Program Description

Statistics is concerned with the development and use of mathematical and computational methods for the collection, analysis, and interpretation of data in support of scientific inquiry, informed decision-making, and risk management. It calls on a broad range of tools from probability theory to computer-intensive techniques. The main areas of research by statisticians in the ISM network include

  • Bayesian inference and Markov chain Monte Carlo methods
  • causal inference
  • computational statistics
  • dependence modeling and multivariate analysis
  • directional statistics
  • empirical process theory
  • extreme-value analysis
  • high-dimensional data modeling
  • machine learning
  • nonparametric statistics
  • statistical learning
  • survey sampling
  • survival analysis
  • time series

Statistical research is largely motivated by collaboration with other disciplines. It finds applications in many fields, including biology, environmental science, finance and insurance, health sciences, hydrology, market research, and social sciences. With the abundance of very large and complex data sets coming, for example, from the social media and digital processes, financial transactions, astronomy, genomics, meteorology or Big Science like the Giant Hadron Collide, the statistical treatment and analysis of Big Data has become a major challenge of modern statistics.

Program Members

Academic Program

The statistics program gives an opportunity to graduate students to study in these two major areas of modern statistics. The curriculum allows the students to get well acquainted with the basic elements of mathematical statistics, decision theory and applied statistics. Furthermore, advanced graduate courses can be offered in some more specialized areas.

This program welcomes graduate students with a good background in calculus, mathematical statistics, numerical analysis, and probability (all at the undergraduate level). To get strong training in decision theory and mathematical statistics students should take the basic course in measure and integration (for PhD students) and at least three courses at the intermediate and advanced levels.

2022-23 Course Listings


Statistical Inference 1

This course is an introduction to statistical inference for parametric models. The following topics will be covered:
1. Distribution of functions of several random variables (distribution function and change of variable techniques), sampling distribution of mean and variance of a sample from Normal distribution.
2. Distribution of order statistics and sample quantiles.
3. Estimation: unbiasedness, Cramér-Rao lower bound and efficiency, method of moments and maximum likelihood estimation, consistency, limiting distributions, delta-method.
4. Sufficiency, minimal sufficiency, completeness, UMVUE, Rao-Blackwell and Lehman-Scheffe theorems.
5. Hypothesis-testing: likelihood-ratio tests.
6. Elements of Bayesian estimation and hypothesis-testing.

Text: Introduction to Mathematical Statistics (6th, 7th or 8th Edition), by R.V. Hogg and A.T. Craig, Prentice Hall Inc., 1994. Recommended reading: (for problems, examples etc) Statistical Inference (2nd Edition), by G. Casella and R. L. Berger, Duxbury, 2002. Evaluation: Assignments (4), Midterm exam, Final exam.

Prof. Arusharka Sen

MAST 672/2 / MAST 881C

Institution: Concordia University

Multivariate Statistics

This course introduces multivariate statistical analysis, both theory and methods, with focus on the multivariate Normal distribution. It can be seen as a preparatory course, although not a formal prerequisite, for Statistical Learning. Topics covered include:

  • Matrix Algebra & Random Vector
  • The Multivariate Normal Distribution
  • Inferences about a Mean Vector
  • Comparisons of Several Multivariate Means
  • Principal Components
  • Factor Analysis and Inference for structured covariance matrices (time permitting)
  • Canonical Correlation Analysis (time permitting)
  • Discrimination and Classification

Text: Applied Multivariate Statistical Analysis, 6th Edition, by R. A. Johnson and D. W. Wichern, Pearson Prentice Hall (2007).

Recommended reading: Linear Statistical Inference and Its Applications, 2nd Edition, by C. R. Rao, Wiley (1973).

Evaluation: Assignments (4), Midterm exam, Final exam

Prof. Arusharka Sen

MAST 679K/ MAST 881K

Institution: Concordia University

Sports Analytics



Institution: Concordia University

Nonparametric Statistics

Distribution free procedures for 2-sample problem: Wilcoxon rank sum, Siegel-Tukey, Smirnov tests. Shift model: power and estimation. Single sample procedures: Sign, Wilcoxon signed rank tests. Nonparametric ANOVA: Kruskal-Wallis, Friedman tests. Association: Spearman's rank correlation, Kendall's tau. Goodness of fit: Pearson's chi-square, likelihood ratio, Kolmogorov-Smirnov tests. Statistical software packages used. 

Prof. Johanna Neslehova

MATH 524

Institution: McGill University

Regression and Analysis of Variance

Multivariate normal and chi-squared distributions; quadratic forms. Multiple linear regression estimators and their properties. General linear hypothesis tests. Prediction and confidence intervals. Asymptotic properties of least squares estimators. Weighted least squares. Variable selection and regularization. Selected advanced topics in regression. Applications to experimental and observational data.

Prof. Abbas Khalil Mahmoudabadi

MATH 533

Institution: McGill University

Mathematical Statistics I

Distribution theory, stochastic models and multivariate transformations. Families of distributions including location-scale families, exponential families, convolution families, exponential dispersion models and hierarchical models. Concentration inequalities. Characteristic functions. Convergence in probability, almost surely, in Lp and in distribution. Laws of large numbers and Central Limit Theorem. Stochastic simulation.

Prof. David Stephens

MATH 556

Institution: McGill University

Statistical Inference

Conditional probability and Bayes’ Theorem, discrete and continuous univariate and multivariate distributions, conditional distributions, moments, independence of random variables. Modes of convergence, weak law of large numbers, central limit theorem. Point and interval estimation. Likelihood inference. Bayesian estimation and inference. Hypothesis testing.


MATH 682

Institution: McGill University

Advanced Topics in Statistics: TBA

Prof. Masoud Asgharian-Dastenaei

MATH 782

Institution: McGill University

Méthode de statistique bayésienne

Principes de l’analyse bayésienne; loi à priori et à postériori, inférence statistique et théorie de la décision. Méthodes computationnelles; méthodes de Monte Carlo par chaînes de Markov. Applications.

Prof. Mylène Bédard


Institution: Université de Montréal

Données catégorielles

Tableaux de contingence. Mesures d'association. Risque relatif et rapport de cote. Tests exacts et asymptotiques. Régression logistique, de Poisson. Modèles log-linéaires. Tableaux de contingence à plusieurs dimensions. Méthodes non paramétriques.

Prof. Alejandro Murua

STT 6516

Institution: Université de Montréal

Séries chronologiques univariées

Méthodes graphiques. Estimation des paramètres d'un processus stationnaire. Inversibilité et prévision. Modèles ARMA, ARIMA et estimations de paramètres. Propriétés des résidus. Séries saisonnières. Données aberrantes.

Prof. Pierre Duchesne

STT 6615

Institution: Université de Montréal

Mathématiques pour l’intelligence artificielle

Notions fondamentales de probabilités appliquées à divers domaines de l’intelligence artificielle. Réseaux bayésiens, champs markoviens, diverses méthodes d’inférence (variationnelle, par maximum a posteriori, recuit simulé, etc.), échantillonnage et méthodes de Monte Carlo par chaînes de Markov, séries chronologiques, partitionnement spectral et modèles à variables latentes. Applications en imagerie, en analyse de textes et sur les réseaux de neurones.

Prof. Félix Camirand-Lemyre

STT 760

Institution: Université de Sherbrooke

Statistique mathématique

Fonctions de variables aléatoires, fonction génératrice des moments, quelques inégalités et identités en probabilité,  familles de distributions dont la famille exponentielle, vecteurs aléatoires, loi multinormale, espérances conditionnelles, mélanges et modèles hiérarchiques.  Théorèmes de convergence, méthodes de simulation, statistiques d'ordre, exhaustivité, vraisemblance.  Estimation ponctuelle et par intervalles : construction d'estimateurs et critères d'évaluation, méthodes bayésiennes.  Normalité asymptotique et efficacité relative asymptotique.

Prof. Éric Marchand

STT 751

Institution: Université de Sherbrooke

Analyse statistique multivariée

Étude des distributions échantillonnales classiques: T2 de Hotelling; loi de Wishart; distribution des valeurs et des vecteurs propres; distribution des coefficients de corrélation. Analyse de variance multivariée. Test d'indépendance de plusieurs sous-vecteurs. Test de l'égalité de matrices de covariance. Sujets spéciaux.

Prof. Mamadou Yauck


Institution: Université du Québec à Montréal

Principes de simulation

Nombre aléatoire. Simulation de lois classiques. Méthodes d'inversion et de rejet. Algorithmes spécifiques. Simulation des chaines de Markov à temps discret et continu. Solution numérique des équations différentielles ordinaires et stochastiques. Méthode numérique d'Euler et de Runge-Kutta. Formule de Feynman-Kac. Discrétisation. Approximation faible et forte, explicite et implicite. Réduction de la variance. Analyse des données simulées. Sujets spéciaux.

Prof. Simon Guillotte


Institution: Université du Québec à Montréal

Méthodes d’analyse des données - UQTR

Théorie et application des méthodes classiques d'analyse de données multivariées : analyse en composantes principales, réduction de la dimensionnalité, analyse des correspondances binaire et multiple, analyse discriminante, classification hiérarchique, classification non hiérarchique, choix optimal du nombre de classes. Initiation aux réseaux de neurones artificiels. Utilisation de logiciels statistiques pour le traitement des données.

Prof. Nadia Ghazzali

MAP 6018

Institution: Université du Québec à Trois-Rivières


Time Series

Statistical analysis of time series in the time domain. Moving average and exponential smoothing methods to forecast seasonal and non-seasonal time series, construction of prediction intervals for future observations, Box-Jenkins ARIMA models and their applications to forecasting seasonal and non-seasonal time series. A substantial portion of the course will involve computer analysis of time series using computer packages (mainly MINITAB). No prior computer knowledge is required.

Prof. Debarej Sen


Institution: Concordia University

Statistical Learning

This course is an introduction to statistical learning techniques. Topics covered include cross-validation, regression methods, classification methods, tree-based methods, introduction to neural networks, unsupervised learning.

Prof. Simone Brugiapaglia


Institution: Concordia University

Operations Research and Simulations Methods

This course is an introduction to simulation and Monte Carlo estimation. The following topics will be covered:
1. Simulation of random variables/vectors from their (joint) probability mass function/density function: methods of inverse-transform, accept-reject, composition and factorization (for random vectors).
2. Simulation of homogeneous and non-homogeneous Poisson processes in 1-dimension: methods of inverse-transform and thinning.
3. Some discrete-event simulation models, e.g., 1-server and 2-server queues, insurance-risk model, machine-repair model.
4. Some variance-reduction techniques: methods of anti-thetic variables, control variables, conditional expectation, stratified sampling.
The software R will be extensively used to write simulation codes and will be demonstrated over a few classes.
Text: Simulation, 5th Edition, by Sheldon M. Ross. Recommended reading: A first course in statistical programming with R, 2nd Edition, by W. John Braun and Duncan J. Murdoch (Cambridge University Press). Evaluation: Assignments (4), Midterm exam, Final exam.

Prof. Arusharka Sen

MAST 729G / MAST 881G

Institution: Concordia University

Generalized Linear Models

Exponential families, link functions. Inference and parameter estimation for generalized linear models; model selection using analysis of deviance. Residuals. Contingency table analysis, logistic regression, multinomial regression, Poisson regression, log-linear models. Multinomial models. Overdispersion and Quasilikelihood. Applications to experimental and observational data.

Prof. Johanna Neslehova

MATH 523

Institution: McGill University

Mathematical Statistics 2

Sampling theory (including large-sample theory). Likelihood functions and information matrices. Hypothesis testing, estimation theory. Regression and correlation theory.

Prof. Masoud Asgharian-Dastenaei

MATH 557

Institution: McGill University

Topics in Probability and Statistics-001

Prof. Archer Yang

MATH 598

Institution: McGill University

Topics in Probability and Statistics-002

Prof. Russell Steele

MATH 598

Institution: McGill University

Séries chronologiques - Sherbrooke

Processus stochastiques (généralités). Description et caractéristiques des séries chronologiques.  Transformées de Fourier. Analyse statistique des séries chronologiques.  Analyse spectrale des processus linéaires. Lissage des estimateurs spectraux.

Prof. Taoufik Bouezmarni

STT 723

Institution: Université de Sherbrooke

Analyse de la variance

Rappels et compléments sur la théorie du modèle linéaire : moindres carrés, théorèmes de Gauss-Markov et de Cochran, inférence. Modèle à effets fixes et aléatoires. Plan incomplet. Plan à mesures répétées.

Prof. Martin Bilodeau

STT 6410

Institution: Université de Montréal


Rappels sur la régression linéaire multiple (inférence, tests, résidus, transformations et colinéarité), moindres carrés généralisés, choix du modèle, méthodes robustes, régression non linéaire, modèles linéaires généralisés.

Prof. Florian Maire

STT 6415

Institution: Université de Montréal

Inférence statistique

Prof. François Perron


Institution: Université de Montréal

Inférence statistique I

Espérance conditionnelle. Prédiction. Modèles statistiques, familles exponentielles, exhaustivité. Méthodes d'estimation: maximum de vraisemblance, moindres carrés etc. Optimalité: estimateurs sans biais à variance minimum, inégalité de l'information. Propriétés asymptotiques des estimateurs. Intervalles de confiance et précision. Éléments de base de la théorie des tests. Probabilité critique, puissance en relation avec la taille d'échantillon. Relation entre tests et intervalles de confiance. Tests pour des données discrètes.



Institution: Université du Québec à Montréal

Modèles de régression

Théorie des modèles linéaires généraux. Théorie des modèles linéaires généralisés. Régression logistique. Modèles log-linéaires.


MAT 7381

Institution: Université du Québec à Montréal

Séminaire en statistique - à venir



Institution: Université du Québec à Montréal