Just to remind everybody that Practical Geostatistics
2000 by Isobel Clark and Bill Harper has finally hit
the streets - well, the Web anyway. You can even get
it on Amazon.com!

The hardcopy book is 442 pages and the "old" Practical
Geostatistics starts half way through Chapter 8!

The book is also available as hypertext on CD. It is
pretty flat at the moment, with only major hypertext
links, but we hope to make it a lot more flexible in
later editions.

The CD also includes a demo copy of the Geostokos
software and 13 data sets for teaching, learning and
generally playing around with.

The software and data sets are also freely available
to anyone -- even cheapskates who won't buy the book.

Check this out at
http://uk.geocities.com/drisobelclark/PG2000_demo.html

There is also information on the Contents of the book
and a rough copy of Chapter 1 on the same site.

The old book is also available as download in a bad
photocopy version or in Latex. The latter is readable
(and printable) using the free Scientific Notebook
Viewer which you can download from
http://www.mackichan.com/products/dwnld-inst.html
[Note: you have to go way down the page to find the
free version!!]

Details on downloading Practical Geostatistics 1979
(yes really, I am only that old) at:
http://uk.geocities.com/drisobelclark/practica.html

I have put all this stuff in folders in my Yahoo
briefcase. If you want to be really rude you can go
straight there:
http://uk.briefcase.yahoo.com/drisobelclark

I would prefer you to at least visit my own pages and
SIGN THE GUESTBOOK!!!!!!!!

Everything in the briefcase is free and freely
distributable. I know we aren't supposed to solicit
data sets, but if you have any you are willing to
share with the geostatistical world, we are willing to
host them in the briefcase and modify for use with the
PG2000 demo software.

Visit http://geoecosse.hypermart.net for Web
purchasing of the book, CD and the 'real' software
(EcoSSe). For direct purchasing contact me for Africa,
Australasia and the Far East and e_cosse@...
for Europe, CIS and the Middle East.

We are currently finishing a separate volume of
"Answers to Exercises". Bona fide teachers can obtain
a free "notes for educators" when buying the second
volume. Now taking suggestions for Volume Two
scheduled for early 2001. So far have simulation,
discrete processes, co-kriging and anecdotes. All
conributions gratefully accepted!

Contact me personally at drisobelclark@...

Enjoy!
Isobel Clark



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Suppose I have a variable (Leaf area index) that shows periodicity in its
semivariograms (at several lags). And this periodicity can be seen in the
E-W direction in a satellite image. There is also a N-S trend (values
increasing to the south). When modeling an omnidirectional variogram, a
nested model including a spherical and hole effect structures fits
adequately the sample variogram. The rose variogram indicates that the
azimuth angle = 160 degrees is the major direction of continuity; so 160 and
70 degrees are the angles selected to approach the problem with anisotropy.
The directional variograms also show periodicity but the hole model effect
cannot be applied in more than one direction (Deutsh and Journel,
Geostatistical Software Library and user's guide, page 25). So each
directional variogram is modeled with a nested model including two spherical
models; this model does not represent the periodicity of the variable. When
performing ordinary kriging or conditional simulation the use of the
omnidirectional model gives better results (visually and statistically)than
the use of the anisotropic model.

Is there a way by which I can include the periodicity in the anisotropic
model or do I just have to accept the omnidirectional approach as the best
one in this case, because it represents better the periodic behavior?

Thanks in advance,
mercedes berterretche
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Hi Mercedes

You have what we call the "Paddington Mix" model -- a
mixture of spherical components with a 'ripple' effect
around it. I have used anisotropic Paddington Mixes
very successfully in several different geological
different applications.

The reason we call it the Paddington Mix is that it
was first included in the Geostokos software for an
application at Paddington Mine in Western Australia.
This is a shear-enhanced gold mineralisation, where
the gold values are not restricted to shear zones
(cyclic) but are richer close to the shears. So we had
a model with a basic two component spherical but with
a cyclic component which varied wildly according to
whether it was parallel to or perpendicular to the
shears. To get the anisotropy, we varied cycle length
and damping parameter to achieve almost pure spherical
'along shears' and strong cycles across shears.

The model has also been used to characterise potholes
or ballrooms in platinum reef mineralisation, and we
(me and Gavin Lind) have a paper to be presented in
South Africa next month on using indicators and the
paddington mix to track down pillars and voids in old
abandoned coal mines.

You can see examples of the Paddington Mix in
Practical Geostatistics 2000, although we don't have
any anisotropic models in the book. Got to leave
something for Volume 2!

Check it out at http://geoecosse.bizland.com and the
book software at
http://uk.geocities.com/drisobelclark/PG2000_demo.html.

Isobel Clark

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Hi-

  Suppose I have some spatial samples with weights (w1 w2 ....)  and I want to
use these weights in addition to  kriging weights and also suppose (and a big
suppose it is) that I have the (a) variogram(gamma).  If I  krige ignoring (w1
w2...) and weight the kriging weights (wk1 wk1 ...) with  (w1 w2) ie

   Answer= Sum(Value1*w1*wk1+Value2*w1*wk2+...)/Sum(w1*wk1+w1*wk2+...)

I get I some cases (zero nugget variogram and some negative weights)
unreasonable results e.g.

V1  w1 wk1
30   .1  1.2
50   .9  -.2
  answer=90

Unreasonable results are a well known result with negative weights and usually
indicate a (local) inconsistency between the data and the variogram but I think
the problem is exacerbated by not allowing for the weights w1.. in the kriging
matrix

My guess is that  the sample weights should be  coupled WITHIN  the kriging
equations something like:
   w1w1Gamma11 w1w2Gamma12 ..... ..... 1               wk1              w1Gamma1b
   w2w1Gamma21 w2w2Gamma22 ..... ....   1               wk2       =   w2Gamma2b
   ......                  ......                  .....  ..... 1                
..               .....
      1                        1                     ..... ......0
mu                      1

Before I work thru the math for my guess and code a solution  I would like input
on
    1) Has this problem been solved before?
    2) Is a C or Fortran or public .exe version of  the solution available (3d
preferred)

thanx

bob sandefur

Principal Geostatistician
Pincock Allen & Holt
International Minerals Consultants
274 Union Suite 200
Lakewood CO 80228
USA
303 914-4467  v
303 987-8907 f




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Hi  All

Could someone please advise me on a decent share/free ware package that has
the ability to run various forms of trend surface analysis on large data
sets (100 000+) e.g. residual, polynomial etc. (URL site for download would
be appreciated), and contour the data set afterwards.

The current software that I am using does not have this functionality built
in and I want to run a number of checks on various parameters that I have in
the data set.

Thank you

Mark Burnett
Evaluation Manager

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Have you checked out the R package available from www.lib.stat.cmu.edu/R and
its various add-on packages.  All free!

Best, Mark Hall


----- Original Message -----
From: "Burnett, Mark" <MBurnett@...>
To: <ai-geostats@...>
Sent: Tuesday, October 24, 2000 10:31 PM
Subject: GEOSTATS: Trend Surface Analysis software


> Hi  All
>
> Could someone please advise me on a decent share/free ware package that
has
> the ability to run various forms of trend surface analysis on large data
> sets (100 000+) e.g. residual, polynomial etc. (URL site for download
would
> be appreciated), and contour the data set afterwards.
>
> The current software that I am using does not have this functionality
built
> in and I want to run a number of checks on various parameters that I have
in
> the data set.
>
> Thank you
>
> Mark Burnett
> Evaluation Manager
>
> --
> *To post a message to the list, send it to ai-geostats@....
> *As a general service to list users, please remember to post a summary
> of any useful responses to your questions.
> *To unsubscribe, send email to majordomo@... with no subject and
> "unsubscribe ai-geostats" in the message body.
> DO NOT SEND Subscribe/Unsubscribe requests to the list!
>
>

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Hi Bob, long time no see

It is traditional in thin reef deposits (such as those
in South Africa) to use an accumulation value which is
length times grade. I have also seen similar composite
values used in iron ore where a weight times grade is
used as the principle variable.

These composite values generally give acceptable
semi-variograms and can then be kriged. The result is
(of course) an accumulation value and has to be
matched with a kriged length, weight or density
variable to achieve estimates in the original grade
units.

As a simple example, in a Wits Reef length times grade
is considered to be the 'natural' variable. This is
modelled and kriged. The width of the reef is also a
natural geological variable and this can be modelled
and kriged. Final grade is then kriged accumulation
divided by kriged width. Error on this is found using
the original combination of relative variances
suggested by Matheron.

This avoids all problems of messing around with
kriging systems and/or the kriging weights.

All of the above is predicated on your "weights" being
a physical phenomenon. If you are talking about
conceptual weights, then you probably need something
like "soft kriging" with a Bayesian input.

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


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Sorry folks about messing up the address for Stat Lib, it is:

http://lib.stat.cmu.edu/

Best, Mark Hall


----- Original Message -----
From: <abedini@...>
To: "Mark Hall" <hall@...>
Sent: Thursday, October 26, 2000 1:55 AM
Subject: Re: GEOSTATS: Trend Surface Analysis software


>
> Dear Mark
>
> I tried to connect to the URl which you provided receiving the following
> reply. Are you sure the address is correct?
>
> Thanks
> Abedini
>
> While trying to retrieve the URL: http://www.lib.stat.cmu.edu/
>
> The following error was encountered:
>
> Unable to determine IP address from host name for www.lib.stat.cmu.edu
> The dnsserver returned:
>
> Name Error: The domain name does not exist.
> This means that:
>
>  The cache was not able to resolve the hostname presented in the URL.
>  Check if the address is correct.
>
> Your cache administrator is root.
>
>
>
> --------------------------------------------------------------------------
------
> Generated Wed, 25 Oct 2000 16:51:46 GMT by proxy.shirazu.ac.ir
> (Squid/2.3.STABLE3)
>
>
>

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26th Oct., 2000

Dear Dr Isobel clark,

I was made part  the list of geostats from yesterday only and it is my
good fortune to see your reply in my first message. I had the opportunity
of corresponding with you on geostatistics during 1983-86.

Currently I am working with iron ore mines of Tata Steel in India. The
ore is won by opencast mining method with 12m high benches. The iron
ore consists of several types of ores each having definable quality
in terms of Fe, Al2O3 and SiO2; and physical characterisics such as
hard ore, soft ore, flaky ore, bluedust etc. making them to be
processed in wet and dry methods. In such a case, using all the iron ore
samples in kriging is leading to over=estimation of lean grade ores
and under-estimation of high grade ores if one sees block-wise. This
type of estiamtes are not acceptable to the production staff. Hence
I used variogram parameters of the entire iron ore samples to specific
ore type estimation for 12m benches with 100mx100m blocks using the
core smaples of that specific ore type, which satisfied the production
staff. Is the procedure correct? If not, can you please suggest a better
method?

In anticipation of your valuable advice.

With regards

Dr P.V. Rao


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Dear Dr. Isobel Clark,

I am new in geostats mail list.

I worked  in Romania many years in geoinformatics, to
use geomathematical and geostatistical methods for
several ores and different geological data, with
commercial, shareware and my own programs. Finally, I
learned ARC/INFO GIS on Silicon Graphics workstation.

In present, I am working as database programmer in
economical field in a private company, for a better
salary, which is a problem for geological domain in
Romania.

My wish is to continue with a better job in
geoinformatics (GIS, geostatistics). Please, give me
an advice to do this. For details see my home page
www7.ewebcity.com/geoinf

Thank you in anticipation.

Best wishes,

George Tudor


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On Wed, 25 Oct 2000, Mark Hall wrote:

> Have you checked out the R package available from www.lib.stat.cmu.edu/R and
> its various add-on packages.  All free!
>
> Best, Mark Hall

The "spatial" package can be used (Venables & Ripley, MASS 3rd
edition; package in the VR bundle on CRAN:

> x <- runif(100000)
> y <- runif(100000)
> z <- 5*x + 3*y + 0.5*x*y + 1*x*x + 1.5*y*y + rnorm(100000, 3, 2)
> summary(z)
    Min. 1st Qu.  Median    Mean 3rd Qu.    Max.
  -4.119   5.855   7.915   7.965  10.040  21.110
> library(spatial)
> tr2 <- surf.ls(2, x, y, z)
> str(tr2)
List of 11
  $ x   : num [1:100000] 0.111 0.793 0.581 0.868 0.254 ...
  $ y   : num [1:100000] 0.7505 0.7083 0.3539 0.0571 0.1982 ...
  $ z   : num [1:100000]  2.12 12.15  8.04  5.71 -1.65 ...
  $ np  : num 2
  $ f   : num [1:600000] 1 1 1 1 1 1 1 1 1 1 ...
  $ r   : num [1:21] -3.16e+02 -3.67e-01 -1.82e+02 -1.05e+02 -7.89e-03 ...
  $ beta: num [1:6] 7.753 3.101 0.273 2.376 0.127 ...
  $ wz  : num [1:100000] -4.620  1.400  0.449 -2.569 -6.682 ...
  $ rx  : num [1:2] 6.04e-06 1.00e-00
  $ ry  : num [1:2] 2.71e-05 1.00e-00
  $ call: language surf.ls(np = 2, x = x, y = y, z = z)
  - attr(*, "class")= chr "trls"
> trsurf2 <- trmat(tr2, 0, 1, 0, 1, 100)
> image(trsurf2)
> contour(trsurf2, add=T)
> tr3 <- surf.ls(3, x, y, z)
> image(trsurf2)
> contour(trsurf3, add=T)

However, R does all its work in memory, so I needed a heap size of 32M to
complete the quadratic trend, and over 40M for the cubic. If this is OK,
then the surf.ls() function and trmat() to generate predictions will do
what you need. If you need predictions for other points than a grid over
your study area, you need to look at the way trmat() works - ask if you
need help.

Best wishes,

Roger

>
> ----- Original Message -----
> From: "Burnett, Mark" <MBurnett@...>
> To: <ai-geostats@...>
> Sent: Tuesday, October 24, 2000 10:31 PM
> Subject: GEOSTATS: Trend Surface Analysis software
>
>
> > Hi  All
> >
> > Could someone please advise me on a decent share/free ware package that
> has
> > the ability to run various forms of trend surface analysis on large data
> > sets (100 000+) e.g. residual, polynomial etc. (URL site for download
> would
> > be appreciated), and contour the data set afterwards.
> >
> > The current software that I am using does not have this functionality
> built
> > in and I want to run a number of checks on various parameters that I have
> in
> > the data set.
> >
> > Thank you
> >
> > Mark Burnett
> > Evaluation Manager
> >
>

--
Roger Bivand
Economic Geography Section, Department of Economics, Norwegian School of
Economics and Business Administration, Breiviksveien 40, N-5045 Bergen,
Norway. voice: +47 55 95 93 55; fax +47 55 95 93 93
e-mail: Roger.Bivand@...
and: Department of Geography and Regional Development, University of
Gdansk, al. Mar. J. Pilsudskiego 46, PL-81 378 Gdynia, Poland.

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Thank you very much.

Your suggestion will be a way for my action.
My message it was already in ai-geostats mail list
and I hope to receive an advice from another
people.

Thank you again.

George Tudor


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If you guys are that desperate I published a program
in Computers and Geosciences in 1977 (I think). The
reference will be in
http://uk.geocities.com/drisobelclark/resume/publications.html

It was called SNARK and was for 3-d data.

Trend Surface Analysis is basically just ordinary
least squares. Any stat package which does least
squares regression should do all the relevant tests as
well.

The `theory' of PTSA and Analysis of Variance testing
is in Practical Geostatistics 2000, Chapter 7.

If you are willing (or allowed) to share your data
with the world, contact me and I'll turn it into a
valid file for the free 'book' software

http://uk.geocities.com/drisobelclark/PG2000_demo.html

Isobel Clark
+27 11 726 3729

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On 26 Oct 2000 08:25:06 EDT Patrick.J.Doran@... (Patrick J.
Doran) writes:

Consider looking at the paper:
Englund, E.J. 1990. A Variance of Geostatisticians. J. Math. Geology.
vol. 22, no. 4, pp. 417-455.
The paper describes an experiment in which 12 geostatisticians analyzed
the same data set, and then the results were compared on over a dozen
measures of estimation quality.  You might find some ideas in the
different measures of estimation quality. Moreover, you might see that
such a comparison would be highly dependent on the methods used to
interpolate values.

Charlie Kufs

~~~~~        TERRABYTE CORPORATION
~~~~~        Statistics, Data Mining, and Modeling
~~~~~        Applied to Solving Environmental Problems
~~~~~        http://terrabyte.ws
~~~~~        terrabyte@...

________________________________________________________________
YOU'RE PAYING TOO MUCH FOR THE INTERNET!
Juno now offers FREE Internet Access!
Try it today - there's no risk!  For your FREE software, visit:
http://dl.www.juno.com/get/tagj.
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2th Oct., 2000

Dear Dr Isobel Clark,

Thanks for your advice on iron ore deposit.  I have a further quiery
to you on the same subject.

You may appreciate that when we take samples (let us say 3m length)
along the vertical boreholes for each 12m bench height, different
ore types with varying lengths willb e encountered. In such a case,
when the mid-slice plans are prepared, usually the maximum length of
ore (core length) is designated in the slice plans. When the variogram
has to be calculated for 12m samples how to composite the radicals
for a given ore type?  if all the samples falling within 12m bench
height are taken for compositing, then the sample assay value don't
truly represent the designated ore type in the slice.

I seek your advice on this please.  You may please note that I do not
have access to internet at my place of work, which is definitely a
constraint in reviewing the published literature.


Dr P.V. RAO
Dy. Divisional Manager (planning)
Tata Steel, India
----------------------------------------------------------------------


On Thu, 26 Oct 2000, [iso-8859-1] Isobel Clark wrote:

> Dear Dr Rao
>
> How lovely to hear from you.
>
> In dealing with an area with several sub-populations
> of different geology, it is always best to use only
> the samples of the relevant geology.
>
> It would improve the estimation further if you can:
>
> (a) produce a semi-variogram model for each ore type
>
> (b) allow for the skewed nature of the data by using
> (say) a modified lognormal transformation.
>
> We have followed this pattern successfully in iron ore
> deposits in South Africa and in the USA.
>
> Let me kno wif I can be of any more help. Perhaps you
> would also like to visit our 'professional' Web pages
> at http://www.stokos.demon.co.uk
>
> With best regards
> Isobel Clark
>
>
>
> ____________________________________________________________
> Do You Yahoo!?
> Get your free @yahoo.co.uk address at http://mail.yahoo.co.uk
> or your free @yahoo.ie address at http://mail.yahoo.ie
>

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DEAR ALL,
This is a provisional summary of the help I received in response to my
question a few weeks ago on non-colocated datasets.  As is customary, I
apologise to correspondents if I have failed to understand or express
important points.  I still have at least as many questions as before, hence
I would be grateful if anyone has further suggestions.

Sections of this summary:
  MY ORIGINAL QUESTION
  CLARIFICATION
  BASIC QUESTIONS
  ADVICE SO FAR
  REMAINING OBSTACLES

MY ORIGINAL QUESTION
> I'm an ecologist with an interest in wildlife disease epidemiology.  I
have
> two unique datasets representing indices of occurrence of the same disease
> in two species, both highly mobile terrestrial mammals.  Visually (in
> postings) the two maps are convincingly similar - i.e. these data are
> ecologically very interesting indeed!  I want to test the spatial
> correlation between the two datasets, because it's likely that one species
> is the reservoir infecting the other.
>
> My problems fall into two categories:
>
> (1) Spatial autocorrelation
>
> A logical first step would seem to be to test whether each dataset is
> spatially autocorrelated.  This seems likely when one examines the
postings,
> but semivariograms suggest that a sill is very quickly reached (at about
20
> km), a distance that seems improbably small as we are dealing with highly
> mobile mammals and epidemics that look to be 100-200 km across.  In both
> datasets, the variogram value is thereafter highly variable with
increasing
> distance, and there is some suggestion of an oscillating 'hole effect'.
> However, as distance increases the variogram is clearly being influenced
by
> the shape of mainland Britain, and the timid faith I have in the variogram
> at small h falls away rapidly as h increases.  For instance, a location in
> south-west Wales is very close to north Cornwall for a bird (by Euclidean
> distance), but quite far away for a terrestrial mammal that must travel by
> land around the Severn estuary.
>
> A further consideration, if I have correctly understood the meaning of
> stationarity, is that both datasets have an underlying trend, with values
> increasing from west to east and north to south.  Despite having read at
> length in the AI-Geostats archives, I am still unsure how to deal with
this
> in practical terms.
>
> For each species alone, the variogram is theoretically of tremendous
> interest.  How local are the epidemics?  How close must an epidemic be
> before a given animal is at risk?  Is there genuinely a rippling effect
> surrounding a disease epicentre?  Unfortunately, from the outset there
seems
> to be a discrepancy between the variogram and my eye.  I am a sworn
disciple
> of objectivity, but I'm not yet convinced that my variogram is doing the
> right thing.
>
> (2) Sampling locations and correlation between the datasets
>
> Both datasets cover the whole UK (including some islands, which are easily
> and logically excluded), but originate from two populations of people
> (hunters and veterinarians) with necessarily different geographical
> distributions - i.e. they are not colocated.  I could convert both
datasets
> to a common regular grid, but this involves interpolation, a number of
> assumptions, and the creation of quite a few new grid locations that have
NO
> data from one or both dataset(s).  If I did convert to a common grid, I am
> then at a loss to know how to proceed further.  The two datasets do not
have
> similar underlying distributions.  One is an incidence (count of diseased
> animals per unit effort), and is easily normalised by a log
transformation.
> The other is a measure of prevalence, with many essential (meaningful)
zeros
> that make transformation awkward and perhaps undesirable; these prevalence
> data can also be weighted by the sample size on which each is based.
>
> Please can anyone suggest a route forward?  I have read (all the easy
words
> in) quite a number of textbooks.  So far as I can judge (I pull up all too
> soon), most books stop short of problems like this because no
> self-respecting miner would burden himself by collecting data so
awkwardly.
> For me, this is a crude pilot study, hence a stratified sampling programme
> to test a hypothesis will be the next stage IF I can formalise the
> correlation that looks so blindingly obvious to the naked eye.  So please
> don't suggest I do my sampling differently..................


CLARIFICATION
I should have explained better what the two datasets (each located by x,y
coordinates) are:

(1).  Prevalence of an infectious disease among wild animals shot (randomly)
by hunters operating within small areas. These data were collected from the
hunters as a percentage (based on recollection of the preceding 12 months),
but we also know the sample size (i.e. the experience) on which this is
based - this could be used to weight values.

(2).  Numbers of domestic dogs with the same disease presented at veterinary
surgeries.  As we don't know the population of dogs from which these
infected dogs are drawn, these data represent 'incidence' rather than
'prevalence'.  One must assume either that veterinary practices saturate the
landscape so that they all draw on similar sized populations of dogs; or
alternatively that time constraints mean that individual vets tend to deal
with similar numbers of dogs (I have eliminated vets who do deal only with
farm animals).

NB:
Neither dataset is normal.  Both can be made approximately normal by
transformation, but the many zeros (dataset 1) and very low values (dataset
2) are essential features of the data, so I am loathe to do this.
The two datasets are not co-located.  This is inevitable because hunters and
vets occupy such different niches.
Data are not evenly spread in x,y space.  The vets data (2) in particular
are highly clumped.  Combining values within cells of a superimposed grid by
averaging (1 and 2) or possibly summing (2) seems conceptually OK to me, but
conversion to a grid loses some of the spatial information present; except
on a very coarse grid it also creates a fresh problem of grid cells in which
one or both data sets are missing.


BASIC QUESTIONS:
A. How is the likelihood of disease at location x,y related to the
likelihood of disease in the same species at increasing distance h?  This is
a really matter of descibing the epidemiology in spatial terms.

B. How is the likelihood of disease at location x,y related to the
likelihood of disease in the other species at increasing distance h?  A
convincing preliminary to this would be to show that the spatial pattern of
the disease is broadly similar in the two species. I suppose I mean by this
that regression-style modelling is attractive, but simple correlation
between the two datasets would be a huge step forward.


ADVICE SO FAR:
Softly, softly
Steve Rushton suggested that the analysis should begin with as little
modelling as possible (I approve the sentiment of this softly-softly
approach because I mistrust the strings of arbitrary choices apparently
involved in modelling), for instance through a randomisation test or a
Mantel test.  The Mantel test, because it operates on matrices, may allow me
to utilise an overland distance matrix (see below) - I need to do some more
reading here.  However, I'm dubious about randomisation tests, as it seems
to me that neither of my datasets fulfills the assumption of independence
(data are constrained by the mobility of the disease organism and its hosts,
and by the underlying distributions of hosts and recorders in Britain).

Deriving and interpreting variograms.
Donald Myers and Klemens Barfuss favoured detrending the data by fitting an
x,y plane and working with the residuals only.  Brian Gray pointed out that
some authors caution against this, arguing that small- and large-scale
trends should be modelled together, but that he personally would suggest the
detrending approach (at least in my case?).  On logical grounds, I favour
detrending, because prior knowledge shows that there are underlying
large-scale trends in the distribution of hosts that one would wish to
remove so far as possible.
It occurred to me (confirmed by Brian) that the calculation of residuals
could proceed by Generalised Linear Modelling, which would take due account
of the non-normal distribution of each dataset.  Fitting a simple
first-order Euclidean x,y plane to either data set using GLM explains a
large proportion of the variation.  We then corresponded about how the
residuals would be distributed after GLM.  Surely residuals of a Poisson
distributed variable would also be Poisson distributed?  Can one 'unlink'
mean and variance by such a process?  Should one transform the residuals?
Which residuals (natural, standardised, Pearson, deviance - there is
probably a confusion of terms here) should one use?  I still don't know the
answer to all this.
Suggested literature:
Gumpertz, ML, et al. (2000)  Logistic regression for Southern Pine Beetle
outbreaks with spatial and temporal autocorrelation.  Forest Science
46:95-107  [THIS IS A MARVELLOUSLY CLEAR PAPER FROM WHICH I HAVE LEARNED A
GREAT DEAL -   THOROUGHLY RECOMMENDED.  However, it deals with a binomial
event, not with count data as in my case, so the detailed methodology is not
applicable.]
Gotway and Stroup (1997) A generalized linear model approach to spatial data
analysis and
prediction, JABES 2:157-178

Discovering the limits of dry land
Steve Rushton favoured my proposal to calculate overland distances to use as
h values.  Manifold v. 4.5 or later offered a simple means to do this.  The
advice was: choose the origin and spacing of your analysis grid (perhaps
need to try several alternatives). Superimpose a grid of points, and build a
nearest neighbour network through these.  Calculate the shortest path
through the network for each pair of points.  Speed of calculation and
accuracy of path length estimation are conflicting aims determined by grid
spacing.  In practice this procedure did not achieve what I wanted. On the
other hand, I think I can write a solver in Manifold to accomplish what I
want. (See www.manifold.net for details of the package.  This company has a
genuinely helpful and FAST technical advice service by email.  The Manifold
package is astoundingly cheap, and it excels in solvers and custom
programming potential.  Despite being an already experienced MapInfo user, I
found Manifold very exciting as a means to prepare data for analysis.)
Steve suggested Floyd's Shortest Path algorithm, which achieves much the
same thing; but for a complex shape like mainland Britain and thousands of
data points it promised too much initial work coding the data.
Using overland distances as the basis for calculating spatial statistics
appears to require me to write my own code to calculate those statistics.  I
am a GenStat user, not SPlus or SASS - but can anyone tell me of clever ways
that allow the use of distance look-up tables in any common package?

Analysis dendrogram
A common feature of advice seems to be to try things two or more ways and
see which works best.  (Perhaps one should say, see how different the
results are.)  Given the number of technical issues here (grid origin, grid
spacing, with and without detrending, different types of residual, with and
without transformation, lag distance, tolerance, etc, etc) a tree of
alternative approaches arises and objectivity seems to recede rapidly.  Are
we looking to see which answer best fits our preconceptions?  This was one
of my original worries about variogram modelling and kriging (see Charles T.
Kufs posting today!), but I now see that it applies to other analytical
decisions too.  Will geostatisticians in due course be able to recommend
objective routes through this branching maze?



REMAINING OBSTACLES:
I am still seriously hung-up over the following, and would much appreciate
further advice:
1.  How to incorporate spatial correlation within and between datasets into
GLM.  Advice in practical terms if possible.
2.  How to calculate semi-variogram and/or correlogram statistics using a
matrix of overland distances.  [This must surely be   a common problem?  How
many study areas are uniform and rectangular?]
3.  Is it technically correct to calculate the semi-variogram on residuals
(of any kind) from a GLM?


With gratitude to all who responded!

Jonathan Reynolds


Dr Jonathan C Reynolds
The Game Conservancy Trust
Fordingbridge
Hampshire  SP6 1EF
UK

tel: +44 (0)1425 652381
FAX: +44 (0)1425 651026
email: jreynolds@...
website: www.gct.org.uk/index.html

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> Thanks for your advice on iron ore deposit.  I have
> a further quiery to you on the same subject.

The semi-variogram should always be calculated on your
basic core section length. Represent a block
(discretisation) by four 'points' in the vertical
direction when it is estimated. All software which
does block estimation should allow you to specify the
number of points in each direcion.

If you have more than one type of ore in a particular
block, the most reliable process is as follows:

(1) krige a value for that block for each ore type
which is present, using only the samples from that ore
type.

(2) use an indicator to krige the proportion of the
block in each ore type. For example, if you have two
ore types, each intersection with ore type A sould be
given a value of 1. Intersections with B should be
given a value of 0. Semi-variograms can then be
constructed on these indicator values and the kriging
result will be an estimated proportion of the block
which is in type A.

If you have more than two ore types, you can start
with A being 1 and all others 0. Then you remove the A
samples, call B 1 and the others 0. This is often
called multiple nested indicators.

We have used this successfully in ore deposits with
several mineralisation types which cannot be separated
geographically.

If (as with other iron ore mines I know) your software
is only operating in two dimensional slices, you can
approximate the best answer by compositing only within
the specific ore types and weighting by length or
physical weight, in the same way that South African
gold miners do with 'accumulation' values in reef
deposits.

I hope this helps. Indicator kriging is illustrated in
Practical Geostatistics 2000, in Chapter 12.

Isobel Clark






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Jonathan

I haven't had time to go through your extensive e-mail
in detail, but here are a couple of thoughts to be
going on with:

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

simple correlation: if you calculate the
non-co-located semi-variogram (or covariance function)
the apparent nugget effect is a direct estimate of
what the correlation between the two variables would
be if you had them co-located. This allows for the
spatial 'auto-correlation' as well as statistical
correlation. I (personally) favour a rank transform as
this is a well established way of finding a
correlation for non-Normal data.

With a rank transform, your zeroes would be given
arbitrary (randomised) ranks and you could do a few
repeats to see if this makes a lot of difference.

References for MUCK can be found at
http://uk.geocities.com/drisobelclark/resume/publications.html

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

Some packages (including EcoSSe) define 'distance' in
a specified module which is used by all of the
routines. This module can be replaced to allow the use
of an algebraic function of look up table for
distances. All routines then use that definition
instead of Euclidean distance.

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

Technically constructing a semi-variogram or other
spatial dependence analysis on the residuals from a
GLM (trend) surface is incorrect. However, we have all
been doing it very successfully for almost 30 years,
so I wouldn't worry about it over muchly. cf.
Practical Geostatistics 2000, Chapter 12.

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

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> Hi.  what is MUCK?  I couldn't access the
> publications section of your web
> page.  thanks.  Brian Gray
Deepest apologies. I was unaware that the geocities
sites were case sensitive!! Link is:

http://uk.geocities.com/drisobelclark/resume/Publications.html

Just when I think I've mastered this Web stuff it
turns around and does something different! You can get
there and to my other pages from the base home page

http://uk.geocities.com/drisobelclark

Back in 1985 or so, when Bill Harper and I invented
non-co-located kriging we didn't know that was what we
were supposed to call it. At the time there was a joke
going round the community about the excessive use of
intials (IK, OK, DK, SK and so on) and there was a
rumour that someone was out there looking into Fuzzy
Universal Co-Kriging (work it out). To distinguish our
approach from the traditional co-kriging, we called it
Multivariable Universal Co-Kriging (MUCK).

The major difference between MUCK and traditional
co-kriging is simply in the definition of the
semi-variogram. We could not use the traditional
approach because we were looking at pressure heads in
water wells in two different aquifers. From the two
surfaces kriged individually, we could see that the
pressure surfaces were highly related. However, we
could not get a semi-varogram which demanded both
measurements at the same location. So we invented the
other one. For a more formal coverage, check out the
relevant section in Noel Cressie's book where he gives
the non-co-located as the standard approach and the
co-located as a historical background.

The kriging equations remain the same. The major
differences are these:

(a) you can use all of your data all of the time to
estimate the semi-variogram

(b) you get a positive definite shape like a normal
semi-variogram. there is no possibility to get
negative values as with the traditional one

(c) the intercept (nugget effect) is directly
analagous to the correlation coefficient which you
woul dget for co-located pairs

The drawbacks are:

(1) if the two measurements are of wildly different
scales, any structure in the semi-variogram would be
masked (same as with all covariance approaches)

(2) the difference between the means of the two
variables is a factor in the MUCK approach. We did not
have this problem in our application, because both
surface had a high degree of trend which had to be
removed, leaving the average for both variables
(residuals) as zero.

Both of these problems can be solved by using a
standardisation (say Normal score) or rank transform
on all of the variables. This will give the correct
model for the semi-variogram (theoretically) which can
then be scaled if necessary or desirable. In the
statistical world an auto-correlation approach such as
this is always given as preferable to a co-variance
approach such as that generally used in kriging.

Does this help?
Isobel Clark


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Dear Dr Isobel Clark,

It seems I am learning more now than what I could do sofar through reading
books/ periodicals. Thanks for your kind response.

I ahve to querries to make:

1)  What is "Practical geostatsics 2000?" Is it a book published by you?
May I have the details of it please? I stay, first of all in India and
then in a remote place like Noamundi (75 year old iron ore mine producing
over 6 mtpa!) where access to internet and other modern means of
communications are yet to be made available.

2) When the directional variograms are made, one finds that sill value
do not reach the total variance of the smaples. Even then, when the
variogram parameters are used in kriging, we try to nullify the
variation in range by giving anisotropy factors in 3 dimensions. However,
the same is not accomodated for sill value in different directions as
there is provision to give only one C0 and one C1 value unless we have
nested variograms.

I hope I could explain my query.

3) Madam, will it be possible to share your worked out examples on
indicator kriging on iron ore deposits?

Thanks

P.V. Rao
---------------------------------------------------------------------
On Fri, 27 Oct 2000, [iso-8859-1] Isobel Clark wrote:

> > Thanks for your advice on iron ore deposit.  I have
> > a further quiery to you on the same subject.
>
> The semi-variogram should always be calculated on your
> basic core section length. Represent a block
> (discretisation) by four 'points' in the vertical
> direction when it is estimated. All software which
> does block estimation should allow you to specify the
> number of points in each direcion.
>
> If you have more than one type of ore in a particular
> block, the most reliable process is as follows:
>
> (1) krige a value for that block for each ore type
> which is present, using only the samples from that ore
> type.
>
> (2) use an indicator to krige the proportion of the
> block in each ore type. For example, if you have two
> ore types, each intersection with ore type A sould be
> given a value of 1. Intersections with B should be
> given a value of 0. Semi-variograms can then be
> constructed on these indicator values and the kriging
> result will be an estimated proportion of the block
> which is in type A.
>
> If you have more than two ore types, you can start
> with A being 1 and all others 0. Then you remove the A
> samples, call B 1 and the others 0. This is often
> called multiple nested indicators.
>
> We have used this successfully in ore deposits with
> several mineralisation types which cannot be separated
> geographically.
>
> If (as with other iron ore mines I know) your software
> is only operating in two dimensional slices, you can
> approximate the best answer by compositing only within
> the specific ore types and weighting by length or
> physical weight, in the same way that South African
> gold miners do with 'accumulation' values in reef
> deposits.
>
> I hope this helps. Indicator kriging is illustrated in
> Practical Geostatistics 2000, in Chapter 12.
>
> Isobel Clark
>
>
>
>
>
>
> ____________________________________________________________
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Hi all,

I am very new to spatial statistics and I have the following problem:
I have an Arc/INFO coverage with two roads: one is from the existing road
network and the other one is the same road modelled with a road modelling
software.
How can I assess the spatial correlation between these two representations
of the same road ?

Thank you,

Ionut

Ionut Aron, MF Candidate
Forest Resources Management
Forest Sciences Centre
2045-2424 Main Mall
University of British Columbia
Vancouver, BC., Canada V6T 1Z4
Telephone: (604) 822-4148



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Hello,

I am interested for collaborations or jobs in
geoinformatics (GIS, geostatistics, geomathematics,
databases, programming), for projects in geological or
environmental fields.

I worked  in Romania many years in geoinformatics, to
use geomathematical and geostatistical methods for
several ores and different geological data, with
commercial, shareware and my own programs. Finally, I
learned ARC/INFO GIS on Silicon Graphics workstation.
In present, I am working as database programmer in
economical field in a private company.

For details see my home page -
www7.ewebcity.com/geoinf

Thank you in anticipation.

Best wishes,

George Tudor

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Must be a symptom of getting old, but I think we
should all say a great big thanks to Jeff Wolfe for
all the efforts over the last 5 years!

Virtual roses to Jeff and to Gregoire.............
Isobel Clark

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> How can I assess the spatial correlation between
> these two representations
> of the same road ?

If your information has the same spatial co-ordinates
in both sets, you can produce a co-located cross
semi-variogram by simply calculating the covariance
for each lag:

         (g_i  - g_j)(f_i - f_j)

where g and f are the two variables, i and j are two
locations a specified distance apart. Average over all
pairs the same distance apart and divide by two. This
is exactly analogous to calculating the covariance
between the two at that specified distance:

         (g_i - gbar)(f_j - fbar)

only you don't need the two means. If your samples are
not at the same locations you need the non-co-located
semi-variogram, referred to by some authors as a
"pseudo cross semi-variogram" and given as standard in
Noel Cressie's book. The basic form of this is

            (g_i - f_j)^2

notation as above. This assumes that the two variables
have the same mean or have been standardised somehow.

Kriging is always the same. Watch out for Volume 2 of
Practical Geostatistics -- PG2001. Lots of
explanations there.

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



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Best regards

Gregoire (Moderator of AI-GEOSTATS)

Ionut Aron <iaron@...> wrote:
> Hi all,
>
> I am very new to spatial statistics and I have the following problem:
> I have an Arc/INFO coverage with two roads: one is from the existing road
> network and the other one is the same road modelled with a road modelling
> software.
> How can I assess the spatial correlation between these two representations
> of the same road ?
>
> Thank you,
>
> Ionut
>
> Ionut Aron, MF Candidate
> Forest Resources Management
> Forest Sciences Centre
> 2045-2424 Main Mall
> University of British Columbia
> Vancouver, BC., Canada V6T 1Z4
> Telephone: (604) 822-4148
>
>
>
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Gregoire Dubois
Institute of Mineralogy and Petrography
Dept. of Earth Sciences
University of Lausanne
Switzerland

Currently detached in Italy

http://www.ai-geostats.org

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Thanks for all the kind words folks.
It has been very enjoyable to work with Gregoire to povide the list service
to all of you.


-Jeff

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