## Re: [AI-GEOSTATS: Cross Validation - Jackknife (Difference)]

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• Hi Peter, I also found the topic frequently unclear. This is what I understood from my readings. In particular, I would recommnend the following excellent
Message 1 of 1 , Sep 2, 2003
Hi Peter,

I also found the topic frequently unclear.

This is what I understood from my readings. In particular, I would recommnend
the following excellent paper:

B. Efron and G. Gong, A leisurely look at the bootstrap, the jackknife and
cross-validation. Am. Stat. 37 (1983), pp. 36–48.

Maciej Tomczak's paper(ftp://ftp.geog.uwo.ca/GIDA/Tomczak.pdf) is a nice
presentation of jackknifing and cross-validation that also points the reader
to the above-mentioned reference.

As mentioned by Isobel, you could have a look at Cressie's book (Statistics
for spatial data, Wiley & Sons, revised edition, 1993), in particular pages
101 and 489-498.

It results from the above references that, although jackknifing and
cross-validations are often used in geostatistics to define the same
technique, they are fundamentally different. Hence, Alexei's Amantov code,
jackknife.bas, has an incorrect name. It is doing cross-validation.

The term k-fold cross-validation also sometimes appear... adding more
confusion.

In k-fold cross-validation, the data set of the n observed values is divided
into k training and n-k testing subsets.
The estimation error of the interpolation algorithm, for example, is then
obtained from an average measure of the errors over the k tests (e.g. mean
absolute errors, root mean squared errors).

The leave-one-out method (what I consider being THE "cross-validation") is a
particular case in which only one point is used at a time as test set and
where each point of the data set has been, in turn, removed one time. Here
again, one will use the average of the n estimations.

Jackknifing involves pseudo-values and I would reuse Maciej's figure to
explain the difference between jackknifing and cross-validations.

Hope this clarifies a bit the issue.

Gregoire

PS: if you look at www.scirus.com for the keywords (jackknife) AND
(cross-validation), you will get 170 peer-reviewed papers. The most recent

"Peter Pinn" <peterpinn@...> wrote:

> Hi again,
>
> I have a question concernig the jackknife.bas for surfer. In the top line it

> says:
>
> 'Jackknife.bas grids the data set n times, leaving one of the data points
> out
> ' each time. Also known as cross-validation. TB - 09 Aug 00.
>
> In Maciej Tomczaks paper of SIC´97 I saw the diagram of his algorithm. He
> distinguished between cross-validation and jackknifing. The above mentioned

> script says jackknifing is also known as cross-validation. I am very
> confused about that. Can anyone explain to me what is the result of gridding

> with the jackknife.bas. Does the result differ from using the
> cross-validation in surfer ?
>
> Finally: Are there any reliable tools for both analysis strategies in
> commercial software other than surfer ?
>
>
> Peter
>
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