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## GEOSTATS: Re:

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• ... some ... as ... Stationarity is a property of the random function model, and not necesarily a quality inherent in the actual data. The assumption can
Message 1 of 3 , May 28, 1998
Andrew Lister wrote:
>1. stationarity of the data: I have read a number of articles in the
>ecology and agronomy literature discussing this concept, and have read
some
>conflicting things (one researcher refers to the concept of stationarity
as
>"troubling").
Stationarity is a property of the random function model, and not necesarily
a quality inherent in the actual data. The assumption can neither be proven
nor refuted. However, this does not mean that it is a trivial decision --
the
way one pools the data would have an impact on decisions made
later on in the kriging process, and could mean the difference between a
map that makes sense and a pretty - though useless - picture. Knowledge
of the underlying data (deterministic processes, experience, etc) can guide
any decision to pool data together, and even give clues to potential
inconsistencies, but an assumption remains an assumption.

>2. checking for stationarity: I just finished reading a paper by Hamlett,
>Horton and Cressie which shows some exploratory techniques for variogram
>analysis. ... Obviously, this is not literal, but nobody
>seems to say just how much change is ok for your data to be stationary,
and
>likewise with the variance.

See previous comment on assuming stationarity. Even Cressie's example
somewhere in his textbook applies two techniques to the same data, i.e.
use of a power law model and after that median polish to filter out the
trend. A cross validation exercise should give some idea of the more
appropriate model to adopt.
>3. trend removal: It's tempting just to say my data are non stationary
and
>do median polish and do my variograms with the residuals. Is this a
valid,
>albeit "black box", approach?

There are two schools of thought here. The problem is inherent in the
way residual variograms are calculated (biasedness) and used to
make predictions. Some people can't live with the bias and use
IRF-k techniques (intrinsic random functions of order k). Some just
derive a trend surface, derive the residuals, calculate the variogram,
perform a simple kriging, and then add the result back to the trend
surface. The difference here IMHO is whether you want to use a
true soup spoon or a normal spoon to eat your French onion
soup. Both can probably get the job done, but you'd probably feel
better doing the right thing by using a soup spoon.

Refer Cressie's text with some results comparing generalized covariances
visually (calculated using IRF-k) with the actual raw covariances. There
seem to be less than a perfect fit. Any automatic fitting is a tricky
process.
>4. Could I simply fit a first or second order trend surface to the data,
model
>the variogram with my residuals, krig using ordinary kriging, and then add
>the trend back in at the end as is suggested in the "final thoughts" of
>Isaaks and Srivastava's book and elswhere (unless I am misinterpreting
what
Rule of thumb is to use the highest order until you've removed the
drift component, but IMHO and practically speaking second order is about
as high as anyone would need.

Regards,

Syed

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• ... I suggest that you look at the Approximate Nearest Neighbors (ANN) algorithm available at http://www/cs.umd/edu/~mount/ANN. ANN is a test bed for doing
Message 2 of 3 , Sep 30, 1998
> > Bharat Lohani wrote:

> > Please could you help me with....
> >

> > 2. I need to carry out some neighborhood operations with the
> > data which is not in grid. This requires searching the
> > full data set (approx. 1 M points ) evertime to find the
> > points in the neighborhood of known locations. <snip>

I suggest that you look at the Approximate Nearest Neighbors (ANN)
algorithm available at http://www/cs.umd/edu/~mount/ANN. ANN is
a "test bed" for doing approximate and _exact_ nearest neighbor
(or k nearest neighbor) searches in multidimensional space....
I haven't used it, but it looks interesting.

Also consider "A Simple Algorithm for Nearest Neighbor Search in
High Dimensions" by Nene and Nayar in IEEE Trans PAMA, Vol 19, No 9,
Sept 97. I have read this article through, and the algorithm looks
to me like the correct solution for 2D problems. I plan to use it
in applications. A C++ implementation is available upon request
from the authors (?) {sameer,nayar}@....

> >
> > Thanks in advance.
> >
> > Bharat.
> > --

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• Not being familiar with landmines, other than the fact that they can maim or kill, I would wish that a bit more detail had been provided, since a majority of
Message 3 of 3 , Feb 3, 2000
Not being familiar with landmines, other than the fact that
they can maim or kill, I would wish that a bit more detail had
been provided, since a majority of the readers can come from
fields as diverse and arcane as pig husbandry and the
population control of fruit bats. To wit:

i. What is being mapped, and what is the potential impact of
such maps on, e.g. human lives, if any?

ii. What is a contaminant? How different is this from a plain
vanilla landmine? Or are they one and the same thing?

Are you trying to map the probabilities that a certain "contaminant"
can exceed a certain level at discrete points in your region of
interest? Perhaps a non-parametric method (indicator kriging) could
be of use. Or are you trying to predict the probability that a landmine
exists at a particular location (a binary on/off variable)? It is mentioned
that the populations studied can be 1000 m2 or 1 million m2. Are these
volumes of measurements? Areal expanse? What is a sample size
of nearly "100%"?

Syed

Wilkinson Ms E <E.Wilkinson@...> on 02/04/2000 12:28:43 AM

To: "'ai-geostats@...'"
<ai-geostats@...>

cc: (bcc: Syed Abdul Rahman/SINGPROD1/Landmark)

Subject:

As a new recruit in the world of Geo-statistics, I feel a bit unsure on
what question to ask first.

I am currently working on a project to evaluate the safety of landmine
fields. I am therefore mainly interested in the estimation of the completely
unknown "contamination" level of the field. The variable of interest is discrete
(landmines) and the populations I will study range from 1000 m2 to 100 million
m2.

I have approached the issue by classical random sampling methods (somehow
inconvenient, but feasible). Unfortunately, to ensure with reasonable confidence
rates of contamination as low as 10-8, I face sample sizes of nearly 100%.

What can I do? Can someone help me with the following questions:
1. How can I tackle this problem of extremely low rates of contamination?
2. Will Bayesian methods be of any use ? And what books can you recommend
3. What about Kriging? I know nothing about it yet, but is it worth
exploring?

Many thanks,

Edith

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