Seminars
Statistics seminars are held on Wednesdays 14:00 – 15:00. Everyone is welcome! We gather for coffee/tea and biscuits for around 15 minutes after the seminar.
The organisers are Andy Lynch (semester 1) and Nathan Kirk (semester 2). University of St Andrews staff who can’t be present in person, can contact Andy or Nathan to request to join seminars online.
Most of the seminars this year will be held in-person and few online. The in-person seminars will be held at the Observatory seminar room (except for the JJ Valletta memorial seminar, which is in the Mathematical Institute). Please see below for more details.
Seminars 2026-27 Semester 1
Click on a seminar for the abstract.
- In 1926, the Scottish-born statistician G. Udny Yule considered the following problem: given two independent and identically distributed (i.i.d.) random walks, what is the distribution of their empirical (Pearson) correlation coefficient $\rho_n$? Yule observed empirically the distribution of this statistic to be heavily dispersed and frequently large in absolute value, leading him to call it “nonsense correlation.” This led to the formulation of two concrete questions, each of which would remain open for more than ninety years: (i) find (analytically) the variance of $\rho_n$ as $n$ tends towards infinity; (ii) find (analytically) the higher-order moments and the density of $\rho_n$ as $n$ tends towards infinity. In 2017, Ernst, Shepp, and Wyner closed question (i) by explicitly calculating the standard deviation of $\rho$ to be approximately 0.5. This talk begins where Ernst et al. (2017) leaves off. I shall explain how Ernst, Rogers, and Zhou (2025) finally succeeded in closing question (ii) by explicitly calculating all moments of $\rho$ (up to order 16). This leads, for the first time, to an approximation to the density of Yule’s nonsense correlation.I will then turn to an investigation of the fluctuations around the convergence of $\rho_n$ to $\rho$ for both standard Brownian motion and long-memory fractional Brownian motion. I will present the key elements of a surprising result of Ernst, Viens, and Yan (2025+) showing the fluctuations are of order $1/n$ rather than $1/n^{1/2}$. To the best of our knowledge, these results provide the first statistical tests of independence for pairs of paths of non-stationary and non-i.i.d. Gaussian processes. I will conclude with a discussion of concrete applications of our work to the study of weather and climate extremes. The latter is part of our ongoing collaboration with the U.S. Office of Naval Research (2018–present) and is also generously supported by a Royal Society Wolfson Fellowship.
The current high-profile case of Lucy Letby, a nurse in the Countess of Chester hospital neonatal ward, has sparked considerable controversy in the UK and internationally. In 2023/24 Letby was convicted of the murder of seven babies and attempted murder of seven others on the neonatal ward. Following her convictions, academics and practitioners from multiple disciplines have raised concerns about the scientific evidence used as part of her case. One of the areas of controversy has been the lack of robust and rigorous statistical approaches for collecting and analysing the healthcare data in the case, another has been the potentially misleading way in which fundamentally probabilistic concepts were presented and discussed at trial. In this talk I will summarise some of the key statistical issues that have arisen in the Letby case, and will present a graphical modelling approach (Chain Event Graphs) that could be used to disentangle the various probabilistic arguments, both in this case, and others. I will finish by discussing some general problems with communicating statistical concepts within the law, and will describe some ongoing initiatives for collaborating with legal and policing practitioners to improve use of statistics.
Individualised study designs, including N-of-1 trials and observational single-case studies, offer a powerful approach to understanding individual variability in health outcomes and behaviours. By collecting repeated measurements over time, these designs allow researchers to investigate within-person relationships, identify individual determinants of health outcomes, and develop personalised interventions. However, the time-dependent nature of N-of-1 data presents unique methodological and statistical challenges that require careful consideration of both study design and analytical approaches.
This presentation will explore the key statistical considerations involved in designing and analysing N-of-1 studies, with a particular focus on dynamic regression modelling. Topics will include accounting for autocorrelation, time trends, periodicity, and lagged effects, as well as the importance of tailoring statistical models to individual study designs. Real-world applications in health psychology and nutrition research will illustrate the potential of these approaches. The presentation will also discuss methodological challenges that have emerged in the application of these designs, highlighting key limitations and considerations for future research.
Title and abstract to follow.
Previous academic years
Seminars from previous academic years (since 2022) are listed here.