Research in Probability and Statistics covers a wide range of theoretical, methodological and applied topics. The Statistics group has extensive contacts within the University in areas such as biostatistics (particularly related to medicine), astronomy, geography, finance, the Genome and Bioinformatics centres, and in computer science.
- Louigi Addario-Berry http://problab.ca/louigi/
- Masoud Asgharian
- Linan Chen
- Christian Genest http://www.math.mcgill.ca/cgenest/
- Abbas Khalili
- Johanna Nešlehová http://www.math.mcgill.ca/neslehova/
- Russell Steele
- David Stephens http://www.math.mcgill.ca/dstephens/
- David Wolfson
- Yi Yang http://www.math.mcgill.ca/yyang/
- Actuarial Science (Genest, Nešlehová)
- Bayesian Methods & Computational Statistics (Steele, Stephens, Wolfson)
- Bioinformatics Applications (Stephens)
- Biostatistics: Methodology and Applications (Asgharian, Steele, Stephens, Wolfson)
- Capture-Recapture (Wolfson)
- Dependence Modelling (Genest, Nešlehová)
- Extreme value theory (Nešlehová)
- High-dimensional statistical methods (Asgharian, Khalili, Yang)
- Quantitative Finance & Insurance (Genest, Nešlehová, Stephens, Yang)
- Mixture models (Khalili, Steele, Stephens)
- Probability (Addario-Berry, Chen)
- Optimization (Asgharian, Wolfson)
Specific research topics have included the following:
Biostatistics – Applications:
Several members of the group have collaborated with medical and biostatistical researchers at several local hospitals. The group has done substantial applied work in diseases such as multiple sclerosis, coronary heart disease, scleroderma, colorectal cancer and early inflammatory arthritis. They have also worked in a variety of public health related applications in perinatal research, maternal anxiety, and neuroimaging. Currently, there is an ongoing interest in methods for the modelling of data in the presence of imperfectly measured, censored, or other types of missing data in a medical research environment. In particular, the group has emphasized methods for discrete (or categorical) data, for example in the analysis of capture-recapture data.
Biostatistics – Methodology:
Several members of the statistics group are actively involved in research related to observational studies in general, and cross-sectional surveys and prevalent cohort studies in particular. The main theme of this work is to propose appropriate methodologies that take into account special features of such surveys. The work has so far generated some deep theoretical and some interesting applied research. The application of this work is vast and ranges from medical to financial data. Cross-sectional sampling is a data collection scheme often used in follow-up studies on duration of a condition when logistic or other constraints preclude the possibility of following-up subjects since initiation of the condition. It is well-known that the duration data collected on prevalent cases are biased. This latter feature of cross-sectional surveys renders any direct application of existing methodologies in classical survival analysis, which represents another core research area within the group. In particular, there has been a focus on the analysis of left truncated right censored survival data, which arise from prevalent cohort studies with follow-up. Both nonparametric and parametric estimation problems are being considered, including the effect on covariates that are subject to selection bias. This work has both strong applied and theoretical components. Data collected on survival with dementia from the 1996 Canadian Study of Health and Aging provide motivation for the methodologies being developed.
Bayesian Methodology and Computation:
Recent work in Bayesian Methodology includes Bayesian non- and semi-parametric modelling in regression and spatial statistics. Collaborative work continues, on the general area of Bayesian optimal design. The main issues being addressed are sample size estimation and optimal design for changepoint problems. Sample size issues are relevant whenever studies are being planned. Optimal designs for changepoint problems have potential applications in the design of clinical trials when there is uncertainty about the delay in the onset of the treatment affect. Work in Bayesian computation includes projects in finite mixture models and model-based clustering, financial time series analysis, and applications in functional genomics and bioinformatics in general. Theoretical aspects of Bayesian computation (specifically, Markov chain Monte Carlo and Sequential Monte Carlo) have also been studied; current interests include population MCMC, and adaptive Monte Carlo methods, with applications in the estimation of normalizing constants (high-dimensional integration) and model selection.
Applications in bioinformatics include model-based clustering of gene expression data, analysis of biological spatial point patterns, statistical genomics in genomewide association studies, and metabonomics and metabolomics.