- Dear Mahdi

Quickly said, you cannot compare both nuggets, because they do not

share units... (well, the logarithmic one may be considered to have no

units, but this does not change the point).

But, why do you want to compare the variograms of your two data sets

in different scales? Probably, it would be more logical to take logs

of the subset, compute its experimental variogram, model it and

afterwards compare both models... always in log scale.

However, if you really want to do such comparison, there's a

relationship between the variogram for Z (a positive regionalized

variable) and Y=ln Z, both second-order stationary:

$$

\gamma_{Z}(h) = E[Z]^2 \cdot \exp{C_{Y}(0)} \cdot (1-\exp{-\gamma_{Y}(h)} )

$$

This comes from the relationship between variogram and covariance

function ( $C(h)=C(0)-\gamma(h)$ ), and between covariances for Z and

Y (which you can find, for instance, in Chilès&Delfiner, 1999, book

"Geostatistics: modelling spatial uncertainty"). Pay attention that

this is only true if Y is a Gaussian regionalized variable, and if

this assumption is false, your variograms may be horribly different.

regards

Raimon Tolosana-Delgado

On 4/27/06, Mahdi Osman <m_osm@...> wrote:

> Dear Isobel Clark,

>

> Dear List,

>

> I have your posting regrding cross validation. Yesterday and this morning I

> had similar, but not identical, problems. So I was wondering if you could

> help me with this.

>

>

> I have got two datasets. One of the datasets was a subset of the other. So I

> did semivariograms of a variable of interest on both datasets. The major

> dataset was logtransformed, whereas the other was not. So now I have got

> semivariogram parameters from the logtransformed data and from the

> non-transformed data. From the logtransformed data, I have got a smaller

> nuget, compared to the nugget from the non-transformed data. My question is:

>

>

> Can I actully compare the two semivariograms directly based on their nuget

> values even though one data was transformed and the other was not?

>

> How can I compare across semivariograms at all, is that possible or not?

>

> Is it possbile to backtransform the values and then compare the

> semivariograms?

>

>

> Thank you very much indeed for your help and time

>

>

> Reagds

>

>

> Mahdi

>

> --

> -----------------------------------

> Mahdi Osman (PhD)

> E-mail: m_osm@...

> -----------------------------------

>

> GMX Produkte empfehlen und ganz einfach Geld verdienen!

> Satte Provisionen für GMX Partner: http://www.gmx.net/de/go/partner

>

>

>

> * By using the ai-geostats mailing list you agree to follow its rules

> ( see http://www.ai-geostats.org/help_ai-geostats.htm )

>

> * To unsubscribe to ai-geostats, send the following in the subject or in the body (plain text format) of an email message to sympa@...

>

> Signoff ai-geostats

>

> - Raimon Tolosana-Delgado,

Many thanks. This was very helpful indeed.

Regards

Mahdi

> --- Ursprüngliche Nachricht ---

--

> Von: "Raimon Tolosana" <raimon.tolosana@...>

> An: "Mahdi Osman" <m_osm@...>

> Kopie: ai-geostats@...

> Betreff: Re: [ai-geostats] Re: about cross-validation

> Datum: Thu, 27 Apr 2006 17:10:09 +0200

>

> Dear Mahdi

>

> Quickly said, you cannot compare both nuggets, because they do not

> share units... (well, the logarithmic one may be considered to have no

> units, but this does not change the point).

>

> But, why do you want to compare the variograms of your two data sets

> in different scales? Probably, it would be more logical to take logs

> of the subset, compute its experimental variogram, model it and

> afterwards compare both models... always in log scale.

>

> However, if you really want to do such comparison, there's a

> relationship between the variogram for Z (a positive regionalized

> variable) and Y=ln Z, both second-order stationary:

> $$

> \gamma_{Z}(h) = E[Z]^2 \cdot \exp{C_{Y}(0)} \cdot

> (1-\exp{-\gamma_{Y}(h)} )

> $$

> This comes from the relationship between variogram and covariance

> function ( $C(h)=C(0)-\gamma(h)$ ), and between covariances for Z and

> Y (which you can find, for instance, in Chilès&Delfiner, 1999, book

> "Geostatistics: modelling spatial uncertainty"). Pay attention that

> this is only true if Y is a Gaussian regionalized variable, and if

> this assumption is false, your variograms may be horribly different.

>

> regards

> Raimon Tolosana-Delgado

>

> On 4/27/06, Mahdi Osman <m_osm@...> wrote:

> > Dear Isobel Clark,

> >

> > Dear List,

> >

> > I have your posting regrding cross validation. Yesterday and this

> morning I

> > had similar, but not identical, problems. So I was wondering if you

> could

> > help me with this.

> >

> >

> > I have got two datasets. One of the datasets was a subset of the other.

> So I

> > did semivariograms of a variable of interest on both datasets. The major

> > dataset was logtransformed, whereas the other was not. So now I have

> got

> > semivariogram parameters from the logtransformed data and from the

> > non-transformed data. From the logtransformed data, I have got a smaller

> > nuget, compared to the nugget from the non-transformed data. My question

> is:

> >

> >

> > Can I actully compare the two semivariograms directly based on their

> nuget

> > values even though one data was transformed and the other was not?

> >

> > How can I compare across semivariograms at all, is that possible or not?

> >

> > Is it possbile to backtransform the values and then compare the

> > semivariograms?

> >

> >

> > Thank you very much indeed for your help and time

> >

> >

> > Reagds

> >

> >

> > Mahdi

> >

> > --

> > -----------------------------------

> > Mahdi Osman (PhD)

> > E-mail: m_osm@...

> > -----------------------------------

> >

> > GMX Produkte empfehlen und ganz einfach Geld verdienen!

> > Satte Provisionen für GMX Partner: http://www.gmx.net/de/go/partner

> >

> >

> >

> > * By using the ai-geostats mailing list you agree to follow its rules

> > ( see http://www.ai-geostats.org/help_ai-geostats.htm )

> >

> > * To unsubscribe to ai-geostats, send the following in the subject or in

> the body (plain text format) of an email message to sympa@...

> >

> > Signoff ai-geostats

> >

> >

>

>

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

Mahdi Osman (PhD)

E-mail: m_osm@...

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

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