Why is the covariance in Universal Kriging modeled this way in lectures by Prof. Edzer Pebesma?

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Why is the covariance in Universal Kriging modeled this way in lectures by Prof. Edzer Pebesma?

Joelle k. Akram
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 nugget-like effect.

thanks,

Chris

        [[alternative HTML version deleted]]

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Re: Why is the covariance in Universal Kriging modeled this way in lectures by Prof. Edzer Pebesma?

edzer


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.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 nugget-like effect.
>
> thanks,
>
> Chris
>
> [[alternative HTML version deleted]]
>
> _______________________________________________
> R-sig-Geo mailing list
> [hidden email]
> https://stat.ethz.ch/mailman/listinfo/r-sig-geo
>

--
Edzer Pebesma
Institute for Geoinformatics
Heisenbergstrasse 2, 48151 Muenster, Germany
Phone: +49 251 8333081

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https://stat.ethz.ch/mailman/listinfo/r-sig-geo
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Re: Why is the covariance in Universal Kriging modeled this way in lectures by Prof. Edzer Pebesma?

Joelle k. Akram
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: R-sig-Geo <[hidden email]> on behalf of Edzer Pebesma <[hidden email]>
Sent: November 22, 2017 6:16 AM
To: [hidden email]
Subject: Re: [R-sig-Geo] 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 spatio-temporal 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 nugget-like effect.
>
> thanks,
>
> Chris
>
>        [[alternative HTML version deleted]]
>
> _______________________________________________
> R-sig-Geo mailing list
> [hidden email]
> https://stat.ethz.ch/mailman/listinfo/r-sig-geo
>

--
Edzer Pebesma
Institute for Geoinformatics
Heisenbergstrasse 2, 48151 Muenster, Germany
Phone: +49 251 8333081

_______________________________________________
R-sig-Geo mailing list
[hidden email]
https://stat.ethz.ch/mailman/listinfo/r-sig-geo

        [[alternative HTML version deleted]]

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Re: Why is the covariance in Universal Kriging modeled this way in lectures by Prof. Edzer Pebesma?

edzer


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:* R-sig-Geo <[hidden email]> on behalf of Edzer
> Pebesma <[hidden email]>
> *Sent:* November 22, 2017 6:16 AM
> *To:* [hidden email]
> *Subject:* Re: [R-sig-Geo] 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 spatio-temporal 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 nugget-like effect.
>>
>> thanks,
>>
>> Chris
>>
>>        [[alternative HTML version deleted]]
>>
>> _______________________________________________
>> R-sig-Geo mailing list
>> [hidden email]
>> https://stat.ethz.ch/mailman/listinfo/r-sig-geo
>>
>
> --
> Edzer Pebesma
> Institute for Geoinformatics
> Heisenbergstrasse 2, 48151 Muenster, Germany
> Phone: +49 251 8333081
>
> _______________________________________________
> R-sig-Geo mailing list
> [hidden email]
> https://stat.ethz.ch/mailman/listinfo/r-sig-geo

--
Edzer Pebesma
Institute for Geoinformatics
Heisenbergstrasse 2, 48151 Muenster, Germany
Phone: +49 251 8333081

_______________________________________________
R-sig-Geo mailing list
[hidden email]
https://stat.ethz.ch/mailman/listinfo/r-sig-geo
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Re: Why is the covariance in Universal Kriging modeled this way in lectures by Prof. Edzer Pebesma?

Joelle k. Akram
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: [R-sig-Geo] 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:* R-sig-Geo <[hidden email]> on behalf of Edzer
> Pebesma <[hidden email]>
> *Sent:* November 22, 2017 6:16 AM
> *To:* [hidden email]
> *Subject:* Re: [R-sig-Geo] 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 spatio-temporal 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 spatio-temporal processes



> github.com
> mstp - Course slides: modelling spatio-temporal 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 nugget-like effect.
>>
>> thanks,
>>
>> Chris
>>
>>        [[alternative HTML version deleted]]
>>
>> _______________________________________________
>> R-sig-Geo mailing list
>> [hidden email]
>> https://stat.ethz.ch/mailman/listinfo/r-sig-geo
R-sig-Geo Info Page - SfS � Seminar for Statistics | ETH ...<https://stat.ethz.ch/mailman/listinfo/r-sig-geo>
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
>
> _______________________________________________
> R-sig-Geo mailing list
> [hidden email]
> https://stat.ethz.ch/mailman/listinfo/r-sig-geo
R-sig-Geo Info Page - SfS � Seminar for Statistics | ETH ...<https://stat.ethz.ch/mailman/listinfo/r-sig-geo>
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]]


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Re: Why is the covariance in Universal Kriging modeled this way in lectures by Prof. Edzer Pebesma?

edzer


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: [R-sig-Geo] 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:* R-sig-Geo <[hidden email]> on behalf of Edzer
>> Pebesma <[hidden email]>
>> *Sent:* November 22, 2017 6:16 AM
>> *To:* [hidden email]
>> *Subject:* Re: [R-sig-Geo] 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 spatio-temporal 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 spatio-temporal processes
>
>
>
>> github.com
>> mstp - Course slides: modelling spatio-temporal 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 nugget-like effect.
>>>
>>> thanks,
>>>
>>> Chris
>>>
>>>        [[alternative HTML version deleted]]
>>>
>>> _______________________________________________
>>> R-sig-Geo mailing list
>>> [hidden email]
>>> https://stat.ethz.ch/mailman/listinfo/r-sig-geo
> R-sig-Geo Info Page - SfS – Seminar for Statistics | ETH ...
> <https://stat.ethz.ch/mailman/listinfo/r-sig-geo>
> 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
>>
>> _______________________________________________
>> R-sig-Geo mailing list
>> [hidden email]
>> https://stat.ethz.ch/mailman/listinfo/r-sig-geo
> R-sig-Geo Info Page - SfS – Seminar for Statistics | ETH ...
> <https://stat.ethz.ch/mailman/listinfo/r-sig-geo>
> 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

_______________________________________________
R-sig-Geo mailing list
[hidden email]
https://stat.ethz.ch/mailman/listinfo/r-sig-geo
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Re: Why is the covariance in Universal Kriging modeled this way in lectures by Prof. Edzer Pebesma?

Joelle k. Akram
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: [R-sig-Geo] 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: [R-sig-Geo] 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:* R-sig-Geo <[hidden email]> on behalf of Edzer
>> Pebesma <[hidden email]>
>> *Sent:* November 22, 2017 6:16 AM
>> *To:* [hidden email]
>> *Subject:* Re: [R-sig-Geo] 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 spatio-temporal 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 spatio-temporal 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 spatio-temporal processes



> github.com
> mstp - Course slides: modelling spatio-temporal 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 spatio-temporal 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 spatio-temporal 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 spatio-temporal processes



> github.com
> mstp - Course slides: modelling spatio-temporal processes
>
>
>
>> github.com
>> mstp - Course slides: modelling spatio-temporal 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 nugget-like effect.
>>>
>>> thanks,
>>>
>>> Chris
>>>
>>>        [[alternative HTML version deleted]]
>>>
>>> _______________________________________________
>>> R-sig-Geo mailing list
>>> [hidden email]
>>> https://stat.ethz.ch/mailman/listinfo/r-sig-geo
R-sig-Geo Info Page - SfS � Seminar for Statistics | ETH ...<https://stat.ethz.ch/mailman/listinfo/r-sig-geo>
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.



> R-sig-Geo Info Page - SfS � Seminar for Statistics | ETH ...
> <https://stat.ethz.ch/mailman/listinfo/r-sig-geo>
R-sig-Geo Info Page - SfS � Seminar for Statistics | ETH ...<https://stat.ethz.ch/mailman/listinfo/r-sig-geo>
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
>>
>> _______________________________________________
>> R-sig-Geo mailing list
>> [hidden email]
>> https://stat.ethz.ch/mailman/listinfo/r-sig-geo
R-sig-Geo Info Page - SfS � Seminar for Statistics | ETH ...<https://stat.ethz.ch/mailman/listinfo/r-sig-geo>
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.



> R-sig-Geo Info Page - SfS � Seminar for Statistics | ETH ...
> <https://stat.ethz.ch/mailman/listinfo/r-sig-geo>
R-sig-Geo Info Page - SfS � Seminar for Statistics | ETH ...<https://stat.ethz.ch/mailman/listinfo/r-sig-geo>
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

        [[alternative HTML version deleted]]


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