## Research

**Research Area:** Probability & Statistics

**Research Profile:***Stochastic models, genetics and medicine, probability bounds*

Stochastic processes are models for describing phenomena which exhibit random fluctuations in their behaviour. Although individual predictions cannot be made, there is remarkable regularity over time which is then exploited in an effort to explain and predict natural phenomena.

My work has been mainly in the following areas:

- population genetics: to develop tools for making inferences about the evolutionary forces in the past which have led to the observed genetic variations among species. In May 1999, I gave a graduate course on this topic at the Fields Institute for Research in Mathematical Sciences. These will be published by the American Mathematical Society.
- combinatorics: to understand the models leading to various related combinatorical structures arising in genetics and ecology.
- large deviations
- probability bounds: to determine optimal upper and lower bounds on the probability of an event using only limited information.
- bootstrap: statistical analyis of channel and bundle power data from Ontario Power Generation CANDU reactors.

In my teaching I have recently begun to experiment with Excel for my undergraduate courses. This represents a departure from the traditional use of specialized statistical software. I have written the Excel Manual which accompanies Introduction to the Practice of Statistics by David Moore and George McCabe. This text is the most widely_used statistics text in North America.

Stochastic models, genetics and medicine, probability bounds

## Courses

**2021/2022**

Stats 3D03

Stats 3Y03

Stats 4D03/6D03

Stats 743

**2020/2021**

Stats 3D03

Stats 3U03

Stats 3Y03

Stats 743

**2019/2020**

Stats 3D03

Stats 3PG3

Math 782

**2018/2019**

Stats 3J04/3Y03

Stats 3U03

Stats 743

**2017/2018**

Stats 3PG3

Stats 3Y03

Stats 743

**2016/2017**

Stats 3D03

Stats 743

**2015/2016**

ArtSci 2R03

Stats 3D03

Stats 3PG3

**2014/2015**

ArtSci 2R03

Stats 3PG3

Stats 743

**2013/2014**

Stats 3D03

Stats 4D03/6D03

Stats 743