- Oct 24, 2000Dear Dr. Sandefur:

I thought about this problem quite a bit for work with finite populations

(lake and stream survey data that had a stratified random sampling design).

I don't think including sample weights as you have is valid (i.e, it won't

give the optimal solution). The point is, you don't know where the other

members of the population represented by the weight on a particular sample

are geographically. We found two solutions.

In one paper, we cokriged to estimate for a finite population of stream

nodes from a unequal-probability sample of nodes. Here we didn't make

any use of sample weights and compared population estimates obtained from

a Horowitz-Thompson estimator to those obtained by cokriging, which brought

in ancillary spatial information (elevation).

In another paper, we kriged by stratum (see the report on Pattern-plus

on my webpage). This means calculating separate variograms, etc.

I never finished, but I was working on creating a full variance-

covariance matrix by assuming that the strata had different sills (total

variances) but the same model form and nugget. The sample data can

then be standardized to have the same diagonal (sill) and the VC matrix can

be filled with entries from the standardized variogram (correlogram).

Then it should be possible to krig the whole system together and back

transform to get the final interpolated estimates. This should work

if you have samples that belong to sub-populations that differ in their

means and variances, but not the degree of autocorrelation. I have a FORTRAN

program written to do this that I've never gotten around to debugging, if

anyone wants to take it on :-).

Good luck, and I'd like to hear about it if you find another solution.

Yetta

At 06:27 AM 10/24/00 -0700, you wrote:>Hi-

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

>

> Suppose I have some spatial samples with weights (w1 w2 ....)>

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

> Answer=>

unreasonable results e.g.

>I get I some cases (zero nugget variogram and some 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

>V1 w1 wk1

>30 .1 1.2

>50 .9 -.2

> answer=90

>

>Unreasonable results are a well known result with negative weights>

WITHIN the kriging equations something like:

>My guess is that the sample weights should be coupled> w1w1Gamma11 w1w2Gamma12 ..... .....

1 wk1 w1Gamma1b> w2w1Gamma21 w2w2Gamma22 ..... ....

1 wk2 = w2Gamma2b>

...... ...... ..... ..... 1 .. .....>

1 1 ..... ......0 mu 1>

would like input on

>Before I work thru the math for my guess and code a solution I> 1) Has this problem been solved before?

solution available (3d preferred)

> 2) Is a C or Fortran or public .exe version of the>

ai-geostats@....

>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

>

>

>

>

>--

>*To post a message to the list, send it to>*As a general service to list users, please remember to post a

summary>of any useful responses to your questions.

and

>*To unsubscribe, send email to majordomo@... with no subject>"unsubscribe ai-geostats" in the message body.

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

>

------------------------------------------------------

Yetta Jager

Environmental Sciences Division

Oak Ridge National Laboratory

P.O. Box 2008, MS 6036

Oak Ridge, TN 37831-6036

U.S.A.

OFFICE: 865/574-8143

FAX: 865/576-8543

Work email: jagerhi@...

Home email: hjager@...

WEBpage: http://www.esd.ornl.gov/~zij/

-----------------------------------------------------

- << Previous post in topic Next post in topic >>