Anisotropic point processes are inhomogeneous?

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Anisotropic point processes are inhomogeneous?

Domenico Giusti
Dear all,

I have an anisotropic point pattern, analyzed by means of directional
correlograms, wavelets and Ksector functions.

I wonder if anisotropy prevents the use of inhomogeneous K-functions.

Thank you in advance,

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Domenico Giusti <[hidden email]>
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Re: Anisotropic point processes are inhomogeneous?

Ege Rubak
At least the typical definition of an inhomogeneous K-function uses a
disc as the structure element and can't capture anisotropy as far as I
can see. It only depends on distance between points and not the vector
difference.
Btw. if you do not assume stationarity of your process I would think
that the results from something like Ksector can be misleading. In
general it seems like a difficult problem to separate inhomogeneity and
anisotropy from each other, but it might be that I just don't know the
right tools.
Sorry for not being more helpful.
Cheers,
Ege

On 11/21/2017 07:02 PM, Domenico Giusti wrote:
> Dear all,
>
> I have an anisotropic point pattern, analyzed by means of directional
> correlograms, wavelets and Ksector functions.
>
> I wonder if anisotropy prevents the use of inhomogeneous K-functions.
>
> Thank you in advance,
>

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Re: Anisotropic point processes are inhomogeneous?

Domenico Giusti
Thank you Ege for your reply,

> In general it seems like a difficult problem to separate inhomogeneity and anisotropy from each other

this point is indeed not very clear to me.

If the homogeneous Poisson point process is defined by the properties of
i) homogeneity, ii) independence and iii) Poisson distribution; the
inhomogeneous Poisson process is a modification of the former with i)
intensity function, ii) independence and iii) Poisson distribution.

An anisotropic point process, defined as directional dependent process,
could be seen as inhomogeneous process having an oriented intensity
function, or violates the assumption of independence in both homogeneous
and inhomogeneous processes?

Similarly, is anisotropy violating the assumptions of independent
labels/components in inhomogeneous multitype point processes?

Thanks,

On 11/21/2017 10:41 PM, Ege Rubak wrote:
> stationarity of your process I would think that the results from
> something like Ksector can be misleading.

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