Some 2 weeks ago I sent a question to all of you concerning spatial

point patterns and the application of Ripley's K-function. The questions

basically were the following :

* Therefore my question : is the K-function a good technique to study

the spatial point pattern? (as I understood from Cressie (1993) it is

one of the best ones?)? How sensitive is it to the estimation of lambda?

And to non-stationarity? Any suggestions?

* Hence my second question : should I consider these marked points as

irregular lattice data? And then calculate a semivariogram, maybe

interpolate a surface? I have the feeling there is quite a lot of

variability in mound height over small areas. How do I express this

best?

I received following answers, for which I would like to thank all

contributors once again!

Subject:

Re: [AI-GEOSTATS: spatial point patterns]

Date:

Wed, 02 Apr 2003 12:14:31 +0200

From:

Gregoire Dubois <gregoire.dubois@...>

To:

Veerle Huvenne <veerle.huvenne@...>

hello Veerle,

a quick and lazy reply: the Crimestat software (Free) has a lot of

various

functions for point pattern analysis. The manual is also well written

and

describes all these functions.

Info on Crimestat can be found at www.ai-geostats.org

Groetjes,

Gregoire

---------------------------

Subject:

Re: AI-GEOSTATS: spatial point patterns

Date:

Wed, 2 Apr 2003 14:28:27 -0800

From:

"Qinghua GUo" <gqh@...>

To:

"Veerle Huvenne" <veerle.huvenne@...>

References:

1

hi, Veerle

Yes, Ripley's K is one of the best approach to study point pattern, but

it

requires stationarity, for the non-stationarity, the result from

ripley's

will be misleading. I have tested it in trend data, and demonstrated

that

riply's K is unable to study the non-stationarity data. You may correct

the

trend first or apply some other methods.

Traditional semivariogram is not suitable for uncontiunous data, which I

think is your case.

Depending on the purpose of this study, some cross (e.g. cross-Riply's

K)

analysis will be more useful.

Regards

Qinghua Guo

-----

Upon further questions, Qinghua Guo gave me some more useful information

:

Dear Huvenne:

>

there is a Ripley'k variant:

> Can you please suggest some references about alternative methods?

r*K(h)=E(number of event within distance h)

r is the intensity or mean number of events per unit area.

Traditionally, r is assumed to be constant, but you can change it

according

to trends (e.g. fitting a surface)

> But when the data is not stationary, can I use a cross-Ripley then?

And

again,> can you please suggest some references?

Trend correction should be applied in order to use cross analysis.

We are ongoing studying these areas, there are few references addressing

point pattern analysis on data with trends.

Regards

Qinghua Guo

-------

Subject:

Fwd: AI-GEOSTATS: spatial point patterns

Date:

Thu, 03 Apr 2003 12:55:28 +0200

From:

Eric Pirard <eric.pirard@...>

To:

veerle.huvenne@...

Hello Veerle,

I have no special experience with the practical use of Ripley's K

But, the kind of problem you are adressing seems to me to be more

related with stochastic geometry and in particular

random processes of discs with variable diameters (I assume diameters

and heights of your mouns are somehow related).

In other words I think it would be more adequate to consider the

random/non-random dispersion of your mounts

including their exact shapes and not only their centres.

A useful (but strong in mathematics) reference book on the topic is

STOYAN, KENDALL MECKE Stochastic Geometry and its Applications, Wiley,

1995

Several papers on similar subjects although more related to material

sciences have also been published by the Ecole des

Mines de Paris and in particular Dominique JEULIN. He has organised a

regular short course in Paris named

"Modélisation des structures aléatoires" that might be of interest to

you.

Finally, I did use for an Image Analysis problem (yours is one!) a

test developed by Bosco and consisting in measuring

the evolution of the total perimeter of particles (in this case

mounds) after successive dilations. (Perimeter-area laws for a

random agglomeration of particles; Bosco Emmanuel in Phys. Rev. E 52,

46814684 (1995))

-----------------

Subject:

RE: AI-GEOSTATS: spatial point patterns

Date:

Fri, 4 Apr 2003 12:10:13 +0100

From:

J.Illian@...

To:

veerle.huvenne@...

Dear Veerle,

there is a paper by Baddeley, Moeller, and Waagepetersen, which

introduces

an inhomgeneous version of the K-function:

Baddeley, A., Møller, J., & Waagepetersen, R. (1998). Non- and

semi-parametric estimation of interaction in inhomogeneous point

patterns.

Statistica Neerlandia, 54, 329-350.

You might find this useful!

Thanks

Janine

--

Veerle Huvenne

Renard Centre of Marine Geology

University of Ghent

Krijgslaan 281, S8

9000 Gent, Belgium

+32/9/264.45.84

--

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