Course 1

Probabilistic aspects of minimal spanning trees

Louigi Addario-Berry, McGill University

Abstracts: This course will survey a range of probabilistic questions related to minimal spanning trees, with a focus on limiting structures and on the connection with critical percolation.

Course 2

Spatial point pattern analysis.  Theory and methods

Carlos Diaz-Avalos, IIMAS, UNAM

Spatial point patter analysis has become an analytical tool widely used in fields like ecology, material science, epidemiology and earth sciences among many other fields, with its theoretical basis being the theory of point processes.  Point processes can be viewed as finite random subsets of R^d or as random counting measures in bounded sets. The fundamental tool for inference is the conditional intensity function, which represents the expected number of events within a neighborhood of an arbitrary point, given the past history of events of the process.  Although MLE and MCMC methods for estimation have been implemented, non parametric approaches based on density estimators or in minimum contrasts are stil popular among practitioners. 

The goals of this short course are:

  1. To review briefly the fundamentals of the theory os point processes and its application to the analysis and inference of natural phenomena.
  2. To give the attendants insight about the common tools and methods for the analysis and statistical inference in point pattern analysis. 

The course includes a case study data set that will be used to illustrate parametric and non parametric methods and to give the students "hands on" experience with data analysis.