## INHOMOGENEOUS MARKOV POINT PROCESSES BY TRANSFORMATION

__Linda Stougaard Nielsen__, Adrian Baddeley, Eva B. Vedel Jensen

Department of Mathematical Sciences

University of Aarhus

Ny Munkegade

8000 Aarhus C

Denmark

Email: lins@imf.au.dk

The position of trees in a forest or the centres of cells in tissue
can be described by a planar or spatial point process, respectively,
where each tree/cell centre is represented by a point.
It is of interest to consider models for point processes that allow
for interaction between the points as well as for inhomogeneity in
the intensity of the points. Markov point process models are very
useful to describe point interaction and can also be used to describe
inhomogeneity. In this talk we will consider a particular type of
inhomogeneous Markov point processes obtained by transforming a homogeneous
Markov point process. We will concentrate on transformations
that replace each of the points from the process in the observation
window and in some sense maintain the ordering of the points.
The major advantage of the transformation model is the nice statistical
properties. A data set will be examined using the transformation model.

#### References

E. B. V. Jensen and L. S. Nielsen (1999)
Inhomogeneous Markov point processes by transformation.
To appear in Bernoulli.