School Seminars and Colloquia

Point processes, stochastic geometry, and spatial statistics

Stochastic Processes Seminar
A short course supported by MASCOS and M.Belz Fund

by Professor G¨unter Last

Institution: Universit¨at Karlsruhe (TH), Germany
Date: Thu 14th December 2006
Time: 3:15 PM
Location: Old Geology Theatre 2, The University of Melbourne

Abstract: These lectures aim at introducing into some basic concepts of the theory of spatial point processes and stochastic geometry. These theories deal with stochastic models for geometric patterns and spatial data and are for
instance applied in material science, stereology, biology, astronomy, and geology.

In the first two lectures we will introduce spatial point processes and some of their summary statistics, as contact distribution functions, the
nearest neighbour distribution, Ripley's K-function and the
pair-correlation function. One focus are tests of a Poisson hypothesis.

The subject of the third lecture are random closed sets with particular emphasis on the stationary Boolean model. We will discuss contact
distributions and covariance functions as well as their empirical counterparts.

For More Information: Associate Professor Kostya Borovkov: