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Graphical models, Markov bases and related topics

Presented by: 
T Kahle & G Pistone & F Rapallo & S Kuhnt & D Bruynooghe
Wednesday 26th October 2011 - 13:30 to 17:00
INI Seminar Room 1

Thomas Kahle (Max-Planck-Institut fur Mathematik, Leipzig) What's new with Markov Bases and hot to understand support sets of log-linear models via polytopes

Gianni Pistone (Università degli Studi di Torino) Hilbert basis in design and loglinear models Abstract - see below.

Fabio Rapallo (Università degli Studi del Piemonte Orientale) Weakened independence models

It is known that in a two-way contingency table the set of all 2 by 2 minors characterizes the independence model. A family of models can be defined by selecting subsets of minors. These models are termed as "weakened independence models'' (Carlini and Rapallo, 2011). Restricted to adjacent minors, some results have been obtained in the study of such models. For instance, the sufficient statistic is fully described. Several problems are still open in this research topic:
  • (a) the use of such models to detect clusters in the contingency tables;
  • (b) to study the connections between weakened independence models and mixture models;
  • (c) to generalize the definition to more complex models; (d) to extend the theory to general 2 by 2 minors.

Sonja Kuhnt (Technische Universität Dortmund) Algebraic identifiability and comparison of generalised linear models

As part of the Collaborative Research Centre 823 at the Technical University of Dortmund we work on a project which is concerned with "Modelling and controlling thermokinetic coating processes". The effect of spraying parameters on the coating quality is indirectly modelled by using in-flight characteristics of the particles. Therefore we study firstly the relationship between machine parameters X and in-flight particles Y and secondly the relationship between the in-flight particles Y and the coating properties Z. Besides the main topic of modelling and controlling of the two step process we are interested in the choice of suitable experimental designs. Here we extract two research questions, which can be set into the algebraic statistics framework. So far generalised linear models have turned out to be a suitable model class. We would like to know which models can be identified based on a chosen design. Secondly we would like to compare the difference in models derived from a direct regression of Z on X compared with a regression of Z on Y, where the regression relationship from X to Y is known. These questions can be reformulated as follows:
  • 1. How can we derive results of algebraic identifiability with respect to generalized linear models?
  • 2. How can we compare direct and two step regression models based on algebraic statistics?
We look forward to a productive discussion of these problems.

Daniel Bruynooghe (London School of Economics) Differential cumulants and monomial ideals

Presentation Material: 
University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons