Jean-Fran¸coisCoeurjolly Introductiontospatialpointprocesses

Examples Definitions, Poisson Summary statistics Modelling and inference

Introduction to spatial point processes

Jean-Fran¸ cois Coeurjolly

http://www-ljk.imag.fr/membres/Jean-Francois.Coeurjolly/

Laboratoire Jean Kuntzmann (LJK), Grenoble University

Preliminary

Files which can de downloaded

http://www-ljk.imag.fr/membres/Jean-Francois.Coeurjolly/documents/Lille/

or more simply on the workshop webpage, program page http://math.univ-lille1.fr/ heinrich/geostoch2014/

introductionSPP cours.pdf : pdf file of the slides. Beamer version.

introductionSPP print.pdf : pdf file of the printed version.

ShortRcode used to illustrate the talks.

The code is using theexcellentRpackagespatstatwhich can be downloaded from the R CRAN website.

Examples Definitions, Poisson Summary statistics Modelling and inference

1 Examples

2 Definitions, Poisson

3 Summary statistics

4 Modelling and inference

Spatial data . . .

. . . can be roughly and mainly classified into three categories :

1

Geostatistical data.

2

Lattice data.

3

Spatial point pattern

Examples Definitions, Poisson Summary statistics Modelling and inference

Geostatistical data

sic.100 dataset (R package

geoR)

Cumulative rainfall in Switzerlan the 8th May.

The observation consists in the

discretization

of a random field,

X =(Xu,u ∈R²)

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Density

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Lattice data (1)

Eire dataset (R package

spdep)

% of people with group A in eire, observed in 26 regions.

The data are aggregated on the region

⇒

random field on a network.

Percentage with blood group A in Eire

under 27.91 27.91 − 29.26 29.26 − 31.02 over 31.02

Examples Definitions, Poisson Summary statistics Modelling and inference

Lattice data (2)

Lennon dataset (R package

fields)

Real-valued random field (gray scale image with values in

[0,

1]).

Defined on the network

{1, . . . ,

256}

²

.

0.0 0.2 0.4 0.6 0.8 1.0

0.00.20.40.60.81.0

Spatial point pattern (1)

Japanesepines dataset (R package

spatstat)

Locations of 65 trees on a bounded domain.

S =R²

(equipped with

k · k).

japanesepines

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Examples Definitions, Poisson Summary statistics Modelling and inference

Spatial point pattern (2)

Longleaf dataset (R package

spatstat)

Locations of 584 trees observed with their diameter at breast height.

S=R²×R⁺

(equipped with max(k · k,

| · |)).

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Spatial point pattern (3)

Ants dataset (R package

spatstat)

Locations of 97 ants categorised into two species.

S =R²× {0,

1} (equipped with the metric

max(

k · k,d_M)

for any distance

dM

on the mark space).

ants

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Examples Definitions, Poisson Summary statistics Modelling and inference

Spatial point pattern (3)

chorley dataset (R package

spatstat)

Cases of larynx and lung cancers and position of an industrial incinerator.

S =R²× {0,

1} (equipped with the metric

max(

k · k,d_M)

for any distance

dM

on the mark space).

Chorley−Ribble Data

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