I am an Associate Professor in the Department of Actuarial Mathematics and Statistics at Heriot-Watt University, also affiliated with the Maxwell Institute for Mathematical Sciences. I am a Fellow of the Higher Education Academy.

I currently serve as director of the Scottish Mathematical Sciences Training Centre (SMSTC).

Email: f(dot)daly(at)hw(dot)ac(dot)uk

Postal address: School of Mathematical and Computer Sciences, Heriot-Watt University, Edinburgh EH14 4AS, UK.

Telephone: +44 (0) 131 451 3212

I gave a talk at the 26th International Congress on Insurance: Mathematics and Economics in July 2023 on the "Central limit theorem and related results for the aggregation of equally correlated claims."

I have recently given invited probability seminars at the University of Liverpool (October 2022) and Soochow University (March 2023) on "Approximations for random sums with equally correlated summands."

My research is in applied probability. In many real-life situations probability distributions of interest are tricky to handle, but can be well approximated by distributions which are much easier to work with (such as a Gaussian or Poisson distribution). Much of my work has been in the theory and application of Stein's method, which allows the quality of such probability approximations to be explicitly evaluated in a wide variety of settings without relying on assumptions of independence. Some of my recent work has applied these techniques to various Markovian and random graph models.

A special issue of QUESTA for Stochastic Networks 2018 of which I was a guest editor was published in December 2019.

A list of my publications and preprints can be found here.

In August 2022 I gave a mini-course on "Probability approximations using Stein's method: Random graphs, Markov chains and beyond" at the LMS Undergraduate Summer School 2022. Materials for this mini-course can be found here.

In August 2020 I gave a talk on "Some approximation results for subcritical Erdős-Rényi random graphs via Stein's method" at the Applied Probability Workshop organized by Novosibirsk State University. See the slides and video of my talk available here.

In April and May 2020 I gave four two-hour lectures introducing Stein's method for graduate students. Lecture notes are available here. Recordings of these lectures are available by clicking on the following links:

- Lecture 1: An introduction to Stein's method for Gaussian approximation
- Lecture 2: Coupling techniques for Gaussian and exponential approximation by Stein's method
- Lecture 3: Approximation of geometric sums and Stein's method for Poisson approximation
- Lecture 4: Coupling techniques for Poisson approximation and monotone dependence

I was an invited speaker at the LMS-EPSRC Durham Symposium on 'Markov Processes, Mixing Times and Cutoff', held in July 2017. Slides and a recording of my talk are available here.

Details of PhD opportunities within the Maxwell Institute are available here. If you are interested in PhD opportunities within my research area, please feel free to get in touch with me.

Former PhD students:

- Alastair Haig (co-supervised with Seva Shneer) - graduated 2023
- Bemsibom Toh (co-supervised with James Cruise) - graduated 2020

Current PhD students:

- Yubo Rasmussen (co-supervised with George Tzougas)
- Hengyue Xie (co-supervised with Sergey Foss)
- Ryan McFadden (co-supervised with Seva Shneer)

This year I am teaching courses in statistics and probability for undergraduate and Masters students. All course materials are available on Canvas. I am also teaching on the Probability SMSTC modules.

Notes from a one-off lecture I gave in December 2013 (on "The central limit theorem and Poisson approximation: An introduction to Stein's method") as part of the SMSTC Probability stream can be found here (now with some minor typos corrected).

A copy of my CV can be found here (last updated February 2023).

I have previously worked in Bristol, Zürich and Nottingham.

The School of Mathematical and Computer Sciences at Heriot-Watt University.

More probability and statistics links.

Please send any comments or corrections to Fraser Daly: f(dot)daly(at)hw(dot)ac(dot)uk. Last updated 11 December 2023.