regression , but I don't know if I can trust the results at this point.

Cokriging should prove better if the secondary variable provides useful
information about the primary one. In the worst case it should theoretically
be equivalent to kriging if the primary and secondary variable are
uncorrelated. Kriging with an external drift using a drift function that's
totally out of whack and unrelated to the primary variable can prove
to be worse than normal kriging. Likewise it can be better than kriging if
the drift provides useful information on how the shape (or trend) of the
variable is distributed in space. "Regression" is kriging assuming no
spatial correlation. Cokriging should always be better than or equivalent to
kriging  which likewise should be better than or equivalent to "regression".
Better, though, is always a subjective word. KED is always "better" than
cokriging because it eliminates tedious cross-covariance modeling. Likewise
neural networks to incorporate more than two secondary variables. MSE is
just one tip of the iceberg. Frequently a transfer function such as a
fluid flow simulator will determine whether the result is "better" or more
realistic. In such a case perhaps sequential simulation will prove "better."
What is "best" or "better" is usually quite an elusive concept, and wholly
dependent on different people's perceptions of what constitutes quality in
their minds taking into account prior and existing prejudices.

Syed


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Hi everybody,

I feel confused and really need some help to straighten things out.

I am currently working with geostatistical methods for marine geological
mapping. My sourcedata consists of sediment samples, interpreted seismic
profiles, bathymetric data and sonardata. In my first, and easiest, case I only
use the sedimentsamples to get a rough picture of the sedimentary boundaries.

So this question concerns the use of one single source of data, sedimentary
samples. The source data is an ascii_file with three columns: (x_location,
y_location, category (i.e soiltype)).

What I have done so far is that for each category (i.e soiltype), I have done an
indicator transform (for example:  value 1 = sand, value 0 = not sand). Then I
have used GSLIB, gamv, to make an omnidirectional semivariogram for my indicator
transformed data. This has worked really nicely but I get semivariogram values
that is larger than 1 and this troubles me. How can I possibly get semivariogram
values that is outside the range 0 - 1 when I have indicator transformed data?
Is there an error in the program or have I misunderstood the mathematics of
semivariograms? Can someone PLEASE help me out.

I reccon this is a basic question, but I just cant proceed if I dont get this
straightened out.

Many thanks in advance
Malin


[Non-text portions of this message have been removed]

Hi Malin,

In theory and under stationary of order 2,
indicator semivariogram values should not exceed
0.25 which is the maximum variance that you could obtain
for indicator variables, for a proportion of 50%.
I am wondering whether you have used the option
"standardize sill" in gamv, which could explain
these values larger than 1.

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

   ________      ________
  |        \    /        |    Pierre Goovaerts
  |_        \  /        _|    Assistant professor
  __|________\/________|__    Dept of Civil & Environmental Engineering
|                        |   The University of Michigan
|     M I C H I G A N    |   EWRE Building, Room 117
|________________________|   Ann Arbor, Michigan, 48109-2125, U.S.A
   _|    |_\    /_|    |_
  |        |\  /|        |    E-mail:  goovaert@...
  |________| \/ |________|    Phone:   (734) 936-0141
                              Fax:     (734) 763-2275
                              http://www-personal.engin.umich.edu/~goovaert/

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


On Tue, 16 Jan 2001, Malin Fahller wrote:

> Hi everybody,
>
> I feel confused and really need some help to straighten things out.
>
> I am currently working with geostatistical methods for marine geological
mapping. My sourcedata consists of sediment samples, interpreted seismic
profiles, bathymetric data and sonardata. In my first, and easiest, case I only
use the sedimentsamples to get a rough picture of the sedimentary boundaries.
>
> So this question concerns the use of one single source of data, sedimentary
samples. The source data is an ascii_file with three columns: (x_location,
y_location, category (i.e soiltype)).
>
> What I have done so far is that for each category (i.e soiltype), I have done
an indicator transform (for example:  value 1 = sand, value 0 = not sand). Then
I have used GSLIB, gamv, to make an omnidirectional semivariogram for my
indicator transformed data. This has worked really nicely but I get
semivariogram values that is larger than 1 and this troubles me. How can I
possibly get semivariogram values that is outside the range 0 - 1 when I have
indicator transformed data? Is there an error in the program or have I
misunderstood the mathematics of semivariograms? Can someone PLEASE help me out.
>
> I reccon this is a basic question, but I just cant proceed if I dont get this
straightened out.
>
> Many thanks in advance
> Malin
>


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> Could anyone tell me what c0 and b mean. These
> appear at the start of
> the interpolation proceedure. I have values of 0 and
> 11580.591
> respectively and I am unsure of what they imply
> about this method.
c0 is standard notation for the 'nugget effect' or
small scale random (unpredictable) component. Some
schools interpret this as sampling error. In mineral
concentration it is usually a feature of the
mineralisation. No matter how close you sample, the
difference between neighbouring samples will always be
non-zero. You nugget effect of zero implies a smooth
continuous surface with no random component.

There is no standard notation for the slope of the
line, but I would guess that is what b is. In that
case your b is the amount by which the squared
difference increases for every unit distance. If you
have a zero nugget effect, the slope is irrelevant
except for calculating the standard error of the
estimation.

I am not familiar with the details of ArcInfo. Does it
calculate and fit the semi-variogram model
automatically? I would be very suspicious of a zero
nugget effect in an application such as you describe.

If I can be of any further help, please let me know.
Isobel Clark
Alloa, Scotland
http://uk.geocities.com/drisobelclark

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Dear Malin:

The semivariogram of an indicator variable is always less than 1.

Proof:
The experimental semivariogram is (1/2) of the mean of the squared
differences Z(xi+h)-Z(xi) but the values of Z are 0 or 1, then the
semivariogram is (1/2) of the mean of the absolutes values of
Z(xi+h)-Z(xi). Now you use the triangular inequality and you get that
the semivariogram is less than 1.

Regards
Marco Alfaro



Malin Fahller wrote:

> Hi everybody, I feel confused and really need some help to straighten
> things out. I am currently working with geostatistical methods for
> marine geological mapping. My sourcedata consists of sediment samples,
> interpreted seismic profiles, bathymetric data and sonardata. In my
> first, and easiest, case I only use the sedimentsamples to get a rough
> picture of the sedimentary boundaries. So this question concerns the
> use of one single source of data, sedimentary samples. The source data
> is an ascii_file with three columns: (x_location, y_location, category
> (i.e soiltype)). What I have done so far is that for each category
> (i.e soiltype), I have done an indicator transform (for example:
> value 1 = sand, value 0 = not sand). Then I have used GSLIB, gamv, to
> make an omnidirectional semivariogram for my indicator transformed
> data. This has worked really nicely but I get semivariogram values
> that is larger than 1 and this troubles me. How can I possibly get
> semivariogram values that is outside the range 0 - 1 when I have
> indicator transformed data? Is there an error in the program or have I
> misunderstood the mathematics of semivariograms? Can someone PLEASE
> help me out. I reccon this is a basic question, but I just cant
> proceed if I dont get this straightened out. Many thanks in
> advanceMalin


[Non-text portions of this message have been removed]

Hi again and thanks for your answers,
you have really helped me out.

Here are the answers I have received so far:

______________________
Pierre Goovaerts answered:

Hi Malin,

In theory and under stationary of order 2,
indicator semivariogram values should not exceed
0.25 which is the maximum variance that you could obtain
for indicator variables, for a proportion of 50%.
I am wondering whether you have used the option
"standardize sill" in gamv, which could explain
these values larger than 1.

Pierre

__________________________

YES I used that option and that seems to explain the situation!

___________________________

Marco Alfaro answered:

Dear Malin:
The semivariogram of an indicator variable is always less than 1.

Proof:
The experimental semivariogram is (1/2) of the mean of the squared differences
Z(xi+h)-Z(xi) but the values of Z are 0 or 1, then the semivariogram is (1/2) of
the mean of the absolutes values of Z(xi+h)-Z(xi). Now you use the triangular
inequality and you get that the semivariogram is less than 1.

Regards
Marco Alfaro

_________________________


Brian Gray wrote:

believe that geostatisticians resolve this by setting "out of bounds" values to
the extremes (eg 0 or 1).  However, statisticians  resolve this issue for
nonspatial data by using an inverse link to a cdf--which, of course, is on
[0,1].  Examples include logistic and probit regression.  See Gotway, CA and WW
Stroup. 1997.  A generalized linear model approach to spatial data analysis and
prediction. JABES 2: 157-178.  Gumpertz, ML, C Wu and JM Pye. 2000. Logistic
regression for Southern Pine Beetle outbreaks with spatial and temporal
correlation. Forest Science 46: 95-107.  Brian

___________________________________



Malin Fahller
Geographical Information Technology
Luleå University of Technology
SE- 971 87 LULEÅ
SWEDEN

phone: (+46) (0)920 914 66
fax: (+46) (0)920 728 30





[Non-text portions of this message have been removed]

Hello

This is my first time on the list and I hope this question is going to
the right place. My appologies if not.

I am using Arc/Info 7.2.1 on an NT workstation.
With GRID I am using linear universal kriging to produce maps of heavy
metal concentration from 127 sample points.

Could anyone tell me what c0 and b mean. These appear at the start of
the interpolation proceedure. I have values of 0 and 11580.591
respectively and I am unsure of what they imply about this method.

Thanks for your time with this.

Jason Sawle

###############################################################
Department of Geography
Canterbury Christ Church University College
North Holmes Road,
Canterbury,                         Tel: 01227 782337
Kent,                               Fax: 01227 767531
CT1 1QU,                            email: j.sawle57@...
United Kingdom                      http://www.cant.ac.uk


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SIMMAP is a simple software for the simulation of categorical
landscape spatial patterns that runs on a PC-Windows environment and is
distributed without charge for non-commercial use. This program allows
obtaining a wide range of patterns with any number of classes in which
fragmentation and classes abundances can be independent and
systematically varied. It is also possible to obtain patterns with
anisotropy and to control the minimum mapped unit of the artificial
landscapes.

     SIMMAP is the result of implementing the modified random clusters
(MRC hereafter) simulation method. This method provides more general and
realist results than other commonly used landscape models, and has been
described in detail in the following reference:

     Saura, S. and J. Martínez-Millán. 2000. Landscape patterns
simulation with a modified random clusters method. Landscape Ecology 15
(7): 661-678.

     SIMMAP 2.0 simulations are very low computational time consuming. In
a standard PC at 333 MHz, typical computational times are less than one
second for 200x200 pixels patterns, around 2 seconds for 400x400 images,
and around 4 seconds for 800x800 pixels landscapes. SIMMAP also computes
several landscape pattern configuration indices on the MRC patterns,
such as those related to edges, number, size and shape of the patches,
and some others. The obtained raster MRC patterns can be saved as image
files in “bmp” format, which may be imported in other image processing
or G.I.S. programmes if necessary.

     Those who might be interested in a copy of SIMMAP 2.0 please contact
the author’s e-mail (santisaura@...). A copy of the software,
along with a short manual, will be sent afterwards. Author acknowledges
receiving brief descriptions of the applications for which SIMMAP is
planned to be used.

     I hope that SIMMAP is of interest for your activities. Kind regards,



                     Santiago Saura Martinez de Toda

______________________________

Santiago Saura Martinez de Toda

Dasometria
E.T.S. Ingenieros de Montes
Universidad Politecnica de Madrid
Ciudad Universitaria s/n
28040   Madrid
Spain

E-mail: santisaura@...
              ssauramt@...
______________________________


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Hi,

I would be very uncertain about the validity of the zero nugget in
your case as sampled variables such as you describe seem to be
almost guaranteed to have some nugget from small-scale
environmental differences alone. Do you have the option of
specifying a variogram in ArcInfo? Are your samples evenly
distributed throughout the area you are kriging?

Martin Roseveare

> Hello
>
> This is my first time on the list and I hope this question is going to the
> right place. My appologies if not.
>
> I am using Arc/Info 7.2.1 on an NT workstation.
> With GRID I am using linear universal kriging to produce maps of heavy
> metal concentration from 127 sample points.
>
> Could anyone tell me what c0 and b mean. These appear at the start of the
> interpolation proceedure. I have values of 0 and 11580.591 respectively
> and I am unsure of what they imply about this method.
>
> Thanks for your time with this.
>
> Jason Sawle
>
> ###############################################################
> Department of Geography
> Canterbury Christ Church University College
> North Holmes Road,
> Canterbury,                         Tel: 01227 782337
> Kent,                               Fax: 01227 767531
> CT1 1QU,                            email: j.sawle57@...
> United Kingdom                      http://www.cant.ac.uk


________________________________
Martin Roseveare
ArchaeoPhysica Ltd.
Phone: 07050 369789
Fax:   07050 369790
email: mail@...
web:   http://www.archaeophysica.co.uk

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Dear listmembers, I tried to send this before, but I don't think anybody but
Jason has seen it. If you have, sorry for the inconvenience. (List Manager,
maybe it is possible to put ai-geostats@... first and
then the author such that a simple reply to a post works?)

           >Hello
           >
           >This is my first time on the list and I hope this question is going
to
           >the right place. My appologies if not.
           >
           >I am using Arc/Info 7.2.1 on an NT workstation.
           >With GRID I am using linear universal kriging to produce maps of
heavy
           >metal concentration from 127 sample points.

           In response to the replies of Isobel Clark and Martin Rosevaere and as
a
           general warning to yourself: Yes, ArcInfo does automatically produce a
           semi-variogram and you can specify its functional form (the {method}
optional
           parameter). Beware, however, of the method that is applied to
parameterize the
           variogram. As is stated in the help file, the Levenberg-Marquardt (LM)
           algorithm is applied. LM is a non-linear least squares method of
function
           estimation from sampled data. It works by minimizing chi square over
the
           sampled data >>>> using the standard deviations of the individual
samples
           <<<<. ArcInfo kriging does not ask for, therefore does not know of nor
use the
           standard deviation of the sample data (your point cover). Instead, and
this
           completely invalidates ArcInfo kriging IMHO, you specify either a
number of
           neighbouring sample points or a radius from which to pick sample
points to
           calculate local sample standard deviation. THIS IS COMPLETELY AND
ABSOLUTELY
           WRONG!!!!! It undermines the essence of kriging. Do not use kriging in
ArcInfo
           if you are trying to do serious work, or if your sample data is of
high
           quality. Use a proper tool instead.

           And to conclude an excerpt from ArcInfo help on kriging:

           [quote]
           Kriging is a complex procedure that requires greater knowledge about
spatial
           statistics than can be conveyed in this command reference. Before
using the
           KRIGING command, you should have a thorough understanding of the
fundamentals
           of kriging and have assessed the appropriateness of your data for
modeling
           with this technique. If you do not have a good understanding of this
           procedure, it is strongly recommended that you review some of the
references
           listed at the end of this command reference.
           [unquote]

           If you have a good understanding of kriging and KRIGING, don't use
ArcInfo!

           Patrick van Laake
           ESRI Certified ArcInfo Instructor (really but ;-) )



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Dear Jason,

I saw few replies to your question and I can imagine you are
a bit lost with these technical terms that are not documented in
Arc/Info's manual.

Versions younger than Arc/Info 8.0 (which has a brand new geostatistical
module) are almost useless for what concerns geostatistics.
More than the estimation algorithm (ordinary
kriging, universal kriging, etc.), it is the analysis and the
modelisation of the spatial correlation which is essential. Since
you can't properly make a decent semivariogram analysis
and since the fitting of the semivariogram is automatic (almost any
geostatistician will tell you to fit your model manually or at least to
have a full control on the parameters you select) in Arc/Info 7, you can
almost forget it ! Three years ago I developed in AML an interface between
UNCERT (see my AI-GEOSTATS web pages for more info) and Arc/Info 7.0.  There
is unfortunately nothing left from the code since I left the
place where I developed it but I'm sure many people on the list
did something similar (with UNCERT, Gstat, GSLIB or the UNIX version of GeoEas
for exemple).

I'm sorry for the bad news but making a spatial interpolation, especially
when you plan to use geostatistical methods, requires some experience from
the users (and this is a radiobiologist that is talking, not a statistician)

Hope this helps a bit,

Gregoire

PS: may I suggest you to download Geoeas (+ manual) and play around with the
semivariograms to better realise how limited the functions are in
Arc/Info 7.

Jason Sawle <j.sawle57@...> wrote:
> Hello
>
> This is my first time on the list and I hope this question is going to
> the right place. My appologies if not.
>
> I am using Arc/Info 7.2.1 on an NT workstation.
> With GRID I am using linear universal kriging to produce maps of heavy
> metal concentration from 127 sample points.
>
> Could anyone tell me what c0 and b mean. These appear at the start of
> the interpolation proceedure. I have values of 0 and 11580.591
> respectively and I am unsure of what they imply about this method.
>
> Thanks for your time with this.
>
> Jason Sawle
>
> ###############################################################
> Department of Geography
> Canterbury Christ Church University College
> North Holmes Road,
> Canterbury,                         Tel: 01227 782337
> Kent,                               Fax: 01227 767531
> CT1 1QU,                            email: j.sawle57@...
> United Kingdom                      http://www.cant.ac.uk
>
>
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Gregoire Dubois
Institute of Mineralogy and Petrography
Dept. of Earth Sciences
University of Lausanne
Switzerland

http://www.ai-geostats.org

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Dear All,

I am new to spatial statistics and am posting this query in the hope that
someone may be able to point me in the right direction.  I am a biological
oceanographer and am interested in statistically describing the
2-dimensional distribution of biological particles, primarily to define the
'patchiness' of the distributions.  I have two data sets which consist of
7x7 and 9x9 point arrays, providing 49 and 81 samples respectively.  Are
there meaningful spatial statistics that can be applied to such small data
sets?

Thank you in advance,

Raechel Waters

`````````````````````````````````````````````````````
Marine Biology
School of Biology
Flinders University
GPO Box 2100
Adelaide
SA 5001

Phone:  08 8201 5234
Fax:            08 8201 3015
Mobile: 0401 304 106


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> Dear Geostatisticians
>
> A field experiment, with 162 genotypes, is laid out in a 3-replicate 9x18
> alpha design. The 3 replicates are contiguous. The experiment can be
> defined as a r (rows) x c (columns) field structure. Following the method
> of Gilmour & Cullis (1997), published in JABES (J of Agricultural,
> Biological and Environmental Statistics), I plan to conduct a spatial
> analysis of this experiment to obtain spatially-adjusted genotype means
> using either the software ASREML or using the VSTRUCTURE command in
> GENSTAT.
>
> In the above context, could someone suggest possibilities to use
> resampling procedures to assess the accuracy and precision of
> spatially-adjusted genotype means.
>
> Many thanks in advance.
>
> Best regards
>
> Subhash :: 24 Jan 2001
>
> <><><><><><><><><><><><><><><><><><><><>
> Dr Subhash Chandra
> Senior Scientist
> Genetic Resources and Enhancement Program
> International Crops Research Institute for the Semi-Arid Tropics
> Patancheru - 502 324, AP, India
>
> Email:         s.chandra@...
> Tel:            +91 40 329 6161
> Fax:           +91 40 329 6182
>                   +91 40 324 1239
> Website:    http://www.icrisat.org
> <><><><><><><><><><><><><><><><><><><><>
>

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Dear All

Some of you may be interested in the two-day meeting on 'Uncertainty in
Remote Sensing and GIS' that we are organising at the University of
Southampton for 3-4th July 2001 (below).

This Email is a reminder of the deadline for abstracts which is 31 January
2001. If you will have trouble meeting this deadline, we can accept
abstracts up until 15th January but not after that.

Best wishes

Peter



Uncertainty in Remote Sensing and GIS

SECOND CALL FOR PAPERS

Two-day meeting
On behalf of the Remote Sensing and Photogrammetry Society MATSIG and GISSIG

University of Southampton
3rd-4th July 2001

The Remote Sensing and Photogrammetry Society's Models and Advanced
Techniques Special Interest Group (MATSIG) and Geographic Information
Systems Special Interest Group (GISSIG) are organising a two-day meeting to
be held at the University of Southampton on 3rd and 4th July 2001. The
meeting will be provide a forum for the presentation of state-of-the-art
research in the field of statistical uncertainty modelling in remote
sensing and other spatial data. A wide range of papers is solicited, but
likely topics to be included are:

Spatial prediction 		 Fuzzy classification accuracy assessment
Spatial simulation 		 Bayesian approaches
Geostatistics 			 Markov chain Monte Carlo (MCMC) analysis
Simulated annealing 		 Sub-pixel analysis
Autoregressive models 	 Propagation of error/uncertainty

The meeting will start at 13:00 on Tuesday 3rd and finish at 15:00 on
Wednesday 4th July allowing delegates time for travel to and from
Southampton. A particular attraction of the meeting will be a social event
organised for the evening of the 3rd July 2001. Key-note addresses will be
given by:

· Prof. Curtis Woodcock, University of Boston, USA
· Dr. Gerard Heuvelink, University of Amsterdam, The Netherlands

The proceedings of the meeting will be published as a book. To present a
paper, please submit an abstract of no more than 350 words to the
organisers (see below) by 31st January 2001.

Dates:
31st January 2001 	 Deadline for submission of abstracts
31st March 2001 	 Authors notified of paper acceptance
31st May 2001 		 Registration deadline
3rd and 4th July 2001  Submission of full papers at meeting

Conference Organisers
Dr. Peter Atkinson Tel: 028 3059 4617 FAX: 023 8059 3295 Email:
pma@...
Prof. Giles Foody Tel: 028 3059 5493  FAX: 023 8059 3295 Email:
gmf@...
Department of Geography, University of Southampton, Highfield, Southampton
SO17 1BJ, UK

SPONSORS: Ordnance Survey, RSPSoc, Erdas UK, RGS-IBG  , University of
Southampton



Uncertainty in Remote Sensing and GIS

Two-day meeting organised by the Remote Sensing and Photogrammetry Society
MATSIG and GISSIG

University of Southampton, Highfield, Southampton SO17 1BJ, UK
3rd and 4th July 2001


REGISTRATION FORM

Name:.......................................................................
...........
Affiliation:................................................................
...........
Address:....................................................................
...........
............................................................................
...........
............................................................................
...........
............................................................................
...........
Telephone:..................................................................
...........
Fax:........................................................................
...........
Email:.....…................................................................
...........

If you wish to present a paper, please submit a one-sided abstract to Dr.
Peter Atkinson or Prof. Giles Foody, either by surface mail, by Email by
31st January 2001 indicating whether you would prefer the oral or poster
presentation format.

Charges will be kept to a minimum through sponsorship making this a highly
accessible meeting, particularly for postgraduates. The meeting will start
13:00 on Tuesday 3rd and finish at 15:00 on Wednesday 4th July allowing
delegates time for travel to and from Southampton. A particular attraction
of the meeting will be an informal social event organised for the evening
of the 3rd July 2001. Accommodation (including breakfast) will be provided
at a University of Southampton hall of residence (see table below for
charges), but a range of other guest houses and hotels are available for
those who require them.

Please indicate your requirements by circling the appropriate charges
below. Please make cheques payable to the University of Southampton.


Registration (includes coffee, lunch and tea):
 		 RSPSoc members (RSS membership no.:.....................): £35
		 Non-RSPSoc-members: 					 £55
		 Students (Institution:................................................):
£10
Bed and breakfast: 							 £25
Bed and breakfast (en-suite): 					 £30

TOTAL 									 £....


Please return with payment by 31st May 2001 to:
Dr. Peter Atkinson Tel: 028 3059 4617 FAX: 023 8059 3295 Email:
pma@...
Prof. Giles Foody Tel: 028 3059 5493  FAX: 023 8059 3295 Email:
gmf@...
Department of Geography, University of Southampton, Highfield, Southampton
SO17 1BJ, UK

__________________________________________________________________
Dr. Peter Atkinson                      Department of Geography
Reader in Geography                     University of Southampton
Tel.        +44 (023) 8059 4617         Highfield
FAX.        +44 (023) 8059 3295         Southampton
E.mail.     pma@...             SO17 1BJ
__________________________________________________________________

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Dear Raechel

The answer to your question is a bit
chicken-and-egg-ish.

If your data is well behaved (simple distribution,
pretty continuous) then you can get meaningful results
from very few samples (probably not less than 20 or
so!!)

We have examples in the book with data sets of 27 and
up. The 27 one is no good for geostatistics but this
has more to do with the fact that the samples are 1km
apart when the range of influence is probably about
125 metres. The main tutorial set in the old book
(available free at
http://uk.geocities.com/drisobelclark/practica.html)
which we now call "Page 95" has 50 samples very
inefficiently placed which still yield good results
for interpretation and estimation purposes. Even more
so for simulation basis.

So, I would say, go ahead and try it but look at your
distribution before you go to geostatistics. Small
data sets will give much better results if Normal
(Gaussian) or normalised or transformed in some other
way.

If I can be of any more help, please let me know
Isobel Clark



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Dear All

MAT SIG & GIS SIG meeting
Uncertainty in Remote Sensing and GIS
SECOND CALL FOR PAPERS

Sorry, I meant that abstracts could be accepted up to 15th February 2001.

Best wishes

Peter


__________________________________________________________________
Dr. Peter Atkinson                      Department of Geography
Reader in Geography                     University of Southampton
Tel.        +44 (023) 8059 4617         Highfield
FAX.        +44 (023) 8059 3295         Southampton
E.mail.     pma@...             SO17 1BJ
__________________________________________________________________

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Dear all,

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?

Thanks,

Rubens Caldeira Monteiro
PhD. candidate on "Geosciences and Environmental Sciences"

University of the State of Sao Paulo at Rio Claro - UNESP-RC
http://www.rc.unesp.br/igce/dga
rubenscm@...

University of North Carolina at Chapel Hill - UNC-CH (visiting scholar)
http://www.unc.edu/~rubenscm
rcmonteiro@...


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Dear Rubens,

removing pairs from a semivariogram is OK if you can justify the reason
why you are doing so. One usually remove pairs because they influence
the spatial structure of the analysed phenomenon in an unexpected way
(i.e. a “jump” in the nugget effect). However, in such a case one will realise
that more than pairs of points it is a point that is making
troubles. Therefore, it makes more sense to me to remove a point from
a data set (and so all the associated pairs) than few pairs. It is the price
to pay to remain coherent during the analysis.

Using the pairs more than once, with a “moving lag” can be done to densify the
number of points of your semivariogram and get so more details. This kind of
moving windows approach has already been done
in:

FLAMM C., KANEVSKY M. & SAVELIEVA E. (1994). Non-regular lag variography and
multi-method mapping to determination of origin of heavy metals. Case study on
Geneva heavy metal survey, Switzerland. In: “Proceedings of the Annual
Conference of the International Association for Mathematical Geology”.
Mont-Tremblant, Canada, pp. 128-133.

Hope this helps

Gregoire

PS: sorry but I can't find this paper anymore and can’t send it to you

Rubens Caldeira Monteiro <rubenscm@...> wrote:
> Dear all,
>
> 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?
>
> Thanks,
>
> Rubens Caldeira Monteiro
> PhD. candidate on "Geosciences and Environmental Sciences"
>
> University of the State of Sao Paulo at Rio Claro - UNESP-RC
> http://www.rc.unesp.br/igce/dga
> rubenscm@...
>
> University of North Carolina at Chapel Hill - UNC-CH (visiting scholar)
> http://www.unc.edu/~rubenscm
> rcmonteiro@...
>
>
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Gregoire Dubois
Institute of Mineralogy and Petrography
Dept. of Earth Sciences
University of Lausanne
Switzerland

http://www.ai-geostats.org

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Hi,

I am wondering whether anyone could advise on a couple of
matters...

a. Is there a published set of algorithms for computing variograms
and semi-variograms? Algorithms or actual code are OK, I'm just
trying to find out what the computational mechanics actually are,
as opposed to the theoretical technique.

b. I'm also trying to find an algorithm for constructing a TIN-type
model automatically from spot data as part of a larger project
investigating techniques of analysing non-topographical data.

Can anyone advise please?

Many thanks,

Martin Roseveare.

p.s. Please feel free to reply off-list if prefered; I can post a
summary of the most useful responses if needed.

________________________________
Martin Roseveare
ArchaeoPhysica Ltd.
Phone: 07050 369789
Fax:   07050 369790
email: mail@...
web:   http://www.archaeophysica.co.uk

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Dear List members,

I am working with two methods for mapping spatial structure in soil water
content (Time Domain Reflectometry and Ground Penetrating Radar). These
methods have a different support. To evaluate the potential of these methods
to map soil water content, we imposed a spatial structure in soil water
content by irrigation with various intensities. After irrigation, we
attempted to retrieve the imposed spatial structure in soil water content
with both methods.

I would like to evaluate the results of this experiment in terms of:
1)Success in retrieval of imposed spatial structure by comparing
interpolated maps of water content (prediction and uncertainty)
2)Semivariograms for both methods (before and after irrigation).

Now I am looking for software that can calculate experimental semivariograms
at block support from point data. I had a look on regularisation theory but
I would be more satisfied if I could calculate the experimental
semivariogram at block support directly.

Any suggestions?

Sander Huisman

Institute for Biodiversity and Ecosystem Dynamics
Universiteit van Amsterdam
Fysische Geografie en Bodemkunde


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Sander

I am uncertain what you mean by calculating an
experimental semi-variogram at block support from
point data?

Calculating an experimental semi-variogram is the same
whatever your basic support. If you mean you want to
model it as a block semi-variogram and find the point
semi-variogram that compares to that, this is not a
problem. We have routines in the EcoSSe software which
would do this. Although we don't currently have a
'public' menu item for this it would take around 15
minutes to implement and would be included if you
specified that when you bought it. Unfortunately
EcoSSe is not free, but this sort of thing is what you
pay for!

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

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