

Greetings,
There is code for Universal Kriging from Prof. Edzer Pebesma in GitHub< https://github.com/edzer/mstp/blob/master/lec7.Rmd>.
The covariance function is defined as follows:
cov = function(h) exp(h)
And defined without any variogram modeling/generation to produce partial sill, range or nugget parameters for defining the covariance matrix.
If I want to include a regularization term to account for singularity effects caused due to close spatial points, how do I modify the matrix computation for computing the 'beta' coefficients ?
I know there are standard formulae for different models (e.g. Matern, Exp,etc). But I would like to retain the simple cov function defined above and possibly use a regularizer (like ridge regression) to account for a nuggetlike effect.
thanks,
Chris
[[alternative HTML version deleted]]
_______________________________________________
RsigGeo mailing list
[hidden email]
https://stat.ethz.ch/mailman/listinfo/rsiggeo


On 11/22/2017 12:09 AM, Joelle k. Akram wrote:
> Greetings,
>
> There is code for Universal Kriging from Prof. Edzer Pebesma in GitHub< https://github.com/edzer/mstp/blob/master/lec7.Rmd>.
https://edzer.github.io/mstp/lec7.htmlgives you the rendered version.
>
> The covariance function is defined as follows:
>
> cov = function(h) exp(h)
>
> And defined without any variogram modeling/generation to produce partial sill, range or nugget parameters for defining the covariance matrix.
Well, it implies nugget=0, sill=1 and range parameter=1, it was the
shortest covariance function I could think of.
>
> If I want to include a regularization term to account for singularity effects caused due to close spatial points, how do I modify the matrix computation for computing the 'beta' coefficients ?
Add a nugget (i.e. add a constant to the diagonal of V)?
>
> I know there are standard formulae for different models (e.g. Matern, Exp,etc). But I would like to retain the simple cov function defined above and possibly use a regularizer (like ridge regression) to account for a nuggetlike effect.
>
> thanks,
>
> Chris
>
> [[alternative HTML version deleted]]
>
> _______________________________________________
> RsigGeo mailing list
> [hidden email]
> https://stat.ethz.ch/mailman/listinfo/rsiggeo>

Edzer Pebesma
Institute for Geoinformatics
Heisenbergstrasse 2, 48151 Muenster, Germany
Phone: +49 251 8333081
_______________________________________________
RsigGeo mailing list
[hidden email]
https://stat.ethz.ch/mailman/listinfo/rsiggeo


thank you for clarifying Prof. Pebesma. I have a couple more question for you regarding the inclusion of a
nugget to the diagonals of V. As we know,there are 2 covariances, V and v; one for the existing coordinates (i.e., V) and the other for the distances between these existing coordinates and other new locations (i.e., v).
I) Assuming unscaled coordinates in latitude/longitude; should the Nugget theoretically be a small value (lets say typically less than <1) or does it depend on other the dataset's spatial distribution,etc?
2) When computing Beta coefficients as in you lecture 7 in github, do we have to add the nugget term to both V and v or only one of them?
thank you,
Chris Akram
________________________________
From: RsigGeo < [hidden email]> on behalf of Edzer Pebesma < [hidden email]>
Sent: November 22, 2017 6:16 AM
To: [hidden email]
Subject: Re: [RsigGeo] Why is the covariance in Universal Kriging modeled this way in lectures by Prof. Edzer Pebesma?
On 11/22/2017 12:09 AM, Joelle k. Akram wrote:
> Greetings,
>
> There is code for Universal Kriging from Prof. Edzer Pebesma in GitHub< https://github.com/edzer/mstp/blob/master/lec7.Rmd>.
edzer/mstp< https://github.com/edzer/mstp/blob/master/lec7.Rmd>
github.com
mstp  Course slides: modelling spatiotemporal processes
https://edzer.github.io/mstp/lec7.htmlgives you the rendered version.
>
> The covariance function is defined as follows:
>
> cov = function(h) exp(h)
>
> And defined without any variogram modeling/generation to produce partial sill, range or nugget parameters for defining the covariance matrix.
Well, it implies nugget=0, sill=1 and range parameter=1, it was the
shortest covariance function I could think of.
>
> If I want to include a regularization term to account for singularity effects caused due to close spatial points, how do I modify the matrix computation for computing the 'beta' coefficients ?
Add a nugget (i.e. add a constant to the diagonal of V)?
>
> I know there are standard formulae for different models (e.g. Matern, Exp,etc). But I would like to retain the simple cov function defined above and possibly use a regularizer (like ridge regression) to account for a nuggetlike effect.
>
> thanks,
>
> Chris
>
> [[alternative HTML version deleted]]
>
> _______________________________________________
> RsigGeo mailing list
> [hidden email]
> https://stat.ethz.ch/mailman/listinfo/rsiggeo>

Edzer Pebesma
Institute for Geoinformatics
Heisenbergstrasse 2, 48151 Muenster, Germany
Phone: +49 251 8333081
_______________________________________________
RsigGeo mailing list
[hidden email]
https://stat.ethz.ch/mailman/listinfo/rsiggeo [[alternative HTML version deleted]]
_______________________________________________
RsigGeo mailing list
[hidden email]
https://stat.ethz.ch/mailman/listinfo/rsiggeo


On 11/22/2017 10:23 PM, Joelle k. Akram wrote:
> thank you for clarifying Prof. Pebesma. I have a couple more question
> for you regarding the inclusion of a
>
> nugget to the diagonals of V. As we know,there are 2 covariances, V and
> v; one for the existing coordinates (i.e., V) and the other for the
> distances between these existing coordinates and other new locations
> (i.e., v).
>
>
> I) Assuming unscaled coordinates in latitude/longitude; should the
> Nugget theoretically be a small value (lets say typically less than <1)
> or does it depend on other the dataset's spatial distribution,etc?
>
I would say it should depend on the data.
>
> 2) When computing Beta coefficients as in you lecture 7 in github, do we
> have to add the nugget term to both V and v or only one of them?
For a nugget, by definition to each of them; if you'd only add it to V
you no longer obtain an exact interpolator (i.e., you no longer predict
the data value at data locations); if your measured process is subject
to a measurement error, this may however be preferred.
>
>
> thank you,
>
> Chris Akram
>
>
>
>
> 
> *From:* RsigGeo < [hidden email]> on behalf of Edzer
> Pebesma < [hidden email]>
> *Sent:* November 22, 2017 6:16 AM
> *To:* [hidden email]
> *Subject:* Re: [RsigGeo] Why is the covariance in Universal Kriging
> modeled this way in lectures by Prof. Edzer Pebesma?
>
>
>
> On 11/22/2017 12:09 AM, Joelle k. Akram wrote:
>> Greetings,
>>
>> There is code for Universal Kriging from Prof. Edzer Pebesma in GitHub< https://github.com/edzer/mstp/blob/master/lec7.Rmd>.
>
> edzer/mstp < https://github.com/edzer/mstp/blob/master/lec7.Rmd>
> github.com
> mstp  Course slides: modelling spatiotemporal processes
>
>
>
>
> https://edzer.github.io/mstp/lec7.html>
> gives you the rendered version.
>
>>
>> The covariance function is defined as follows:
>>
>> cov = function(h) exp(h)
>>
>> And defined without any variogram modeling/generation to produce partial sill, range or nugget parameters for defining the covariance matrix.
>
> Well, it implies nugget=0, sill=1 and range parameter=1, it was the
> shortest covariance function I could think of.
>
>>
>> If I want to include a regularization term to account for singularity effects caused due to close spatial points, how do I modify the matrix computation for computing the 'beta' coefficients ?
>
> Add a nugget (i.e. add a constant to the diagonal of V)?
>
>>
>> I know there are standard formulae for different models (e.g. Matern, Exp,etc). But I would like to retain the simple cov function defined above and possibly use a regularizer (like ridge regression) to account for a nuggetlike effect.
>>
>> thanks,
>>
>> Chris
>>
>> [[alternative HTML version deleted]]
>>
>> _______________________________________________
>> RsigGeo mailing list
>> [hidden email]
>> https://stat.ethz.ch/mailman/listinfo/rsiggeo>>
>
> 
> Edzer Pebesma
> Institute for Geoinformatics
> Heisenbergstrasse 2, 48151 Muenster, Germany
> Phone: +49 251 8333081
>
> _______________________________________________
> RsigGeo mailing list
> [hidden email]
> https://stat.ethz.ch/mailman/listinfo/rsiggeo
Edzer Pebesma
Institute for Geoinformatics
Heisenbergstrasse 2, 48151 Muenster, Germany
Phone: +49 251 8333081
_______________________________________________
RsigGeo mailing list
[hidden email]
https://stat.ethz.ch/mailman/listinfo/rsiggeo


hi Prof. Pebesma,
just to follow up on my question about adding the nugget term to both V and v from your lecture 7 on github.
I do not want an exact interpolator. Instead I want to do a smoothing interpolator using UnivKrig. Would you
recommend only adding the nugget to V only ? and set the nugget=0 for defining v (whilst retaining the same psill and range used for defining V).
thanks
Chris Akram
________________________________
From: Edzer Pebesma < [hidden email]>
Sent: November 22, 2017 2:55 PM
To: Joelle k. Akram; [hidden email]
Subject: Re: [RsigGeo] Why is the covariance in Universal Kriging modeled this way in lectures by Prof. Edzer Pebesma?
On 11/22/2017 10:23 PM, Joelle k. Akram wrote:
> thank you for clarifying Prof. Pebesma. I have a couple more question
> for you regarding the inclusion of a
>
> nugget to the diagonals of V. As we know,there are 2 covariances, V and
> v; one for the existing coordinates (i.e., V) and the other for the
> distances between these existing coordinates and other new locations
> (i.e., v).
>
>
> I) Assuming unscaled coordinates in latitude/longitude; should the
> Nugget theoretically be a small value (lets say typically less than <1)
> or does it depend on other the dataset's spatial distribution,etc?
>
I would say it should depend on the data.
>
> 2) When computing Beta coefficients as in you lecture 7 in github, do we
> have to add the nugget term to both V and v or only one of them?
For a nugget, by definition to each of them; if you'd only add it to V
you no longer obtain an exact interpolator (i.e., you no longer predict
the data value at data locations); if your measured process is subject
to a measurement error, this may however be preferred.
edzer/mstp< https://github.com/edzer/mstp/blob/master/lec7.Rmd>
github.com
mstp  Course slides: modelling spatiotemporal processes
>
> edzer/mstp < https://github.com/edzer/mstp/blob/master/lec7.Rmd>
[ https://avatars2.githubusercontent.com/u/520851?s=400&v=4]< https://github.com/edzer/mstp/blob/master/lec7.Rmd>
edzer/mstp< https://github.com/edzer/mstp/blob/master/lec7.Rmd>
github.com
mstp  Course slides: modelling spatiotemporal processes
> github.com
> mstp  Course slides: modelling spatiotemporal processes
>
>
>
>
> https://edzer.github.io/mstp/lec7.html>
> gives you the rendered version.
>
>>
>> The covariance function is defined as follows:
>>
>> cov = function(h) exp(h)
>>
>> And defined without any variogram modeling/generation to produce partial sill, range or nugget parameters for defining the covariance matrix.
>
> Well, it implies nugget=0, sill=1 and range parameter=1, it was the
> shortest covariance function I could think of.
>
>>
>> If I want to include a regularization term to account for singularity effects caused due to close spatial points, how do I modify the matrix computation for computing the 'beta' coefficients ?
>
> Add a nugget (i.e. add a constant to the diagonal of V)?
>
>>
>> I know there are standard formulae for different models (e.g. Matern, Exp,etc). But I would like to retain the simple cov function defined above and possibly use a regularizer (like ridge regression) to account for a nuggetlike effect.
>>
>> thanks,
>>
>> Chris
>>
>> [[alternative HTML version deleted]]
>>
>> _______________________________________________
>> RsigGeo mailing list
>> [hidden email]
>> https://stat.ethz.ch/mailman/listinfo/rsiggeoRsigGeo Info Page  SfS � Seminar for Statistics  ETH ...< https://stat.ethz.ch/mailman/listinfo/rsiggeo>
stat.ethz.ch
A mailing list for discussing the development and use of R functions and packages for handling and analysis of spatial, and particularly geographical, data.
stat.ethz.ch
A mailing list for discussing the development and use of R functions and packages for handling and analysis of spatial, and particularly geographical, data.

Edzer Pebesma
Institute for Geoinformatics
Heisenbergstrasse 2, 48151 Muenster, Germany
Phone: +49 251 8333081
[[alternative HTML version deleted]]
_______________________________________________
RsigGeo mailing list
[hidden email]
https://stat.ethz.ch/mailman/listinfo/rsiggeo


On 12/05/2017 04:35 PM, Joelle k. Akram wrote:
> hi Prof. Pebesma,
>
>
> just to follow up on my question about adding the nugget term to both V
> and v from your lecture 7 on github.
>
> I do not want an exact interpolator. Instead I want to do a smoothing
> interpolator using UnivKrig. Would you
>
> recommend only adding the nugget to V only ? and set the nugget=0 for
> defining v (whilst retaining the same psill and range used for defining V).
Yes.
>
>
> thanks
> Chris Akram
>
> 
> *From:* Edzer Pebesma < [hidden email]>
> *Sent:* November 22, 2017 2:55 PM
> *To:* Joelle k. Akram; [hidden email]
> *Subject:* Re: [RsigGeo] Why is the covariance in Universal Kriging
> modeled this way in lectures by Prof. Edzer Pebesma?
>
>
>
> On 11/22/2017 10:23 PM, Joelle k. Akram wrote:
>> thank you for clarifying Prof. Pebesma. I have a couple more question
>> for you regarding the inclusion of a
>>
>> nugget to the diagonals of V. As we know,there are 2 covariances, V and
>> v; one for the existing coordinates (i.e., V) and the other for the
>> distances between these existing coordinates and other new locations
>> (i.e., v).
>>
>>
>> I) Assuming unscaled coordinates in latitude/longitude; should the
>> Nugget theoretically be a small value (lets say typically less than <1)
>> or does it depend on other the dataset's spatial distribution,etc?
>>
>
> I would say it should depend on the data.
>
>>
>> 2) When computing Beta coefficients as in you lecture 7 in github, do we
>> have to add the nugget term to both V and v or only one of them?
>
> For a nugget, by definition to each of them; if you'd only add it to V
> you no longer obtain an exact interpolator (i.e., you no longer predict
> the data value at data locations); if your measured process is subject
> to a measurement error, this may however be preferred.
>
>>
>>
>> thank you,
>>
>> Chris Akram
>>
>>
>>
>>
>> 
>> *From:* RsigGeo < [hidden email]> on behalf of Edzer
>> Pebesma < [hidden email]>
>> *Sent:* November 22, 2017 6:16 AM
>> *To:* [hidden email]
>> *Subject:* Re: [RsigGeo] Why is the covariance in Universal Kriging
>> modeled this way in lectures by Prof. Edzer Pebesma?
>>
>>
>>
>> On 11/22/2017 12:09 AM, Joelle k. Akram wrote:
>>> Greetings,
>>>
>>> There is code for Universal Kriging from Prof. Edzer Pebesma in GitHub< https://github.com/edzer/mstp/blob/master/lec7.Rmd>.
> < https://github.com/edzer/mstp/blob/master/lec7.Rmd>
>
> edzer/mstp < https://github.com/edzer/mstp/blob/master/lec7.Rmd>
> github.com
> mstp  Course slides: modelling spatiotemporal processes
>
>
>
>>
>> edzer/mstp < https://github.com/edzer/mstp/blob/master/lec7.Rmd>
> < https://github.com/edzer/mstp/blob/master/lec7.Rmd>
>
> edzer/mstp < https://github.com/edzer/mstp/blob/master/lec7.Rmd>
> github.com
> mstp  Course slides: modelling spatiotemporal processes
>
>
>
>> github.com
>> mstp  Course slides: modelling spatiotemporal processes
>>
>>
>>
>>
>> https://edzer.github.io/mstp/lec7.html>>
>> gives you the rendered version.
>>
>>>
>>> The covariance function is defined as follows:
>>>
>>> cov = function(h) exp(h)
>>>
>>> And defined without any variogram modeling/generation to produce partial sill, range or nugget parameters for defining the covariance matrix.
>>
>> Well, it implies nugget=0, sill=1 and range parameter=1, it was the
>> shortest covariance function I could think of.
>>
>>>
>>> If I want to include a regularization term to account for singularity effects caused due to close spatial points, how do I modify the matrix computation for computing the 'beta' coefficients ?
>>
>> Add a nugget (i.e. add a constant to the diagonal of V)?
>>
>>>
>>> I know there are standard formulae for different models (e.g. Matern, Exp,etc). But I would like to retain the simple cov function defined above and possibly use a regularizer (like ridge regression) to account for a nuggetlike effect.
>>>
>>> thanks,
>>>
>>> Chris
>>>
>>> [[alternative HTML version deleted]]
>>>
>>> _______________________________________________
>>> RsigGeo mailing list
>>> [hidden email]
>>> https://stat.ethz.ch/mailman/listinfo/rsiggeo> RsigGeo Info Page  SfS – Seminar for Statistics  ETH ...
> < https://stat.ethz.ch/mailman/listinfo/rsiggeo>
> stat.ethz.ch
> A mailing list for discussing the development and use of R functions and
> packages for handling and analysis of spatial, and particularly
> geographical, data.
>
>
>
>>>
>>
>> 
>> Edzer Pebesma
>> Institute for Geoinformatics
>> Heisenbergstrasse 2, 48151 Muenster, Germany
>> Phone: +49 251 8333081
>>
>> _______________________________________________
>> RsigGeo mailing list
>> [hidden email]
>> https://stat.ethz.ch/mailman/listinfo/rsiggeo> RsigGeo Info Page  SfS – Seminar for Statistics  ETH ...
> < https://stat.ethz.ch/mailman/listinfo/rsiggeo>
> stat.ethz.ch
> A mailing list for discussing the development and use of R functions and
> packages for handling and analysis of spatial, and particularly
> geographical, data.
>
>
>
>
> 
> Edzer Pebesma
> Institute for Geoinformatics
> Heisenbergstrasse 2, 48151 Muenster, Germany
> Phone: +49 251 8333081

Edzer Pebesma
Institute for Geoinformatics
Heisenbergstrasse 2, 48151 Muenster, Germany
Phone: +49 251 8333081
_______________________________________________
RsigGeo mailing list
[hidden email]
https://stat.ethz.ch/mailman/listinfo/rsiggeo


Thanks Prof. Pebesma.
In your opinion, by setting nugget=0 for unmeasured locations, what does it represent physically?
From my understanding, it means the unmeasured locations we want to predict/interpolate has no measurement error.
But is this a valid assumption? ( given that for the known, measure locations we use a nugget to define the covariance) .
Chris
________________________________
From: Edzer Pebesma < [hidden email]>
Sent: December 5, 2017 8:59 AM
To: Joelle k. Akram; [hidden email]
Subject: Re: [RsigGeo] Why is the covariance in Universal Kriging modeled this way in lectures by Prof. Edzer Pebesma?
On 12/05/2017 04:35 PM, Joelle k. Akram wrote:
> hi Prof. Pebesma,
>
>
> just to follow up on my question about adding the nugget term to both V
> and v from your lecture 7 on github.
>
> I do not want an exact interpolator. Instead I want to do a smoothing
> interpolator using UnivKrig. Would you
>
> recommend only adding the nugget to V only ? and set the nugget=0 for
> defining v (whilst retaining the same psill and range used for defining V).
Yes.
>
>
> thanks
> Chris Akram
>
> 
> *From:* Edzer Pebesma < [hidden email]>
> *Sent:* November 22, 2017 2:55 PM
> *To:* Joelle k. Akram; [hidden email]
> *Subject:* Re: [RsigGeo] Why is the covariance in Universal Kriging
> modeled this way in lectures by Prof. Edzer Pebesma?
>
>
>
> On 11/22/2017 10:23 PM, Joelle k. Akram wrote:
>> thank you for clarifying Prof. Pebesma. I have a couple more question
>> for you regarding the inclusion of a
>>
>> nugget to the diagonals of V. As we know,there are 2 covariances, V and
>> v; one for the existing coordinates (i.e., V) and the other for the
>> distances between these existing coordinates and other new locations
>> (i.e., v).
>>
>>
>> I) Assuming unscaled coordinates in latitude/longitude; should the
>> Nugget theoretically be a small value (lets say typically less than <1)
>> or does it depend on other the dataset's spatial distribution,etc?
>>
>
> I would say it should depend on the data.
>
>>
>> 2) When computing Beta coefficients as in you lecture 7 in github, do we
>> have to add the nugget term to both V and v or only one of them?
>
> For a nugget, by definition to each of them; if you'd only add it to V
> you no longer obtain an exact interpolator (i.e., you no longer predict
> the data value at data locations); if your measured process is subject
> to a measurement error, this may however be preferred.
>
>>
>>
>> thank you,
>>
>> Chris Akram
>>
>>
>>
>>
>> 
>> *From:* RsigGeo < [hidden email]> on behalf of Edzer
>> Pebesma < [hidden email]>
>> *Sent:* November 22, 2017 6:16 AM
>> *To:* [hidden email]
>> *Subject:* Re: [RsigGeo] Why is the covariance in Universal Kriging
>> modeled this way in lectures by Prof. Edzer Pebesma?
>>
>>
>>
>> On 11/22/2017 12:09 AM, Joelle k. Akram wrote:
>>> Greetings,
>>>
>>> There is code for Universal Kriging from Prof. Edzer Pebesma in GitHub< https://github.com/edzer/mstp/blob/master/lec7.Rmd>.
[ https://avatars2.githubusercontent.com/u/520851?s=400&v=4]< https://github.com/edzer/mstp/blob/master/lec7.Rmd>
edzer/mstp< https://github.com/edzer/mstp/blob/master/lec7.Rmd>
github.com
mstp  Course slides: modelling spatiotemporal processes
> < https://github.com/edzer/mstp/blob/master/lec7.Rmd>
[ https://avatars2.githubusercontent.com/u/520851?s=400&v=4]< https://github.com/edzer/mstp/blob/master/lec7.Rmd>
edzer/mstp< https://github.com/edzer/mstp/blob/master/lec7.Rmd>
github.com
mstp  Course slides: modelling spatiotemporal processes
>
> edzer/mstp < https://github.com/edzer/mstp/blob/master/lec7.Rmd>
[ https://avatars2.githubusercontent.com/u/520851?s=400&v=4]< https://github.com/edzer/mstp/blob/master/lec7.Rmd>
edzer/mstp< https://github.com/edzer/mstp/blob/master/lec7.Rmd>
github.com
mstp  Course slides: modelling spatiotemporal processes
> github.com
> mstp  Course slides: modelling spatiotemporal processes
>
>
>
>>
>> edzer/mstp < https://github.com/edzer/mstp/blob/master/lec7.Rmd>
[ https://avatars2.githubusercontent.com/u/520851?s=400&v=4]< https://github.com/edzer/mstp/blob/master/lec7.Rmd>
edzer/mstp< https://github.com/edzer/mstp/blob/master/lec7.Rmd>
github.com
mstp  Course slides: modelling spatiotemporal processes
> < https://github.com/edzer/mstp/blob/master/lec7.Rmd>
[ https://avatars2.githubusercontent.com/u/520851?s=400&v=4]< https://github.com/edzer/mstp/blob/master/lec7.Rmd>
edzer/mstp< https://github.com/edzer/mstp/blob/master/lec7.Rmd>
github.com
mstp  Course slides: modelling spatiotemporal processes
>
> edzer/mstp < https://github.com/edzer/mstp/blob/master/lec7.Rmd>
[ https://avatars2.githubusercontent.com/u/520851?s=400&v=4]< https://github.com/edzer/mstp/blob/master/lec7.Rmd>
edzer/mstp< https://github.com/edzer/mstp/blob/master/lec7.Rmd>
github.com
mstp  Course slides: modelling spatiotemporal processes
> github.com
> mstp  Course slides: modelling spatiotemporal processes
>
>
>
>> github.com
>> mstp  Course slides: modelling spatiotemporal processes
>>
>>
>>
>>
>> https://edzer.github.io/mstp/lec7.html>>
>> gives you the rendered version.
>>
>>>
>>> The covariance function is defined as follows:
>>>
>>> cov = function(h) exp(h)
>>>
>>> And defined without any variogram modeling/generation to produce partial sill, range or nugget parameters for defining the covariance matrix.
>>
>> Well, it implies nugget=0, sill=1 and range parameter=1, it was the
>> shortest covariance function I could think of.
>>
>>>
>>> If I want to include a regularization term to account for singularity effects caused due to close spatial points, how do I modify the matrix computation for computing the 'beta' coefficients ?
>>
>> Add a nugget (i.e. add a constant to the diagonal of V)?
>>
>>>
>>> I know there are standard formulae for different models (e.g. Matern, Exp,etc). But I would like to retain the simple cov function defined above and possibly use a regularizer (like ridge regression) to account for a nuggetlike effect.
>>>
>>> thanks,
>>>
>>> Chris
>>>
>>> [[alternative HTML version deleted]]
>>>
>>> _______________________________________________
>>> RsigGeo mailing list
>>> [hidden email]
>>> https://stat.ethz.ch/mailman/listinfo/rsiggeoRsigGeo Info Page  SfS � Seminar for Statistics  ETH ...< https://stat.ethz.ch/mailman/listinfo/rsiggeo>
stat.ethz.ch
A mailing list for discussing the development and use of R functions and packages for handling and analysis of spatial, and particularly geographical, data.
> RsigGeo Info Page  SfS � Seminar for Statistics  ETH ...
> < https://stat.ethz.ch/mailman/listinfo/rsiggeo>
RsigGeo Info Page  SfS � Seminar for Statistics  ETH ...< https://stat.ethz.ch/mailman/listinfo/rsiggeo>
stat.ethz.ch
A mailing list for discussing the development and use of R functions and packages for handling and analysis of spatial, and particularly geographical, data.
> stat.ethz.ch
> A mailing list for discussing the development and use of R functions and
> packages for handling and analysis of spatial, and particularly
> geographical, data.
>
>
>
>>>
>>
>> 
>> Edzer Pebesma
>> Institute for Geoinformatics
>> Heisenbergstrasse 2, 48151 Muenster, Germany
>> Phone: +49 251 8333081
>>
>> _______________________________________________
>> RsigGeo mailing list
>> [hidden email]
>> https://stat.ethz.ch/mailman/listinfo/rsiggeoRsigGeo Info Page  SfS � Seminar for Statistics  ETH ...< https://stat.ethz.ch/mailman/listinfo/rsiggeo>
stat.ethz.ch
A mailing list for discussing the development and use of R functions and packages for handling and analysis of spatial, and particularly geographical, data.
> RsigGeo Info Page  SfS � Seminar for Statistics  ETH ...
> < https://stat.ethz.ch/mailman/listinfo/rsiggeo>
RsigGeo Info Page  SfS � Seminar for Statistics  ETH ...< https://stat.ethz.ch/mailman/listinfo/rsiggeo>
stat.ethz.ch
A mailing list for discussing the development and use of R functions and packages for handling and analysis of spatial, and particularly geographical, data.
> stat.ethz.ch
> A mailing list for discussing the development and use of R functions and
> packages for handling and analysis of spatial, and particularly
> geographical, data.
>
>
>
>
> 
> Edzer Pebesma
> Institute for Geoinformatics
> Heisenbergstrasse 2, 48151 Muenster, Germany
> Phone: +49 251 8333081

Edzer Pebesma
Institute for Geoinformatics
Heisenbergstrasse 2, 48151 Muenster, Germany
Phone: +49 251 8333081
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_______________________________________________
RsigGeo mailing list
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https://stat.ethz.ch/mailman/listinfo/rsiggeo

