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Bayesian identifiability for log-linear models.


School of Mathematics and Statistics

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Dr M Papathomas Applications accepted all year round

About the Project

Log-linear modelling is the standard approach for investigating the full joint dependence structure between categorical variables such as phenotypes and SNPs. Complex dependence structures can be easily discerned using graphical log-linear models (Papathomas and Richardson, 2016). This can potentially lead to identifying functionally important pathways. The number of cells in the associated contingency table increases rapidly with the number of variables, creating sparse contingency tables with a number of zero cell counts, even for a large number of subjects. The presence of zero cell counts can potentially make some model parameters non-estimable, also referred to as non-identifiable. Non-identifiability is a major impediment to evaluating how risk factors interact, and understanding important biological mechanisms. Problems associated with identifiability are currently not sufficiently understood, and have not been addressed in a systematic manner. The aim of this project is to develop methods that will utilize information pertaining to the Bayesian identifiability of interaction parameters, towards choosing the best log-linear model given the data.



Funding Notes

Multiple sources of scholarship funding are potentially available, including university, research council (EPSRC) and research group. Some are open to international students, some to EU and some UK only.

Applicants should have a good first degree in mathematics, statistics or another discipline (e.g., biology, computer science), with substantial statistical component. A masters-level degree is an advantage.

Further details of the application procedure, including contact details for the Postgraduate Officer, are available at http://tinyurl.com/StAndStatsPhD

References

Papathomas, M. and Richardson, S. (2016): Exploring dependence between categorical variables: benefits and limitations of using variable selection within Bayesian clustering in relation to log-linear modelling with interaction terms. Journal of Statistical Planning and Inference. 173, 47-63
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