University of Newcastle upon Tyne

School of Mathematics and Statistics

Statistics Seminars 2004-2005

26 November 2004, L401, 2:15pm

Dr Vanessa Didelez, Department of Statistical Science, University College London

Abstract

Graphical models are used to encode the (conditional) independence structure of a multivariate random vector in a graphical way. One of their benefits is that certain computational simplifications can immediately be read off the graph, e.g. the property of collapsibility. We can collapse onto a set of variables if the (conditional) independence structure and the distributional assumptions are preserved when ignoring the remaining variables. In this talk I will give two examples of the use of collapsibility.

(1) In graphical time series models collapsibility has been exploited to refine the model selection strategy (Fried & Didelez, 2003). This will be illustrated with an example from on-line monitoring.

(2) Graphical conditions for collapsibility and decomposability in conditional Gaussian regression models have been derived by Didelez & Edwards (2004). These are multivariate regression models for mixed, continuous and discrete response variables, simple linear regression and logistic regression being special cases. If such a CG-regression model is decomposable (i.e. successively collapsible) it is equivalent to a series of univariate regressions.

References

Didelez & Edwards (2004). Collapsibility in Graphical CG-Regression Models, Scandinavian Journal of Statistics (to appear).

Fried & Didelez (2003). Decomposability and selection of graphical models for time series, Biometrika, 2003, 90, 251-267

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