Wednesday 5 December, from 15:00 to 17:00Linda Stougaard Nielsen
Aud. G2, IMF, Building 532
Exploring the Strauss point process
Data sets consisting of positions of events or objects are
often observed in nature. Examples are the positions of
detected alpha-particles generated by decay of Radon
gases, stain centres in methylene-blue colored clay observed
in a horizontal slice, position of cells in tissue, trees in
a forest, or bronze particles in a filter.
Point process models are stochastic models for point
patterns. The point process model chosen to describe a given
point pattern must be able to describe the characteristics
of the pattern. For illustrating purposes, we will in this
talk consider the Strauss point process model which is
suitable for describing homogeneous regular point patterns.
The density of a point process is intractable, and iterative
methods are therefore needed for simulating realizations
from a given model and for computing likelihoods and other
statistics such as means and variances. Markov chain Monte
Carlo methods are very powerful and useful tools for this.
The most basic ideas including an example of the
Metropolis-Hastings birth-death algorithm are shortly
presented, and it is argued that object oriented programming
is well suited for handling point processes.
Monte Carlo inference for point processes involves repeating
the same procedures for various parameter values, and the
programs are therefore highly suited for being parallelised,
which is desirable since such programs are very time
consuming. The same procedures can be run independently of
each other on different machines, and a parallel program is
therefore simple to construct. Such a program is called
embarrassing parallel. The basic ideas for converting a
program into an embarrassing parallel program are presented.
In order to find maximum likelihood estimates in the Strauss
process, we need to compute the expected values of the
number of points, and the number of pairs of points closer
than a distance r apart. The Strauss process has
apart from r two more parameters, and we have
investigated how and how much the two means depend on the