MATH 3090: Advanced Calculus - Fall 2006
MATH/CSCI 2112: Discrete Structures I - Winter 2007
MATH 2051: Problems in Geometry - Fall 2007
MATH/CSCI 2113: Discrete Structures II - Winter 2008
MATH 1115: Mathematics for Commerce - Winter 2011
MATH 1115: Mathematics for Liberal Arts - Winter 2012
MATH/STAT 3460: Intermediate Statistical Theory - Winter 2014
ACSC/STAT 3703: Actuarial Models I - Winter 2015
I have interests in a wide variety of topics in areas of pure mathematics, data science and actuarial science.
In data science my particular area of interest is the application of statistical techniques to microbiome data. Some particular topics of interest include understanding the temporal dynamics of the microbiome; developing methods for discerning discriminating patterns in 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 and model adequacy testing.
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 universal algebra, logic an combinatorics. Particular areas of interest include partition and congruence lattices; and Coxeter groups.
|Y. Cai, H. Gu and T. Kenney||Learning Microbial Community Structures with Supervised and Unsupervised Non-negative Matrix Factorization.||Microbiome 5 (2017), (27 pages)|
|T. Kenney||Partial Sup Lattices||Theory and Applications of Categories 30 (2015), 305-331|
|M. Abeysunderra, T. Kenney, C. Field and H. Gu||Combining Distance Matrices on Identical Taxon Sets for Multi-Gene Analysis with Singular Value Decomposition.||PLoS ONE 9 (2014), e94279. doi:10.1371/journal.pone.0094279 (14 pages)|
|T. Kenney||Coxeter Groups, Coxeter Monoids and the Bruhat Order.||Journal of Algebraic Combinatorics 39 (2014), 719-731|
|T. Kenney and H. Gu||Hessian Calculation for Phylogenetic Likelihood based on the Pruning Algorithm and its Applications||Statistical Applications in Genetics and Molecular Biology, 11 (2012), issue 4, article 14|
|T. Kenney and R. Paré||Categories as Monoids in Span, Rel and Sup,||Cahiers de e Topologie et Géométrie Différentielle Catégoriques, 52 (2011), 209-240|
|T. Kenney||The Path Relation for Directed Planar Graphs, and its Relation to the Free Diad.||Discrete Mathematics 311 (2011), 441-456|
|T. Kenney||Injective Power Objects and the Axiom of Choice||Journal of Pure and Applied Algebra 215 (2011), 131-144|
|T. Kenney||Graphical algebras - a new approach to congruence lattices||Algebra Universalis 64 (2010), 313-338|
|H. Gu, T. Kenney and M. Zhu||Partial Generalized Additive Models: an Information-Theoretic Approach to Selecting Variables and Dealing with Concurvity.||Journal of computational and graphical statistics 19 (2010), 531-551|
|T. Kenney||The General Theory of Diads||Appl. Cat. Struct. 18 (2010), 523-572|
|T. Kenney and R. J. Wood||Tensor Products of Sup Lattices and generalized sup-arrows.||Theory and Applications of Categories 24 (2010), 266-287|
|T. Kenney||Diads and Their Application to Topoi,||Appl. Cat. Struct. 17 (2009), 567-590|
|T. Kenney||Copower Objects and their applications to Finiteness in Topoi,||Theory and Applications of Categories 16 (2006), 923-956|
|T. Kenney||Generating Families in a Topos,||Theory and Applications of Categories 16 (2006), 896-922|
|T. Kenney, H. He and H. Gu.||Prior Distributions for Ranking Problems.|
|W. Chen, T. Kenney, J. Bielawski and H. Gu.||Testing Adequacy for DNA Substitution Models.|
|T. Kenney, H. Gu, J.Bielawski and K. Dunn.||Detecting Adaptive Protein Evolution under Generalised Codon-Based models.|
|T. Kenney and H. Gu.||The Adequate Bootstrap.|
|L. Liu, T. Kenney, J. Van Limbergen and H. Gu.||Microbiomic Non-Taxonomically- Restricted Variable Selection for Prediction in Microbiome Data Analysis.|
|T. Kenney, T. Huang and H. Gu.||Poisson corrected Principal Component Analysis.|
|Lihui Liu||PhD. (Co-supervised with H. Gu and J. Van Limbergen)||Interaction between Host-genome and Metagenomic risk-factors for Irritable Bowel Disease.|
|Yun Cai||PhD. (Co-supervised with H. Gu)||Non-negative matrix factorisation for classification of metagenomic data.|
|Junqiu Gao||MSc. (Co-supervised with H. Gu)||Temporal dynamics of microbiome data.|
|Mingzhu Wang||MSc.||The Influence of Utility Functions on Insurance Choices|
|Tianshu Huang||MSc. (Co-supervised with H. Gu)||Semi-Parametric Principal Component Analysis for Poisson Count Data with Application to Microbiome Data Analysis.|
|Hao He||MSc. (Co-supervised with H. Gu)||Robust Ranking and Selection with Heavy-tailed Priors and its Application to Market Basket Analysis.|
|Li Li||MSc. (Co-supervised with H. Gu)||Recombination Detection Based on Likelihood and Clustering for DNA and Amino Acid Sequences.|
|Yun Cai||MSc. (Co-supervised with H. Gu)||Non-negative matrix factorisation for classification of metagenomic data.|
|Wei Dai||MSc. (Co-supervised with H. Gu)||A new Test to Build Confidence Regions using Balanced Minimum Evolution.|
These guides give advice on what are new topics for a number of graduate students, and are based on common mistakes I have seen when supervising students.
COLD (Codon Optimal Likelihood Discoverer) is a program for estimating phylogenetic parameters using maximum likelihood for codon models.
Simple Plot is a program for adaptively projecting multidimensional data into two dimensions.
Adequate Bootstrap is a program for estimating confidence intervals for parameter values that take into account the uncertainty due to model misspecification.
Here are a number of
R packages written by me or my students. These will probably be submitted to CRAN when the relevant papers are published.