Earlier today I watched as my friend Lorna finished her Ph.D. It was, without a doubt, a thing of beauty.
As expected, Lorna’s presentation was amazing and altogether satisfying as she has always managed to connect with the audience in a way that few people can. I think it’s a result of knowing her stuff inside and out, and clearly having fun while she’s presenting. Her sense of humour also helps.
I think the best part of this day is the fact that I got to watch not just a colleague – but a friend – finish a huge chapter in her life. You see, it’s one thing to watch the defence of someone whom you don’t know and appreciate the work they put into their dissertation; it’s an altogether different experience to listen to the defence of someone you are fortunate enough to call a friend.
I met Lorna when she was an undergraduate student. She stood out even then as an exceptional student and a remarkable person. I watched as she began her graduate work. I spent hours chatting with her over coffee and tea and cookies, learning first hand how amazing she really is. I watched with pride as she finished her Masters and beamed when she went on to begin her PhD. We’ve continued to spend time talking about mathematics and statistics, and many more hours chatting about life in general. I was honoured when she asked me to co-author a paper with her and her PhD advisor. I would work with her again in a heartbeat. She is an exceptional researcher, a hard worker, and an amazing person.
I’m proud to call her my friend. I’m even prouder of her today because of all that she has accomplished.
Congratulations Dr. Deeth. I can’t wait to celebrate this amazing accomplishement with you.
Individual-level models are a class of complex statistical models, often fitted within a Bayesian Markov chain Monte Carlo framework, that have been effectively used to model the spread of infectious diseases. The ability of these models to incorporate individual-level covariate information allows them to be highly flexible, and to account for such characteristics as population heterogeneity. However, these models can be subject to inherent uncertainties often found in infectious disease data. As well, their complex nature can lead to a significant computational expense when fitting these models to epidemic data, particularly for large populations.
An individual-level model that incorporates a latent grouping structure into the modeling procedure, based on some heterogeneous population characteristic, is investigated. The dependence of this latent conditional individual-level model on a discrete latent grouping variable alleviates the need for explicit, although possibly unreliable, covariate information. A simulation study is used to assess the posterior predictive ability of this model, in comparison to individual-level models that utilize the full covariate information, or that assume population homogeneity. These models are also applied to data from the 2001 UK foot-and-mouth disease epidemic.
When attempting to compare complex models fitted within the Bayesian framework, the identification of appropriate model selection tools would be beneficial. The use of deviance information criterion (DIC) as model comparison tool, particularly for the latent conditional individual-level models, is investigated. A simulation study is used to compare five variants of the DIC, and the ability of each DIC variant to select the true model is determined.
Finally, an investigation into methods to reduce the computational burden associated with individual-level models is carried out, based on an individual-level model that also incorporates population heterogeneity through a discrete grouping variable. A simulation study is used to determine the effect of reducing the overall population size by aggregating the data into spatial clusters. Reparameterized individual-level models, accounting for the aggregation effect, are fitted to the aggregated data. The effect of data aggregation on the ability of two reparameterized individual-level models to identify a covariate effect, as well as on the computational expense of the model fitting procedure, is explored.