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Timetable (DAEW06)

Algebraic Method in Experimental Design

Wednesday 26th October 2011 to Thursday 27th October 2011

Tuesday 25th October 2011
19:30 to 22:00 Welcome Dinner at Cocum Restaurant (71 Castle Street)
Wednesday 26th October 2011
09:00 to 09:25 Registration
09:25 to 09:30 Welcome from John Toland (INI Director) INI 1
09:30 to 12:30 Monomial Ideals

Eduardo Saenz (Universidad de La Rioja) Introduction to monomial ideals and reliability

The analysis of system reliability can be performed using the algebra of monomial ideals. In this short introduction we give an idea of what algebraic tools are used, the advantages and drawbacks of this method and some directions of future work.

Henry Wynn (London School of Economics) Monomial ideals, Alexander duality

Hugo Maruri-Aguilar (Queen Mary, University of London) Aberration and Betti numbers

12:30 to 13:30 Lunch at Wolfson Court
13:30 to 17:00 T Kahle & G Pistone & F Rapallo & S Kuhnt & D Bruynooghe
Graphical models, Markov bases and related topics

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

17:00 to 18:00 Drinks Reception
19:30 to 22:00 Conference Dinner at Christ's College
Thursday 27th October 2011
09:00 to 12:30 R Bailey & H Warren & M Piera Rogantin & R Fontana & H Maruri-Aguilar
Algebraic Approaches to Combinatorial Design

Hugo Maruri-Aguilar(Queen Mary, University of London)Some computational results for block designs

Rosemary Bailey (Queen Mary, University of London) Connectivity in block design, and Laplacian matrices

Helen Warren (London School of Hygiene and Tropical Medicine) Robustness of block designs

A new robustness criteria, Vulnerability, measures the likelihood of an incomplete block design resulting in a disconnected eventual design due to the loss of random observations during the course of the experiment. Formulae have been derived for calculating the vulnerability measure, which aids in design selection and comparison, by producing a full vulnerability ranking of a set of competing designs. For example, this provides a new method for distinguishing between non-isomorphic BIBDs, since despite them all having identical optimality properties, their vulnerabilities can vary. Theory has been developed relating design concurrences to block intersection counts. These combinatorial results have provided further insight into the properties and characteristics of robust designs. Furthermore these have led to interesting closure properties for vulnerability between BIBDs and their complements, between BIBDs and non-balanced designs constructed from them by the removal of or addition of blocks (e.g. Regular Graph Designs, Nearly Balanced Designs), and between BIBDs and replicated BIBDs. It would be interesting to investigate the combinatorial properties of replicated designs in more detail, from connectedness and optimality perspectives, especially since other work on crossover designs has similarly found that replication leads to less robustness, and in order to extend the concept of vulnerability to other blocked designs, e.g. row-column designs, crossover designs and factorial designs. Finally it would be interesting to incorporate prior knowledge of varying probabilities for each observation being lost, rather than assuming observation loss to be random.

Maria Piera Rogantin (Università degli Studi di Genova) Use of indicator functions in design

Roberto Fontana (Politecnico di Torino) Algebra and factorial designs

12:30 to 13:30 Lunch at Wolfson Court
University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons