Intensity Estimation Methods

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Intensity Estimation Methods

R-sig-geo mailing list
Hello list,,

I have a spatial point pattern . I am trying to estimate its intensity both with a fixed bandwidth and  with an adaptive bandwidth.
How could I compare the goodness of these two fits? I mean are there any things like mse, aic or any other criteria???
I want to compare the difference between the estimated intensity and the original pattern's intensity.

Thanks
Cenk





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Bu elektronik posta ve onunla iletilen bütün dosyalar sadece yukarıda isimleri belirtilen kişiler arasında özel haberleşme amacını taşımakta olup gönderici tarafından alınması amaçlanan yetkili gerçek ya da tüzel kişinin kullanımına aittir. Eğer bu elektronik posta size yanlışlıkla ulaşmışsa, elektronik postanın içeriğini açıklamanız, kopyalamanız, yönlendirmeniz ve kullanmanız kesinlikle yasaktır. Bu durumda, lütfen mesajı geri gönderiniz ve sisteminizden siliniz. Anadolu Üniversitesi bu mesajın içerdiği bilgilerin doğruluğu veya eksiksiz olduğu konusunda herhangi bir garanti vermemektedir. Bu nedenle bu bilgilerin ne şekilde olursa olsun içeriğinden, iletilmesinden, alınmasından ve saklanmasından sorumlu değildir. Bu mesajdaki görüşler yalnızca gönderen kişiye aittir ve Anadolu Üniversitesinin görüşlerini yansıtmayabilir.

This electronic mail and any files transmitted with it are intended for the private use of the people named above. If you are not the intended recipient and received this message in error, forwarding, copying or use of any of the information is strictly prohibited. Any dissemination or use of this information by a person other than the intended recipient is unauthorized and may be illegal. In this case, please immediately notify the sender and delete it from your system. Anadolu University does not guarantee the accuracy or completeness of any information included in this message. Therefore, by any means Anadolu University is not responsible for the content of the message, and the transmission, reception, storage, and use of the information. The opinions expressed in this message only belong to the sender of it and may not reflect the opinions of Anadolu University.

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Re: Intensity Estimation Methods

Rolf Turner
On 15/12/17 01:01, Cenk İÇÖZ via R-sig-Geo wrote:
> Hello list,,
>
> I have a spatial point pattern . I am trying to estimate its
> intensity both with a fixed bandwidth and  with an adaptive
> bandwidth. How could I compare the goodness of these two fits? I mean
> are there any things like mse, aic or any other criteria??? I want to
> compare the difference between the estimated intensity and the
> original pattern's intensity.

I think that the following fortune (fortunes::fortune(340)) might be
relevant:

> Bandwidth selection is an unresolved (and possibly unsolvable) problem in
> smoothing, so you're perfectly justified in trying/choosing an arbitrary value
> if it produces good pictures!
>    -- Adrian Baddeley (answering a user's question about the choice of
>       smoothing parameter when using the density.ppp() function from the
>       spatstat package)
>       private communication (March 2013)

I am cc-ing to the man himself to see if he has further comment.

cheers,

Rolf Turner

--
Technical Editor ANZJS
Department of Statistics
University of Auckland
Phone: +64-9-373-7599 ext. 88276

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Re: Intensity Estimation Methods

R-sig-geo mailing list
Thanks a lot.
I did superimpose the original pattern to pixel images of intensities. With adaptive smothing intensity higher zones are too narrowed.
Also the differences of intensities are getting higher in the study region. The fixed bandwidth choosen with bw.ppl( ) in spatstat give me a better Picture. This is my opinion and also this is in my case . I use this bandwidth as a global bandwidth for adaptive smoothing.


-----Original Message-----
From: Rolf Turner [mailto:[hidden email]]
Sent: Thursday, December 14, 2017 11:14 PM
To: Cenk İÇÖZ <[hidden email]>
Cc: [hidden email]; [hidden email]; Ege Rubak <[hidden email]>
Subject: Re: [R-sig-Geo] Intensity Estimation Methods

On 15/12/17 01:01, Cenk İÇÖZ via R-sig-Geo wrote:
> Hello list,,
>
> I have a spatial point pattern . I am trying to estimate its intensity
> both with a fixed bandwidth and  with an adaptive bandwidth. How could
> I compare the goodness of these two fits? I mean are there any things
> like mse, aic or any other criteria??? I want to compare the
> difference between the estimated intensity and the original pattern's
> intensity.

I think that the following fortune (fortunes::fortune(340)) might be
relevant:

> Bandwidth selection is an unresolved (and possibly unsolvable) problem
> in smoothing, so you're perfectly justified in trying/choosing an
> arbitrary value if it produces good pictures!
>    -- Adrian Baddeley (answering a user's question about the choice of
>       smoothing parameter when using the density.ppp() function from the
>       spatstat package)
>       private communication (March 2013)

I am cc-ing to the man himself to see if he has further comment.

cheers,

Rolf Turner

--
Technical Editor ANZJS
Department of Statistics
University of Auckland
Phone: +64-9-373-7599 ext. 88276


________________________________

Bu elektronik posta ve onunla iletilen bütün dosyalar sadece yukarıda isimleri belirtilen kişiler arasında özel haberleşme amacını taşımakta olup gönderici tarafından alınması amaçlanan yetkili gerçek ya da tüzel kişinin kullanımına aittir. Eğer bu elektronik posta size yanlışlıkla ulaşmışsa, elektronik postanın içeriğini açıklamanız, kopyalamanız, yönlendirmeniz ve kullanmanız kesinlikle yasaktır. Bu durumda, lütfen mesajı geri gönderiniz ve sisteminizden siliniz. Anadolu Üniversitesi bu mesajın içerdiği bilgilerin doğruluğu veya eksiksiz olduğu konusunda herhangi bir garanti vermemektedir. Bu nedenle bu bilgilerin ne şekilde olursa olsun içeriğinden, iletilmesinden, alınmasından ve saklanmasından sorumlu değildir. Bu mesajdaki görüşler yalnızca gönderen kişiye aittir ve Anadolu Üniversitesinin görüşlerini yansıtmayabilir.

This electronic mail and any files transmitted with it are intended for the private use of the people named above. If you are not the intended recipient and received this message in error, forwarding, copying or use of any of the information is strictly prohibited. Any dissemination or use of this information by a person other than the intended recipient is unauthorized and may be illegal. In this case, please immediately notify the sender and delete it from your system. Anadolu University does not guarantee the accuracy or completeness of any information included in this message. Therefore, by any means Anadolu University is not responsible for the content of the message, and the transmission, reception, storage, and use of the information. The opinions expressed in this message only belong to the sender of it and may not reflect the opinions of Anadolu University.

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Re: Intensity Estimation Methods

Adrian Baddeley-3

Cenk ���Z <[hidden email]> writes:


 I have a spatial point pattern . I am trying to estimate its intensity
> both with a fixed bandwidth and  with an adaptive bandwidth. How could
> I compare the goodness of these two fits? I mean are there any things
> like mse, aic or any other criteria??? I want to compare the
> difference between the estimated intensity and the original pattern's
> intensity.


If you know the 'true' intensity then you could compute, for example, the integrated squared error.

In the spatstat package, if 'lamtrue' is the true intensity and 'lamest' the estimated intensity, given as pixel images (class 'im') then you can just do

     ISE <- integral((lamtrue-lamest)^2)


Alternatives include the Kulback-Leibler divergence

     KL <- integral(log(lamest/lamtrue) * lamtrue)

and the total variation distance

     TV <- integral(abs(lamtrue-lamest))/2


However if you have two competing estimates of the intensity of an observed point pattern, you're probably best to use the point process likelihood. Suppose lam1 and lam2 are pixel images giving  two competing estimates of the intensity of the same point pattern X. Then you could do


      lik1 <- sum(log(lam1[X])) - integral(lam1)

      lik2 <- sum(log(lam2[X])) - integral(lam2)


and compare the likelihoods.


Adrian Baddeley


________________________________
From: Cenk ���Z <[hidden email]>
Sent: Friday, 15 December 2017 8:23 PM
To: Rolf Turner
Cc: [hidden email]; Adrian Baddeley; Ege Rubak
Subject: RE: [R-sig-Geo] Intensity Estimation Methods

Thanks a lot.
I did superimpose the original pattern to pixel images of intensities. With adaptive smothing intensity higher zones are too narrowed.
Also the differences of intensities are getting higher in the study region. The fixed bandwidth choosen with bw.ppl( ) in spatstat give me a better Picture. This is my opinion and also this is in my case . I use this bandwidth as a global bandwidth for adaptive smoothing.


-----Original Message-----
From: Rolf Turner [mailto:[hidden email]]
Sent: Thursday, December 14, 2017 11:14 PM
To: Cenk ���Z <[hidden email]>
Cc: [hidden email]; [hidden email]; Ege Rubak <[hidden email]>
Subject: Re: [R-sig-Geo] Intensity Estimation Methods

On 15/12/17 01:01, Cenk ���Z via R-sig-Geo wrote:
> Hello list,,
>
> I have a spatial point pattern . I am trying to estimate its intensity
> both with a fixed bandwidth and  with an adaptive bandwidth. How could
> I compare the goodness of these two fits? I mean are there any things
> like mse, aic or any other criteria??? I want to compare the
> difference between the estimated intensity and the original pattern's
> intensity.

I think that the following fortune (fortunes::fortune(340)) might be
relevant:

> Bandwidth selection is an unresolved (and possibly unsolvable) problem
> in smoothing, so you're perfectly justified in trying/choosing an
> arbitrary value if it produces good pictures!
>    -- Adrian Baddeley (answering a user's question about the choice of
>       smoothing parameter when using the density.ppp() function from the
>       spatstat package)
>       private communication (March 2013)

I am cc-ing to the man himself to see if he has further comment.

cheers,

Rolf Turner

--
Technical Editor ANZJS
Department of Statistics
University of Auckland
Phone: +64-9-373-7599 ext. 88276


________________________________

Bu elektronik posta ve onunla iletilen b�t�n dosyalar sadece yukar�da isimleri belirtilen ki�iler aras�nda �zel haberle�me amac�n� ta��makta olup g�nderici taraf�ndan al�nmas� ama�lanan yetkili ger�ek ya da t�zel ki�inin kullan�m�na aittir. E�er bu elektronik posta size yanl��l�kla ula�m��sa, elektronik postan�n i�eri�ini a�klaman�z, kopyalaman�z, y�nlendirmeniz ve kullanman�z kesinlikle yasakt�r. Bu durumda, l�tfen mesaj� geri g�nderiniz ve sisteminizden siliniz. Anadolu �niversitesi bu mesaj�n i�erdi�i bilgilerin do�rulu�u veya eksiksiz oldu�u konusunda herhangi bir garanti vermemektedir. Bu nedenle bu bilgilerin ne �ekilde olursa olsun i�eri�inden, iletilmesinden, al�nmas�ndan ve saklanmas�ndan sorumlu de�ildir. Bu mesajdaki g�r��ler yaln�zca g�nderen ki�iye aittir ve Anadolu �niversitesinin g�r��lerini yans�tmayabilir.

This electronic mail and any files transmitted with it are intended for the private use of the people named above. If you are not the intended recipient and received this message in error, forwarding, copying or use of any of the information is strictly prohibited. Any dissemination or use of this information by a person other than the intended recipient is unauthorized and may be illegal. In this case, please immediately notify the sender and delete it from your system. Anadolu University does not guarantee the accuracy or completeness of any information included in this message. Therefore, by any means Anadolu University is not responsible for the content of the message, and the transmission, reception, storage, and use of the information. The opinions expressed in this message only belong to the sender of it and may not reflect the opinions of Anadolu University.

        [[alternative HTML version deleted]]


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Re: Intensity Estimation Methods

R-sig-geo mailing list
Adrian and Rolf.
Adrian's second example will solve my problem I guess.
Because I do not know the original intensity of the pattern. I only have an observed point pattern.

Thanks a lot.
Cenk


From: Adrian Baddeley [mailto:[hidden email]]
Sent: Saturday, December 16, 2017 11:58 AM
To: Cenk ���Z <[hidden email]>; Rolf Turner <[hidden email]>
Cc: [hidden email]; Ege Rubak <[hidden email]>
Subject: Re: [R-sig-Geo] Intensity Estimation Methods




Cenk ���Z <[hidden email]<mailto:[hidden email]>> writes:



 I have a spatial point pattern . I am trying to estimate its intensity
> both with a fixed bandwidth and  with an adaptive bandwidth. How could
> I compare the goodness of these two fits? I mean are there any things
> like mse, aic or any other criteria??? I want to compare the
> difference between the estimated intensity and the original pattern's
> intensity.



If you know the 'true' intensity then you could compute, for example, the integrated squared error.

In the spatstat package, if 'lamtrue' is the true intensity and 'lamest' the estimated intensity, given as pixel images (class 'im') then you can just do

     ISE <- integral((lamtrue-lamest)^2)



Alternatives include the Kulback-Leibler divergence

     KL <- integral(log(lamest/lamtrue) * lamtrue)

and the total variation distance

     TV <- integral(abs(lamtrue-lamest))/2



However if you have two competing estimates of the intensity of an observed point pattern, you're probably best to use the point process likelihood. Suppose lam1 and lam2 are pixel images giving  two competing estimates of the intensity of the same point pattern X. Then you could do



      lik1 <- sum(log(lam1[X])) - integral(lam1)

      lik2 <- sum(log(lam2[X])) - integral(lam2)



and compare the likelihoods.



Adrian Baddeley



________________________________
From: Cenk ���Z <[hidden email]<mailto:[hidden email]>>
Sent: Friday, 15 December 2017 8:23 PM
To: Rolf Turner
Cc: [hidden email]<mailto:[hidden email]>; Adrian Baddeley; Ege Rubak
Subject: RE: [R-sig-Geo] Intensity Estimation Methods

Thanks a lot.
I did superimpose the original pattern to pixel images of intensities. With adaptive smothing intensity higher zones are too narrowed.
Also the differences of intensities are getting higher in the study region. The fixed bandwidth choosen with bw.ppl( ) in spatstat give me a better Picture. This is my opinion and also this is in my case . I use this bandwidth as a global bandwidth for adaptive smoothing.


-----Original Message-----
From: Rolf Turner [mailto:[hidden email]]
Sent: Thursday, December 14, 2017 11:14 PM
To: Cenk ���Z <[hidden email]<mailto:[hidden email]>>
Cc: [hidden email]<mailto:[hidden email]>; [hidden email]<mailto:[hidden email]>; Ege Rubak <[hidden email]<mailto:[hidden email]>>
Subject: Re: [R-sig-Geo] Intensity Estimation Methods

On 15/12/17 01:01, Cenk ���Z via R-sig-Geo wrote:
> Hello list,,
>
> I have a spatial point pattern . I am trying to estimate its intensity
> both with a fixed bandwidth and  with an adaptive bandwidth. How could
> I compare the goodness of these two fits? I mean are there any things
> like mse, aic or any other criteria??? I want to compare the
> difference between the estimated intensity and the original pattern's
> intensity.

I think that the following fortune (fortunes::fortune(340)) might be
relevant:

> Bandwidth selection is an unresolved (and possibly unsolvable) problem
> in smoothing, so you're perfectly justified in trying/choosing an
> arbitrary value if it produces good pictures!
>    -- Adrian Baddeley (answering a user's question about the choice of
>       smoothing parameter when using the density.ppp() function from the
>       spatstat package)
>       private communication (March 2013)

I am cc-ing to the man himself to see if he has further comment.

cheers,

Rolf Turner

--
Technical Editor ANZJS
Department of Statistics
University of Auckland
Phone: +64-9-373-7599 ext. 88276


________________________________

Bu elektronik posta ve onunla iletilen b�t�n dosyalar sadece yukar�da isimleri belirtilen ki�iler aras�nda �zel haberle�me amac�n� ta��makta olup g�nderici taraf�ndan al�nmas� ama�lanan yetkili ger�ek ya da t�zel ki�inin kullan�m�na aittir. E�er bu elektronik posta size yanl��l�kla ula�m��sa, elektronik postan�n i�eri�ini a��klaman�z, kopyalaman�z, y�nlendirmeniz ve kullanman�z kesinlikle yasakt�r. Bu durumda, l�tfen mesaj� geri g�nderiniz ve sisteminizden siliniz. Anadolu �niversitesi bu mesaj�n i�erdi�i bilgilerin do�rulu�u veya eksiksiz oldu�u konusunda herhangi bir garanti vermemektedir. Bu nedenle bu bilgilerin ne �ekilde olursa olsun i�eri�inden, iletilmesinden, al�nmas�ndan ve saklanmas�ndan sorumlu de�ildir. Bu mesajdaki g�r��ler yaln�zca g�nderen ki�iye aittir ve Anadolu �niversitesinin g�r��lerini yans�tmayabilir.

This electronic mail and any files transmitted with it are intended for the private use of the people named above. If you are not the intended recipient and received this message in error, forwarding, copying or use of any of the information is strictly prohibited. Any dissemination or use of this information by a person other than the intended recipient is unauthorized and may be illegal. In this case, please immediately notify the sender and delete it from your system. Anadolu University does not guarantee the accuracy or completeness of any information included in this message. Therefore, by any means Anadolu University is not responsible for the content of the message, and the transmission, reception, storage, and use of the information. The opinions expressed in this message only belong to the sender of it and may not reflect the opinions of Anadolu University.

        [[alternative HTML version deleted]]


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