- Dear Koen,

> I did measure the point values in a grid in a plot/block. I don't have to

Thats my view of the forest:

> estimate them, I just need a spacially depended estimate of the whole

> plot/block variance.

>

> The problem is that I would like to automate the procedure of calculating

> that within block variance because variogram models need to be fit

> visually most of the time, wich is time consuming. When repeating

> calculations on randomized data this isn't an option. So if gamma(V,V)

> really is model property rather then a data property I have a problem...

>

> If you can see the trees for the forest, because I don't.

> Koen.

When you directly measure the mean value of blocks, with the blocks all of

equal shape B, that is nothing else than measuring points x in another random

process Y , which is related to original process Z by the simple relation

Y(x) = \int_{B} Z(x+w) dw / Area(B). (1)

But anyway that is a random process in its own right and can be handled by

ordinary pointwise geostatistics. That is in the same way true, when we have

a block approximated by datapoints:

Y(x) = 1/|B| \sum_{w in B} Z(x+w) (2)

That the variograms of Z and Y are related in the way

gamma_Y(x,x') = 1/|B|^2 \int \int gamma_Z(x+w,x'+w') dw dw'

or resp.

gamma_Y(x,x') = 1/|B|^2 \sum_{w in B} \sum_{w' in B} gamma_Z(x+w,x'+w')

stays a biproduct, which would more or less (or more less) allow to infer

gamma_Z from gamma_Y. However you don't seem to need relation. You can go

along with gamma_Y only.

The first problem is that you measure according to equation (2) but you want

to estimate according to equation (1). Anyway (2) should well approximate

(1).

The second problem is: The variogram of Y should be very smooth in the

origing, but it is most sure not Gaussian.

Gerald

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Professor als Juniorprofessor für Statistik

http://www.math-inf.uni-greifswald.de/statistik/

office: Franz-Mehring-Str. 48, 1.Etage rechts

e-mail: Gerald.Boogaart@...

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* Support to the list is provided at http://www.ai-geostats.org - If you have gridded observed data at close and regular spacing for the block, then why bother with a Gamma(V,V)? Just calculate the variance for the block directly.

On the one hand you need "a spatially dependent estimate of the whole plot/block variance" but on the other hand you want to dispense with modelling any correlation (whether variogram, or correlogram, etc) because it's "time consuming." Not sure how to tackle this one, something has to give. How about implementing an inverse distance weighting scheme to derive the within block variance instead of working with a variogram measure?

Cheers,

Syed

>> Note that gamma(V,V) is a variogram model property, not a data

--

>> property: in the figure you mention, the big dots are data points,

>> the small dots discretize the block but do not indicate observed

>> data.

>

>I know that you can discretize block estimates with a pretty good accuracy

>with a limited amount of points. But, I was convinced that I could use

>grided observed data and gamma(V,V) as an estimate for the variance within

>my grided block.

>

>To clarify,

>

>I did measure the point values in a grid in a plot/block. I don't have to

>estimate them, I just need a spacially depended estimate of the whole

>plot/block variance.

>

>The problem is that I would like to automate the procedure of calculating

>that within block variance because variogram models need to be fit

>visually most of the time, wich is time consuming. When repeating

>calculations on randomized data this isn't an option. So if gamma(V,V)

>really is model property rather then a data property I have a problem...

>

>If you can see the trees for the forest, because I don't.

>Koen.

>

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>

>

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* Support to the list is provided at http://www.ai-geostats.org > If you have gridded observed data at close and regular spacing for the

This is indeed an option and a simple one. The original sampling design

> block, then why bother with a Gamma(V,V)? Just calculate the variance

> for the block directly.

was roughly tested with a RMSE/MSE analysis. Or, taking the statistics of

all the grid data as a reference and then sampling smaller and smaller

portions of this data to get an idea of the block variance and how many

samples could suffice.

> On the one hand you need "a spatially dependent estimate of the whole

Time consuming isn't exactly bad but I think that if I have to repeat

> plot/block variance" but on the other hand you want to dispense with

> modelling any correlation (whether variogram, or correlogram, etc)

> because it's "time consuming."

fitting curves a lot of times because of the randomizations etc. Result, I

would be fitting curves more then I would like and probably is useful.

> Not sure how to tackle this one, something has to give.

Indeed, that's what I'm finding out right now. Implementing a technique in

my work that's as efficient as possible without losing to much accuracy.

> How about implementing an inverse distance weighting scheme to derive

I'll look into that...

> the within block variance instead of working with a variogram measure?

Thanks,

Koen.

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* Support to the list is provided at http://www.ai-geostats.org> ...

Hard one without the mathematical writing, I looked it up and you refer to

> gamma_Y(x,x') = 1/|B|^2 \sum_{w in B} \sum_{w' in B} gamma_Z(x+w,x'+w')

>

> stays a biproduct, which would more or less (or more less) allow to infer

> gamma_Z from gamma_Y. However you don't seem to need relation. You can go

> along with gamma_Y only.

following calculations I presume (end of the page):

http://uk.geocities.com/drisobelclark/PG1979/Chapter_3/Part2.htm

> The first problem is that you measure according to equation (2) but you

It could do the trick, but then again... as someone asked before is it

> want

> to estimate according to equation (1). Anyway (2) should well approximate

> (1).

worth the effort, considering the pretty dense sampling grid in the

plot/block maybe this isn't the best way to approach the problem!?

> The second problem is: The variogram of Y should be very smooth in the

Correct on that one.

> origing, but it is most sure not Gaussian.

Or, I've got data that is highly skewed (LAI, leaf area indexes) and other

data that isn't (that much, reflectance/albedo measurements). So getting a

variogram in the first place has horror qualities (transforming,

backtransforming and that mess) even if I do the actual fitting on all the

data from multiple plots/blocks.

Thanks for all the input,

Koen.

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