- Andrew Lister wrote:
>1. stationarity of the data: I have read a number of articles in the

some

>ecology and agronomy literature discussing this concept, and have read

>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,

and

>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,

>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

what

>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

>I read)?

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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DO NOT SEND Subscribe/Unsubscribe requests to the list! > > Bharat Lohani wrote:

I suggest that you look at the Approximate Nearest Neighbors (ANN)

> > 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>

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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DO NOT SEND Subscribe/Unsubscribe requests to the list!- 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

(easy reading please!)

3. What about Kriging? I know nothing about it yet, but is it worth

exploring?

Many thanks,

Edith

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