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Bayesian identifiability for log-linear models.

   School of Mathematics and Statistics

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  Dr Michail Papathomas  Applications accepted all year round  Competition Funded PhD Project (Students Worldwide)

About the Project

Log-linear modelling is the standard approach for investigating the full joint dependence structure between categorical variables. Applications include discerning the relation between phenotypes and environmental, anthropometric or genetic risk factors. Complex dependence structures can be easily discerned using graphical log-linear models (Papathomas and Richardson, 2016). This can lead to the identification of functionally important pathways. Another application concerns the size of hidden populations, such as victims of modern slavery (Cruyff, M., Overstall, Papathomas, McRea (2020)). 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 (Sharifi Far, Papathomas, King, 2019). Non-identifiability is a major impediment to evaluating how 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.

For more information, please see the School's Postgraduate Research page, and in particular the information about Statistics PhD opportunities.

Funding Notes

Full funding (fees, plus stipend of approx. £15,840) is available for well-qualified students; we encourage applications as soon as possible to maximize your chances of being funded. UK, EU and other overseas students are all encouraged to apply. New PhD students would typically start in September 2022, but this is flexible. More information is available School's Postgraduate Research web page -- please see the link at the bottom of the project description.


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
Sharifi Far, S., Papathomas, M. & King, R. (2019). Parameter redundancy and the existence of maximum likelihood estimates in log-linear models. Statistica Sinica, 31, 1125-1143
Cruyff, M., Overstall, A., Papathomas, M. & McCRea, R. (2020) Multiple system estimation of victims of human trafficking: model assessment and selection. Crime and Delinquency. Online First, 17p

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