Toby Kenney

I am responsible for maintaining and developing the Actuarial Science program at Dalhousie. Here is a website giving some details of the current program.

The Society of Actuaries has a scheme where the university can apply for reimbursement of the exam fees of up to three students per year sitting SoA exams. Here is a summary of this program, how to apply and the policy for how the university will choose which students to apply for.

I have interests in a wide variety of topics in areas of pure mathematics, data science and actuarial science.

In data science, I am interested in the application of abstract mathematical modelling to statistical methodology. I am interested in general statistical methodology, and in development of statistical techniques to analyse microbiome data. Some particular topics of interest include understanding the temporal dynamics of the microbiome; and handling the unique measurement error structure in microbiome data. In other areas of data science, I am working on a project on automatic diagnosis of emergency department data. This is a big project involving dealing with many difficulties from a statistical standpoint including: the large quantities of free text data; the amount of missing data, with the potential for the missing pattern to change between training and test data; and the structure of the data and diagnoses. In statistical methodology, I have several projects relating to various areas such as ranking problems; measurement error and variable selection. I have recently been working on unfolding and deconvolution problems which aim to estimate the distribution of a quantity from a sample with measurement error.

I am also interested in general machine-learning methods. These methods use mathematical structures to create flexible functions that can approximate any true distribution of the data. While the flexibility allows these functions to approximate the complicated relationships that can arise in real data, it also results in hard-to-interpret predictions. Furthermore, avoiding overfitting can be a challenge. By studying the mathematical structures underlying the methods, I hope to find improvements that address these issues.

I am beginning to develop a research program in Actuarial Science. Topics of interest include: estimating utility functions to find optimal insurance choices for individuals; and assessing the value of information for calculating insurance costs.

In pure mathematics, my research interests mostly fall between Category theory, universal algebra, logic and combinatorics. Particular areas of interest include partition and congruence lattices; and Coxeter groups. I have also recently worked on topological convexity spaces.