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