Toby Kenney

Assistant Professor
Department of Mathematics and Statistics,
Dalhousie University
Halifax, Nova Scotia,
B3H 3J5

Office: 102 Chase Building

Toby Kenney


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 3030X/Y: Abstract Algebra - Fall 2012 and Winter 2013

MATH/STAT 3360: Probability - Fall 2014, Fall 2013, Fall 2012, Fall 2011

MATH/STAT 2600: Theory of interest - Fall 2014, Fall 2013, Fall 2010

MATH/STAT 3460: Intermediate Statistical Theory - Winter 2014

ACSC/STAT 3703: Actuarial Models I - Winter 2015

ACSC/STAT 3720: Life Contingencies I - Winter 2015, Winter 2016, Winter 2017

ACSC/STAT 4703: Actuarial Models II - Fall 2015, Fall 2016, Fall 2017

ACSC/STAT 4720: Life Contingencies II - Fall 2015, Fall 2016, Fall 2017

Actuarial Science Program

I am working on developing the new Actuarial Science program at Dalhousie. Here is a website giving some details of the new program.


Research Interests

I have interests in a wide variety of topics, mostly related to algebra, logic, combinatorics, and statistical genetics, phylogeny, and metagenomics. Particular topics of interest include: lattice theory, particularly partition lattices and congruence lattices; Coxeter groups; statistical models for molecular evolution; metagenomics. The current trend in my research direction is incorporating abstract mathematical structures into statistical modelling of complex data. I am mostly focusing on bioinformatics data, though many of the techniques are general, and can be applied to structured data from a variety of other areas. I have also begun to develop some research interests in Actuarial Science. These involve both applying techniques from Actuarial Science to other statistical problems, and applying new techniques to problems in Actuarial Science.


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

Papers submitted or under revision

W. Chen, T. Kenney, J. Bielawski and H. Gu. Testing Adequacy for DNA Substitution Models.
M. Butler, H. Gu, A. Carter, T. Kenney and S. Ling. A Prospective Diagnostic Support Tool for the Differentiation of Abdominal Pain in the Adult Emergency Department Population.
T. Kenney and H. Gu. The Adequate Bootstrap.

Papers in preparation

T. Kenney, H. Gu, J.Bielawski and K. Dunn. Detecting Adaptive Protein Evolution under Generalised Codon-Based models.
L. Liu, T. Kenney, H. Gu and J. Van Limbergen. Metagenomic Classification of Inflammation Condition Following Ileal Pouch-Anal Anastomosis, Using a Non-taxonomically Restricted Method.

Graduate Students

Current Students

Lihui LiuPhD. (Co-supervised with H. Gu and J. Van Limbergen)Interaction between Host-genome and Metagenomic risk-factors for Irritable Bowel Disease.
Yun CaiPhD. (Co-supervised with H. Gu) Non-negative matrix factorisation for classification of metagenomic data.
Mingzhu WangMSc. The Influence of Utility Functions on Insurance Choices

Completed Students

Tianshu HuangMSc. (Co-supervised with H. Gu) Semi-Parametric Principal Component Analysis for Poisson Count Data with Application to Microbiome Data Analysis.
Hao HeMSc. (Co-supervised with H. Gu) Robust Ranking and Selection with Heavy-tailed Priors and its Application to Market Basket Analysis.
Li LiMSc. (Co-supervised with H. Gu)Recombination Detection Based on Likelihood and Clustering for DNA and Amino Acid Sequences.
Yun CaiMSc. (Co-supervised with H. Gu) Non-negative matrix factorisation for classification of metagenomic data.
Wei DaiMSc. (Co-supervised with H. Gu)A new Test to Build Confidence Regions using Balanced Minimum Evolution.


  • COLD (latest version: 1.1.1)
  • COLD (Codon Optimal Likelihood Discoverer) is a program for estimating phylogenetic parameters using maximum likelihood for codon models.

  • Simple Plot (latest version: 1.0.0)
  • Simple Plot is a program for adaptively projecting multidimensional data into two dimensions.

  • Adequate Bootstrap (latest version: 1.0.0)
  • Adequate Bootstrap is a program for estimating confidence intervals for parameter values that take into account the uncertainty due to model misspecification.