kernel density: units of bandwidth

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kernel density: units of bandwidth

Tadaishi Yatabe-Rodriguez
Hello community,

I did a lovely kernel density from a point pattern, but now I'm wondering
what was the actual bandwidth I used. The value I used was 0.2770598, but
what does this mean? I suppose it's an area, but what is the unit? Is there
a way to transform this into a meaningful area unit?

Thanks,

Tada

--
*Tadaishi Yatabe*
DVM, MPVM, PhD (C)
Center for Animal Disease Modeling and Surveillance (CADMS)
Department of Medicine and Epidemiology
School of Veterinary Medicine
University of California Davis

http://tadaishi.wix.com/tada

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Re: kernel density: units of bandwidth

Roman Luštrik
Hi,

have you seen https://en.wikipedia.org/wiki/Kernel_density_estimation and
the section on how to select binwidth
<https://en.wikipedia.org/wiki/Kernel_density_estimation#Practical_estimation_of_the_bandwidth>
?

lp,
Roman


On Sat, Feb 20, 2016 at 1:48 AM, Tadaishi Yatabe-Rodriguez <
[hidden email]> wrote:

> Hello community,
>
> I did a lovely kernel density from a point pattern, but now I'm wondering
> what was the actual bandwidth I used. The value I used was 0.2770598, but
> what does this mean? I suppose it's an area, but what is the unit? Is there
> a way to transform this into a meaningful area unit?
>
> Thanks,
>
> Tada
>
> --
> *Tadaishi Yatabe*
> DVM, MPVM, PhD (C)
> Center for Animal Disease Modeling and Surveillance (CADMS)
> Department of Medicine and Epidemiology
> School of Veterinary Medicine
> University of California Davis
>
> http://tadaishi.wix.com/tada
>
>         [[alternative HTML version deleted]]
>
> _______________________________________________
> R-sig-Geo mailing list
> [hidden email]
> https://stat.ethz.ch/mailman/listinfo/r-sig-geo
>



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Re: [FORGED] kernel density: units of bandwidth

Rolf Turner
In reply to this post by Tadaishi Yatabe-Rodriguez
On 20/02/16 13:48, Tadaishi Yatabe-Rodriguez wrote:
> Hello community,
>
> I did a lovely kernel density from a point pattern, but now I'm wondering
> what was the actual bandwidth I used. The value I used was 0.2770598, but
> what does this mean? I suppose it's an area, but what is the unit? Is there
> a way to transform this into a meaningful area unit?

As the help for density.ppp tells you, sigma is the standard deviation
of the isotropic Gaussian "smoothing kernel" (i.e. density function with
mean c(0,0) and standard deviation of both "X" and "Y" equal to sigma,
and cov(X,Y) = 0).  Consequently the units of sigma are the units in
which X and Y are measured.

Thus if, for example, your point coordinates are in metres, then the
units of sigma are metres.  (So sigma is measured not in area but in
length or distance.)

HTH

cheers,

Rolf Turner

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

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Re: [FORGED] Re: [FORGED] kernel density: units of bandwidth

Rolf Turner
On 23/02/16 10:34, Tadaishi Yatabe-Rodriguez wrote:

> Thanks, Rolf. This ,makes it clearer. I've another question though: the
> ppp object I get the Kernel density from is not projected, then what
> would be the unit of projection of this un-projected object? The
> projection of the object from which it was created from (e.g.
> SpatialPoints object)?
>
> Thanks again,

You should probably keep this discussion on-list; others who subscribe
to the list are much more knowledgeable than I and may have useful
contributions to make (and may correct my errors).  I have taken the
liberty of including the list in my reply.

I think that your question is not well-posed.  The density.ppm()
function treats the coordinates of points as Euclidean coordinates (with
the same units on both the x and y axes).  If your point pattern is
"un-protected" then I presume that x and y are in longitude and latitude
in which case the coordinates are not Euclidean and the x and y axis
units are different, since longitude and latitude are constructed in
different ways.

If the region in question is "small" (and not too near either pole, I
guess) then this probably doesn't make much difference, and the units of
sigma would, roughly speaking, be "degrees".  Otherwise it seems to me
there is no meaningful answer to your question.

It would probably be best to project your data before forming the ppp
object.

Ege has been doing some work on point patterns on the sphere which might
possibly be of relevance here.  He may feel like chiming in on this issue.

cheers,

Rolf

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

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Re: [FORGED] Re: [FORGED] kernel density: units of bandwidth

Tadaishi Yatabe-Rodriguez
Sorry, Rolf. I didn't realize I was replying only to you!
Thanks for your reply. I'll project before making the ppp object that I'll
use in my Kernel.

Thanks,

T

On Mon, Feb 22, 2016 at 1:53 PM, Rolf Turner <[hidden email]>
wrote:

> On 23/02/16 10:34, Tadaishi Yatabe-Rodriguez wrote:
>
> Thanks, Rolf. This ,makes it clearer. I've another question though: the
>> ppp object I get the Kernel density from is not projected, then what
>> would be the unit of projection of this un-projected object? The
>> projection of the object from which it was created from (e.g.
>> SpatialPoints object)?
>>
>> Thanks again,
>>
>
> You should probably keep this discussion on-list; others who subscribe to
> the list are much more knowledgeable than I and may have useful
> contributions to make (and may correct my errors).  I have taken the
> liberty of including the list in my reply.
>
> I think that your question is not well-posed.  The density.ppm() function
> treats the coordinates of points as Euclidean coordinates (with the same
> units on both the x and y axes).  If your point pattern is "un-protected"
> then I presume that x and y are in longitude and latitude in which case the
> coordinates are not Euclidean and the x and y axis units are different,
> since longitude and latitude are constructed in different ways.
>
> If the region in question is "small" (and not too near either pole, I
> guess) then this probably doesn't make much difference, and the units of
> sigma would, roughly speaking, be "degrees".  Otherwise it seems to me
> there is no meaningful answer to your question.
>
> It would probably be best to project your data before forming the ppp
> object.
>
> Ege has been doing some work on point patterns on the sphere which might
> possibly be of relevance here.  He may feel like chiming in on this issue.
>
> cheers,
>
> Rolf
>
>
> --
> Technical Editor ANZJS
> Department of Statistics
> University of Auckland
> Phone: +64-9-373-7599 ext. 88276
>



--
*Tadaishi Yatabe*
DVM, MPVM, PhD (C)
Center for Animal Disease Modeling and Surveillance (CADMS)
Department of Medicine and Epidemiology
School of Veterinary Medicine
University of California Davis

http://tadaishi.wix.com/tada

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