Edzer,
the kriging variance is not data-dependent, which means that, no matter how perfectly the second order assumption applies to your domain, on a point by point or block by block basis, the kriging variance cannot be used to give you confidence intervals on individual estimated points.
The reason is that, for most variables, the estimation error is dependent on sample values, a property called heteroscedasticity; the only exception is if the errors are Gaussian.
Using the KV to provide local uncertainties (point-by-point) can only be done if the error distribution is homoscedastic,a property that only the Gaussian dist. has; in practice, error distributions tend to be far from Gaussian, even if the original variable
is quasi-Gaussian at the univariate (histogram) level.
In cases where you averaging up your points to large (very large) blocks, then the use of the KV becomes
more acceptable (realistic) because the Central Limit Theorem will help in making those errors "more" Gaussian-like.
Hope this helps,
Regards,
Mario
"Edzer J. Pebesma" <[EMAIL PROTECTED]> wrote:
Dear Kerry and Gustavo,
The kriging variance is a perfect measure for estimation uncertainty as
long as a second order stationary model is a good representation of the
data under study. Obviously, if variability and/or spatial correlation
varies over the field of interest and you have sufficient data to
characterize this, or e.g. do a non-linear transform such as a
log-transform to correct for a proportional effect, than you can and
will do better when taking this into account.
In my opinion papers such as those by Journel and Rossi have
over-shouted their point, and have ignored that for many cases a second
order stationary random field is a suitable model, if not the only possible.
The argument that after rejecting the kriging variance, conditional
simulation is suddenly needed as the solution get some measure of
uncertainty is invalid: if you create a large enough set of conditional
Gaussian simulations, their mean value equals the kriging mean and their
variance equals the kriging variance. Nothing is gained, only an
expensive approximation of something rather cheap is obtained.
You will not find many papers that make this point, as the only point is
that someone else is wrong. Not many people like to write such stuff.
Below is a reference that may be hard to get (but you can google for the
first author). I for instance didn't enjoy writing this email.
Best regards,
--
Edzer
Heuvelink, G.B.M. and E.J. Pebesma, 2002, Is the ordinary kriging
variance a proper measure of interpolation error? In: Proceedings of the
fifth International Symposium on Spatial Accuracy Assessment in Natural
Resources and Environmental Sciences (eds. G. Hunter and K. Lowell).
Melbourne: RMIT University, 179-186.
Gustavo G. Pilger wrote:
> Hi,
>
> Indeed the kriging variance is only semi-variogram and spatial data
> configuration dependent. The kriging variance is calculated taking
> into account only the geometry of the samples, i.e. their spatial
> arrangement and the semi-variogram. Basically, kriging variance do not
> take into account the value of the samples, but only their location
> (and the semi-variogram), consequently ignoring the local variability.
> Therefore this parameter is not appropriate to measure uncertainty.
> For this purpose you should consider the use of conditional simulation
> methods.
>
> I wrote some papers about this subject some years ago. For exemple:
>
> PILGER, Gustavo G.; COSTA, Joao Felipe Coimbra Leite; KOPPE, Jair
> Carlos, 2001. Additional Samples: Where they Should be Located?.
> Natural Resources Research, New York, v. 10, n. 3, p. 197-207.
>
> I can send you a copy if you wish.
>
> I hope this helps you.
>
> Cheers.
> <><><><><><><><><><><><><><><><><><><><><><><>
> Gustavo G. Pilger, Mining Engineer, MSc, PhD
> Senior Geostatistician
> MBR - Brazil
> <><><><><><><><><><><><><><><><><><><><><><><>
>
>
>
>> Hi. I just read through Journel and Rossi's 1999 paper, "When do we
>> need a trend model in Kriging". In the appendix they say "A kriging
>> variance is but a variogram-model dependent ranking of data
>> configurations; being data-value independent, it is generally not a
>> measure of local accuracy...This fact is unfortunately not yet fully
>> appreciated by some practitioners". Can someone explain the
>> implications of this in terms of determining cost-efficiency analysis
>> for sample designs? Specifically, can we use kriging variance
>> estimates across potential sampling grids, (from modeled variograms
>> estimated from say a pilot study) to estimate the variability
>> associated with different sampling densities/configurations. In
>> addition, can someone provide some references that address this topic.
>>
>> Thanks,
>> Kerry
>> +
>> + To post a message to the list, send it to ai-geostats@jrc.it
>> + To unsubscribe, send email to majordomo@ jrc.it with no subject and
>> "unsubscribe ai-geostats" in the message body. DO NOT SEND
>> Subscribe/Unsubscribe requests to the list
>> + As a general service to list users, please remember to post a summary
>> of any useful responses to your questions.
>> + Support to the forum can be found at http://www.ai-geostats.org/
>
>
> +
> + To post a message to the list, send it to ai-geostats@jrc.it
> + To unsubscribe, send email to majordomo@ jrc.it with no subject and
> "unsubscribe ai-geostats" in the message body. DO NOT SEND
> Subscribe/Unsubscribe requests to the list
> + As a general service to list users, please remember to post a
> summary of any useful responses to your questions.
> + Support to the forum can be found at http://www.ai-geostats.org/
+
+ To post a message to the list, send it to ai-geostats@jrc.it
+ To unsubscribe, send email to majordomo@ jrc.it with no subject and "unsubscribe ai-geostats" in the message body. DO NOT SEND Subscribe/Unsubscribe requests to the list
+ As a general service to list users, please remember to post a summary of any useful responses to your questions.
+ Support to the forum can be found at http://www.ai-geostats.org/
Do you Yahoo!?
Everyone is raving about the all-new Yahoo! Mail.
