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Research Project This page was last updated Jan 4 14:56 2001
Laboratory for Computational Stochastics

Wednesday 5 December, from 15:00 to 17:00
Aud. G2, IMF, Building 532

Linda Stougaard Nielsen

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 three parameters.