Dear Reza:

I can recommend:
Jensen, J.L., Lake, L.W., Corbett, P.W.M. & Goggin, D.J.: "Statistics for
Petroleum Engineers and Geoscientists", Elsevier

Good engineering view on (geo)statistics.

Regards,
Tomislav

-----Original Message-----
From: Reza Nazarian [mailto:rnazarian@...]
Sent: Friday, August 05, 2005 3:12 PM
To: ai-geostats@...
Subject: [ai-geostats] Need Your Advises on Books



Dear Experts
I am going to order some Geostatistical Books. I need them for self
training and need to contain numerical examples and practices. I have
already ordered Practical Geostatistics written by Isobel Clark. It would
be highly appreciated.
if you could please advise me more specially on books with trend in Oil
Reservoir.
Waiting for your suggestions.
Very Best Regards
Reza Nazarian
Geophysicist

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Perry Collier

Senior Mine Geologist
Ernest Henry Mine  
Xstrata Copper Australia
( (07) 4769 4527
4  (07) 4769 4555
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Hi!
I need to generate a number of correlated gaussian random fields to be able to gradually deform them later.
I can do this through the RandomField package in R-software, by specifying my correlation length and sill (no nugget effect),using for example, a spherical variogram model.But does anyone know what is behind the RandomField package or how to introduce a certain theoretical variogram onto the Gaussian White noise field to make it correlated.

Thank you! :)

Iryna Petrovska,
____________________________________
PhD student
Earth Science and Engineering Department,
Imperial College London

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-----Original Message-----
From: PCollier@... [mailto:PCollier@...]
Sent: 06 August 2005 05:50
To: ai-geostats@...
Subject: [ai-geostats] Calculation of fields in models

Hi list

 

I would appreciate some feedback on standard/common practice for calculation of fields in models.

 

eg:

 

If I interpolate X and Y in my model from X and Y data (eg: drill holes), and I ultimately want Z = X + Y, what is the difference between calculating Z = X + Y in samples and then interpolating Z versus calculating Z AFTER X and Y have been interpolated (besides the obvious potential change in spatial characteristics of the variable)...?

 

Cheers

Perry

 

 

Perry Collier

Senior Mine Geologist
Ernest Henry Mine  
Xstrata Copper Australia
( (07) 4769 4527
4  (07) 4769 4555
* PCollier@...
" http://www.xstrata.com
 
PO Box 527
Cloncurry QLD 4824
Australia
 
"Light travels faster than sound. That is why some people appear bright until you hear them speak"

 

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Dear Experts
I am going to order some Geostatistical Books. I need them for self
training and need to contain numerical examples and practices. I have
already ordered Practical Geostatistics written by Isobel Clark. It would
be highly appreciated.
if you could please advise me more specially on books with trend in Oil
Reservoir.
Waiting for your suggestions.
Very Best Regards
Reza Nazarian
Geophysicist

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Perry Collier

Senior Mine Geologist
Ernest Henry Mine  
Xstrata Copper Australia
( (07) 4769 4527
4  (07) 4769 4555
* PCollier@...
" http://www.xstrata.com
 
PO Box 527
Cloncurry QLD 4824
Australia
 
"Light travels faster than sound. That is why some people appear bright until you hear them speak"

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Hello list

Can you help me with references about:

the minimum sample size necessary to use kriging, 

the best interpolator when the data have particular abbundance or lack of foraminifera species (example; 1, 4, 5, 12, 30, 50).

 

Thanks in advance for your help

ines

 

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

From: Ines

To: ai-geostats@...

Sent: Wednesday, August 03, 2005 4:39 AM

Subject: [ai-geostats] min sample size

Hello list

Can you help me with references about:

the minimum sample size necessary to use kriging, 

the best interpolator when the data have particular abbundance or lack of foraminifera species (example; 1, 4, 5, 12, 30, 50).

 

Thanks in advance for your help

ines

 

---

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hello

how  can  I visualize DEM error ?
how can I interpret whether DEM which I have created is correct ?


could you give me hints ?

regards

Ahmet Temiz

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The views and opinions expressed in this e-mail message are the sender's own
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Research Dept.
of General Directorate of Disaster Affairs.

Bu e-postadaki fikir ve gorusler gonderenin sahsina ait olup, yasal olarak T.C.
B.I.B. Afet Isleri Gn.Mud. Deprem Arastirma Dairesi'ni baglayici nitelikte
degildir.

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Dear listers,

I have a copy of Simon Houlding's Practical Geostatistics - Modeling and Spatial
Analysis published by Springer in 2000. Unfortunately the CD-ROM is missing from
the cover. Would anyone have a copy of the CD-ROM available?

Regards,

Dave



~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Dave Miller
GIS Research Assistant
The Macaulay Institute
Craigiebuckler
Aberdeen
AB15 8QH

tel: +44 (0) 1224 498200 (switchboard) ext. 2261
fax +44 (0) 1224 311556
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http://www.macaulay.ac.uk/LADSS/ladss.shtml

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Dear Digby,

In my experience, it is short for prediction error variance, i.e. the variance
of the prediction error (Z(x)-Z^(x)), where Z^(x) is the (kriging) predictor of
Z(x).

Gerard

Gerard B.M. Heuvelink
Soil Science Centre
Wageningen University and Research Centre
P.O. Box 47
6700 AA Wageningen
The Netherlands

tel +31 317 474628 / 482420
email gerard.heuvelink@...
http://www.dow.wur.nl/UK/cb/ls/sfi/sfi_alg.htm


-----Original Message-----
From: Digby Millikan [mailto:digbym@...]
Sent: woensdag 24 augustus 2005 14:08
To: ai-geostats
Subject: [ai-geostats] Prediction variance



What is prediction variance?

Digby

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What is prediction variance?

Digby

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Well, there is also a good book of Deutsch: "Geostatistical Reservoir
Modeling" (Oxford University press). Itcould be useful to pick
up Isaaks and Srivastava' book.

Bye
   S. Trevisani
At 15.12 05/08/2005, Reza Nazarian wrote:

>Dear Experts
>I am going to order some Geostatistical Books. I need them for self
>training and need to contain numerical examples and practices. I have
>already ordered Practical Geostatistics written by Isobel Clark. It would
>be highly appreciated.
>if you could please advise me more specially on books with trend in Oil
>Reservoir.
>Waiting for your suggestions.
>Very Best Regards
>Reza Nazarian
>Geophysicist
>
>
>
>
>
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>
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hello, i'm looking for a user manual of Variowin.
I know the book from Pannatier, Y., "VARIOWIN: Software for Spatial
Data Analysis in 2D," from Springer-Verlag is sold out, but i hope
someone knows a book or note-book where i can learn how to work with
variowin (without loosing hours to learn how to build a variogram, or
see which points are responsible for "bad" variograms...).
Thank you
Manuel

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-----Original Message-----
From: Harper, William V [mailto:WHarper@...]
Sent: Thursday, June 23, 2005 8:43 AM
To: Kathryn E.L. Smith; ai-geostats@...
Subject: RE: [ai-geostats] kriging with 'walls'

Kathryn,

 

We (Isobel Clark and moi) have been dealing with such for some time - especially faults.  You specify the location of the fault or shoreline and the software will not consider pairs of points in the development of the semi-variogram that are located on opposing sides of this boundary.  Likewise it is properly handled in the subsequent kriging.  But 1^st it is important to model the spatial variability structure properly prior to the subsequent estimation (kriging).  See http://geoecosse.bizland.com/softwares/ for demos to examine.  I hope this helps.

 

Best,

 

Bill

 

--

William V Harper, Mathematical Sciences

Otterbein College, Towers Hall 139, 1 Otterbein College

Westerville OH 43081-2006  USA

Office phone: 614-823-1417     Office Fax 614-823-3201

Faculty page: http://www.otterbein.edu/home/fac/WLLVHRPR

For the best in geostatistics: http://geoecosse.hypermart.net/

 

 

---

From: Kathryn E.L. Smith [mailto:kelsmith@...]
Sent: Thursday, June 23, 2005 9:31 AM
To: ai-geostats@...
Subject: [ai-geostats] kriging with 'walls'

 

Hello,
Does anyone know of a program that does kriging, but allows for 'walls' such as a shoreline or faults? ie. data points on one side of the 'wall' will not influence what is interpolated from data on the other side. I've checked into ESRI and Surfer, neither will allow you to have 'faults' or 'walls' with their kriging program. Thanks for your input!
kathryn

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Dear Reza,

the proof goes as follows:

your question: why does one set empirical variance = s^2 =
(sum(xi-xm)^2)/(n-1), where xm := sum(xi)/n  (i=1...n),
the estimated mean, is equivalent to asking: is s^2 an unbiased estimator
of the variance of the parent distribution, E(s^2) = Var(x) ?
(E = expectation value)

First, remember, Var(x) := E((x-Ex)^2) = E(x^2) - (Ex)^2.

Now, (n-1)*s^2 = sum(xi-xm)^2 = (calculate the square) =
(sum(xi^2)-sum(xm^2)) = (sum(xi^2) - n*xm^2)

Next take the expectation value of this,

(n-1)*E(s^2) = n*(E(x^2)-E(xm^2))

We know from the central limit theorem that E(xm) = E(x), and Var(xm) =
Var(x)/n. Therefore,

(n-1)*E(s^2) = n*(E(x^2) - (Ex)^2 + (Exm)^2 - E(xm^2)) ....(the 2nd and
3rd term cancel)

.... = n*((E(x^2)-(Ex)^2) - (E(xm^2)-(Exm)^2))=

= n*(Var(x) - Var(xm)) = n*Var(x)*(1-(1/n)) = (n-1) * Var(x), or

E(s^2) = Var(x)   q.e.d.


There are different (very similar) versions of this proof, this one
follows closely Roger Barlow, Statistics, John Wiley & Sons 1989 (chapter
5.2.2.),  which I find a good introduction into basic statistics.

best regards,
Peter



>Dear Experts
>> Sorry may be the question is so basic .After searching my statistics
>books
>> to find an answer with no great success, could you please explain me
>why we
>> consider degree of freedom as n-1 in calculating variance. Thanks for
>your
>> kind advises.




=================================================================
Dr. Peter Bossew
Division of Physics and Biophysics, University of Salzburg, Austria

home: A-1090 Vienna, Austria, Georg Sigl-Gasse 13/11, ph: +43-1-3177627
telefonino: +43-650-8625623
peter.bossew@...
peter.bossew@...

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Very Best Regards
Reza Nazarian
Schlumberger Information Solutions
SONILS Oil Services Centre, Porto de Luanda, Angola

(Via UK: +44 (0)207 576 6306
* rnazarian@...
http://www.sis.slb.com

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Content-type: multipart/alternative;
 boundary="Boundary_(ID_IIuAYacrun97cWTh9BuI0g)"
Content-class: urn:content-classes:message

Reza,
 
If you are just asking why n-1 in the formula commonly found in stat books for computing the sample variance s^2, it is so that we have an unbiased estimate of the population variance – look at a good calculus based probability and stat book.
 
Other estimation methods (e.g., maximum likelihood) divide by n instead of n-1. 
 
Oh, while the n-1 does make the sample variance s^2 an unbiased estimate of the population variance sigma^2, taking the square root and getting the sample standard deviation s does not result in an unbiased estimated of the population standard deviation sigma.  Another reason some prefer m.l.e.
 
Best,
 
Bill
 
--
William V Harper, Mathematical Sciences
Otterbein College, Towers Hall 139, 1 Otterbein College
Westerville OH 43081-2006  USA
Office phone: 614-823-1417     Office Fax 614-823-3201
Faculty page: http://www.otterbein.edu/home/fac/WLLVHRPR
For the best in geostatistics: http://geoecosse.hypermart.net/
 

---

From: Reza Nazarian [mailto:rnazarian@...]
Sent: Thursday, August 25, 2005 3:23 PM
To: ai-geostats@...
Subject: [ai-geostats] Why degree of freedom is n-1
 
Dear Experts
Sorry may be the question is so basic .After searching my statistics books to find an answer with no great success, could you please explain me why we consider degree of freedom as n-1 in calculating variance. Thanks for your kind advises.


Very Best Regards
Reza Nazarian
Schlumberger Information Solutions
SONILS Oil Services Centre, Porto de Luanda, Angola

(Via UK: +44 (0)207 576 6306
* rnazarian@...
http://www.sis.slb.com
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Hello Reza,
i think it is because variance needs mean to be estimated. while you
assume that every observation are i.i.d when you estimate the mean (so
you divide by n), that's not true when you estimate variance, because
1 observation depends on the mean you previously calculated (you can
get the value of any observation from your sample, knowing all others
and the mean value, right?)
hum, hope it helps.
PS: Please if i'm wrong somewhere in my explanation (i don't think so,
but...), i would appreciate comments about it. Thanks
Greetings, Manuel

On 8/25/05, Reza Nazarian <rnazarian@...> wrote:
> Dear Experts
> Sorry may be the question is so basic .After searching my statistics books
> to find an answer with no great success, could you please explain me why we
> consider degree of freedom as n-1 in calculating variance. Thanks for your
> kind advises.
>
>
>
> Very Best Regards
> Reza Nazarian
> Schlumberger Information Solutions
> SONILS Oil Services Centre, Porto de Luanda, Angola
>
> (Via UK: +44 (0)207 576 6306
> * rnazarian@...
> http://www.sis.slb.com
>
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> ( see http://www.ai-geostats.org/help_ai-geostats.htm )
>
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> Signoff ai-geostats
>
>

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This follow-up is slighlty aside the subject line of the mailing list, but
as a geologist, this is the only statistically-flavoured one I am
subscribed to. Therefore :

Federico Pardo said:
> Having N samples, and then n degrees of freedom.
> One degree of freedom is used (or taken) by the mean calculation.
> Then when you calculate the variance or the standard deviation, you only
> have left n-1 degrees of freedom.

Apart a rigorous calculation I am aware of that in this very case (cf.
Peter Bossew's contribution on the same thread, that details it), gives a
proof for this rule-of-thumb, what more or less rigourous statistical
developments gives consistance to it ?

I mean, for the empirical correlation coefficient,
rhoXiYi = SUM_i=1..N( (x_i - mx).(y_i - my) / sx / sy ) / WHAT_NUMBER
Must WHAT_NUMBER be, for a kind of unbiased estimate ("a kind of" meaning
"with some eventual Fisher z-transform"...):
* N for simplicity,
* N-2 as I have most frequently seen in books that dare give this formula
(N points, minus 1 for position and 1 for dispersion ?),
* or 2N-4 -- 2N for the (x_i,y_i), minus 4 for {mx,my,sx,sy} -- as a
strict application of the rule-of-thumb seems to suggest ?

And what about, when fitting for instance a 3-parameter non-linear
function, reducing the number of degrees of freedom, to N-3 (number of
points, minus one for each function parameter ? I have never read any kind
of explanation to support it, though it seems widely

Thanks in advance for enlightments or simply tracks for other resources of
explanations.
-- Éric L.

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David Reid
-----Original Message-----
From: Colin Badenhorst [mailto:CBadenhorst@...]
Sent: Wednesday, 31 August 2005 8:58 PM
To: ai-geostats@...
Subject: [ai-geostats] Sum of Estimates

Dear List,

 

I have a rather interesting problem with my Kriged estimates for a base metal mine. I am estimating Zn, Pb and Fe, as percentage, the sum of which should total to no more than 100% total sulphides.

 

All Zn comes from sphalerite (ZnS) at 0.671 proportion. Sphalerite SG = 3.80

All Pb comes from galena (PbS) at 0.866 proportion. Galena SG = 7.40

All Fe comes from pyrite (FeS2) at 0.466 proportion. Pyrite SG = 4.80

Total Sulphides = (Zn estimate x 1.4903) + (Pb estimate x 1.1547) + (Fe x 2.1459)

 

What I have discovered is that I have areas in which the total sulphides are greater than 100% - with very few exceptions, the total is no more than 105% total sulphide.

 

My estimation domains for Zn and Pb are well constrained and validated, and the variogram models and estimation parameters are robust, and have been tested and validated to ensure they match the geological expectations. My domains for Fe are less well constrained but the variogram models are robust, as are the estimation parameters, and these also match the geological expectation. So, at the time of the estimation, there was very little I could do to improve on these. The estimation database (composited drillhole samples) have upper data value limits (or cut-offs if you wish to use that terminology) imposed on them such that :

 

Zn > 40% is never used to estimate a block

Pb > 10% is never used to estimate a block

Fe > 46.6% is never used to estimate a block

 

Thus, there is no combination of Zn, Pb and Fe in the estimation database that totals more than 100% total sulphide

 

The areas with the anomalous (erroneous?) total sulphide summation all correlate, without fail, to areas of thick ore with very dominant pyrite content - there are individual blocks scattered across the mine that buck this trend. This leads me to suspect that the Fe estimates may be erroneous, or simply speaking, the Fe content is being overestimated, hence the total sulphide count exceeds the theoretical limit.

 

The only solution to this problem is modifying the Fe variograms and estimation parameters, but currently, in my judgment, there is nothing I can modify that would lead to better variograms or estimation parameters. Of course there may be blocks where the total sulphide is actually underestimated, but that is impossible to determine, so the overestimates may balance the underestimates in which case there is no bias, but that needs to be tested.

 

Has anyone heard of similar issues on other base metal mines? In the absence of revisiting the estimation parameters, is there anything I can do to realistically address this issue?

 

Regards,

Colin 

 

 

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-----Original Message-----
From: seba [mailto:sebastiano.trevisani@...]
Sent: 30 August 2005 18:17
To: ai-geostats@...
Subject: [ai-geostats] natural neighbor applied to indicator transforms

Dear list members

I would like to have some comments, suggestions or critics about the following topic:
building a (preliminary) local uncertainty model of the spatial distribution of discrete (categorical) variables by means of natural neighbor interpolation method applied to indicator transforms.

From my perspective, interpolating  indicator variables (well, at the end an indicator variable is the probability of occurrence of a given class) by means of a method like natural neighbor is an easy and quick way to build a (preliminary) model of local uncertainty of the studied properties, avoiding problems of order relation violations.
In my specific case I apply natural neighbor interpolation to indicator transforms representing lithological classes in the same way in which direct indicator kriging is applied. In this way, looking at the spatial distribution of the probability of occurrence of lithologies (or at the distribution of the lithological classes, if some classification algorithm is applied) I can have a first idea of the spatial distribution of lithologies. Clearly this method is utilized only as an explorative and preliminary data analysis tool.

Thank you in advance for your replies.
 
S. Trevisani

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To answer to Gregoire's question, for some comparisons between SVM and
Indicator Kriging, here is a very basic paper (from 1999):

http://baikal-bangkok.org/~nicolas/publi/acai99-svm.pdf

and a thesis chapter (chapter 6), perhaps more interesting (from 2002):

http://baikal-bangkok.org/~nicolas/cartann/these_gilardi.pdf

My personnal feeling about the distinction between using a
classification algorithm or a regression one is the importance you put
on the boundaries.
If you look for smooth boundaries, with uncertainty estimations, etc.,
then a regression algorithm (like indicator kriging) is certainly a good
approach.
Now, if you don't care much about how the categories mix together at the
interface, or if you want clear decision boundaries, then a real
classification algorithm (like SVM) is certainly a better choice.

However, it is true that many algorithms can be used in either cases,
often with a small or no modification. The best examples are the
algorithms for density estimation (RBF, Parzen Windows...).
Algorithms of the category of SVM (i.e. large margin classifiers) are
interesting for classification because they are concentrating on finding
a separation between classes, not finding the "centre" of classes. In my
opinion, the interest of this technic for regression isn't obvious...

Best regards,

Nico

Gregoire Dubois wrote:
> I recently attended a presentation about the mapping of soil properties.
> Kriging was applied and I was wondering why a regression technique was
> used instead of a classification algorithm.
> Delineating soil properties seemed to be, at first sight, a
> classification problem than a regression case. This was at first sight
> and we didn't debate much on this issue unfortunately.
> Indicator kriging (IK) is somehow a bridge between these two issues
> (regression versus classification) and its simplicity in use and concept
> makes it very attractive to solve many problems.
> Now I wonder (again) if there are some fundamental papers comparing IK
> to classification algorithms (e.g. Support Vector Machine, SVM). In the
> same way, SVM used for regression seems to be not that uncommon as well.
> So where is the borderline? When are we facing a classification problem
> and when is it a regression problem? I am not sure the borderline is
> always that obvious.
>
> I am not answering Sebastiano's mail here but would be curious to see on
> this list a debate on "regression versus classification"... I presume
> there may there some material as well regarding the issue discussed below.
>
> Best regards,
>
> Gregoire

--
Nicolas Gilardi

Particle Physics Experiment group
University of Edinburgh, JCMB
Edinburgh EH9 3JZ, United Kingdoms

tel: +44 (0)131 650 5300     ; fax: +44 (0)131 650 7189
e-mail: ngilardi@... ; web: http://baikal-bangkok.org/~nicolas

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I'm also forwarding this answer from Dr Samy Bengio who hasn't
subscribed to ai-geostats. His e-mail address is available at the end of
his e-mail.

Best regards

--
Nicolas Gilardi

Particle Physics Experiment group
University of Edinburgh, JCMB
Edinburgh EH9 3JZ, United Kingdoms

tel: +44 (0)131 650 5300     ; fax: +44 (0)131 650 7189
e-mail: ngilardi@... ; web: http://baikal-bangkok.org/~nicolas

Hello,

My own contribution to the following question:

> I recently attended a presentation about the mapping of soil properties.
> Kriging was applied and I was wondering why a regression technique was
> used instead of a classification algorithm.

It is always possible to use a regression technique to solve a classification
task, while the converse is in general much harder (although never impossible).

Now why one should use one technique instead of another is a much wider
question. First, one has to think of the criterion that is optimized by the
underlying technique and compare it to the criterion that is seeked in the
problem at hand. The better these criteria fit one to the other, the more
fitted will be the technique. For instance, using a mean-squared error criterion
when solving a classification task is not optimal, although it opens the door
to many possible techniques. For classification tasks, it is better to have
a criterion that minimizes the number of errors (if this is what is expected),
and possibly while maximizing the distance between the classes in the feature
space (the so-called margin). Hence, SVMs are a good choice for classification.

However, some regression techniques, while not minimizing the best criterion,
offers other advantages that may prove interesting for the problem at hand,
such as smoothness, stochastic training, etc.

> So where is the borderline? When are we facing a classification problem
> and when is it a regression problem? I am not sure the borderline is
> always that obvious.

The border between problems is in general obvious: is the target of
your task in N or in R ? and if in N, are the elements ordered or not? these
two simple questions decide whether it is a regression or a classification
task (although you might also have other types of tasks such as density
estimation or ranking).


> -----Original Message-----
> From: seba [mailto:sebastiano.trevisani@...]
> Sent: 30 August 2005 18:17
> To: ai-geostats@...
> Subject: [ai-geostats] natural neighbor applied to indicator transforms
>
>
> Dear list members
>
> I would like to have some comments, suggestions or critics about the
> following topic:
> building a (preliminary) local uncertainty model of the spatial
> distribution of discrete (categorical) variables by means of natural
> neighbor interpolation method applied to indicator transforms.
>
>> From my perspective, interpolating  indicator variables (well, at the
> end an indicator variable is the probability of occurrence of a given
> class) by means of a method like natural neighbor is an easy and quick
> way to build a (preliminary) model of local uncertainty of the studied
> properties, avoiding problems of order relation violations.
> In my specific case I apply natural neighbor interpolation to indicator
> transforms representing lithological classes in the same way in which
> direct indicator kriging is applied. In this way, looking at the spatial
> distribution of the probability of occurrence of lithologies (or at the
> distribution of the lithological classes, if some classification
> algorithm is applied) I can have a first idea of the spatial
> distribution of lithologies. Clearly this method is utilized only as an
> explorative and preliminary data analysis tool.
>
> Thank you in advance for your replies.
>
> S. Trevisani
>
>
>

----
Samy Bengio
Senior Researcher in Machine Learning.
IDIAP, CP 592, rue du Simplon 4, 1920 Martigny, Switzerland.
tel: +41 27 721 77 39, fax: +41 27 721 77 12.
mailto:bengio@..., http://www.idiap.ch/~bengio

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I recently attended a presentation about the mapping of soil properties. Kriging was applied and I was wondering why a regression technique was used instead of a classification algorithm.
Delineating soil properties seemed to be, at first sight, a classification problem than a regression case. This was at first sight and we didn't debate much on this issue unfortunately.
Indicator kriging (IK) is somehow a bridge between these two issues (regression versus classification) and its simplicity in use and concept makes it very attractive to solve many problems.
Now I wonder (again) if there are some fundamental papers comparing IK to classification algorithms (e.g. Support Vector Machine, SVM). In the same way, SVM used for regression seems to be not that uncommon as well. So where is the borderline? When are we facing a classification problem and when is it a regression problem? I am not sure the borderline is always that obvious.
 
I am not answering Sebastiano's mail here but would be curious to see on this list a debate on "regression versus classification"... I presume there may there some material as well regarding the issue discussed below.
 
Best regards,
 
Gregoire

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

From: seba [ mailto:sebastiano.trevisani@...]

Sent: 30 August 2005 18:17

To: ai-geostats@...

Subject: [ai-geostats] natural neighbor applied to indicator transforms

Dear list members

I would like to have some comments, suggestions or critics about the following topic:

building a (preliminary) local uncertainty model of the spatial distribution of discrete (categorical) variables by means of natural neighbor interpolation method applied to indicator transforms.

From my perspective, interpolating  indicator variables (well, at the end an indicator variable is the probability of occurrence of a given class) by means of a method like natural neighbor is an easy and quick way to build a (preliminary) model of local uncertainty of the studied properties, avoiding problems of order relation violations.

In my specific case I apply natural neighbor interpolation to indicator transforms representing lithological classes in the same way in which direct indicator kriging is applied. In this way, looking at the spatial distribution of the probability of occurrence of lithologies (or at the distribution of the lithological classes, if some classification algorithm is applied) I can have a first idea of the spatial distribution of lithologies. Clearly this method is utilized only as an explorative and preliminary data analysis tool.

Thank you in advance for your replies.

 

S. Trevisani

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Hello list

I am a PhD student looking at developing a statistical model to predict
the size-distribution of an area's oil and gas fields.

It is clear that previous investigators prefer either a Pareto power law
or a lognormal distribution to approximate field-size distributions.

The data I am using does not look like it comes from a Pareto distribution
- which I explain as being a result of undersampling - which previous
investigators have reported - that undersampling occurs because the small
fields are not sampled or recoded.  However by using basin-modelling
software to simulate oil and gas fields (for the same basin that my
discovered empirical data comes from) I notice that this sample is also
undersampled - that is fields under a certain size are not being simulated
- which is probably due to the resolution of my input data but what is
interesting is that the undersampling actually occurs throughout all the
size ranges - including the medium to larger sizes - which I would not
have expected.  Like the discovery dataset (n = 25)  the simulated dataset
(n = 140) looks like it is more from a lognormal distribution than a
Pareto distribution.

My conclusion is that without being able to say that a Pareto is better
than a lognormal and vise-versa it appears only logical to use both
distributions.

Geologically there does not seems to be a reason why a modal size (greater
than what is detectable by exploration methods) of fields should exist  -
which would be the case if the data was from a  lognormal distribution -
except if the distribution is highly right skewed (at the small field
size) and the mode is actually just below the detection of size.

Geologically there does seem reason for fields to become so small that
they become entities (that trap oil and gas)  - and this relationship may
be better approximated by a Pareto.


The Pareto and lognormal form is similar but maybe one is better to
approximate field sizes than the other.
My question is do you think a Pareto distribution better approximates an
oil and gas size distribution than a  lognormal (or vise-versa) and if so
why.


I am currently working on goodness of fit test to throw some more light on
this - but if anyone has any thing to say I'd appreciate some comments.

Thank you,

Kind regards

Beatrice

Geological and Nuclear Sciences
New Zealand
www.gns.cri.nz

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This follow-up is slighlty aside the subject line of the mailing list, but
as a geologist, this is the only statistically-flavoured one I am
subscribed to. Therefore :

Federico Pardo <federico.pardo@...> said:
> Having N samples, and then n degrees of freedom.
> One degree of freedom is used (or taken)  by the mean calculation.
> Then when you calculate the variance or the standard deviation, you only
> have left n-1 degrees of freedom.

Apart a rigorous calculation I am aware of that in this very case (cf.
Peter Bossew's contribution on the same thread, that details it), gives a
proof for this rule-of-thumb, what more or less rigourous statistical
developments gives consistance to it ?

I mean, for the empirical correlation coefficient,
   rhoXiYi = SUM_i=1..N( (x_i - mx).(y_i - my) / sx / sy ) / WHAT_NUMBER
Must WHAT_NUMBER be, for a kind of unbiased estimate ("a kind of" meaning
"with some eventual Fisher z-transform"...):
  * N for simplicity,
  * N-2 as I have most frequently seen in books that dare give this formula
(N points, minus 1 for position and 1 for dispersion ?),
  * or 2N-4 -- 2N for the (x_i,y_i), minus 4 for {mx,my,sx,sy} -- as a
strict application of the rule-of-thumb seems to suggest ?

And what about, when fitting for instance a 3-parameter non-linear
function, reducing the number of degrees of freedom, to N-3 (number of
points, minus one for each function parameter ? I have never read any kind
of explanation to support it, though it seems widely

Thanks in advance for enlightments or simply tracks for other resources of
explanations.
-- Éric L.

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