The Young Researchers' meeting (YRM) is a weekly seminar for postgraduate students and postdocs. It provides an informal forum where we discuss our research and exchange ideas.
Everyone is welcome to attend. Unless otherwise stated, meetings take place every Thursday at 5pm in the Statistics Common Room (MSB) during term time. The organisers for the 2026鈥�27 academic year are Usman Ladan and Hugo Queniat. If you are interested in giving a talk get in touch with us.
Title: Tempered Bouncy Particle sampler for sampling Heavy-tailed targets
Piecewise Deterministic Markov Processes (PDMPs) are stochastic processes initially proposed in physics and chemistry and later applied to MCMC (Markov Chain Monte Carlo) and ML. Most standard MCMC methods fail at sampling heavy-tailed target distributions. We generalise a standard PDMP (the Bouncy Particle Sampler) to optimally sample heavy-tailed targets and prove fast convergence to the target distribution. In this talk, we will also cover ideas for estimating the rate of convergence to stationarity for nonreversible processes, including methods under the umbrella term hypocoercivity.
Title: Tempered Langevin diffusions with polynomial-tailed targets: explosions, moment thresholds and ergodicity
For tempered Langevin diffusions (TLDs) targeting polynomially tailed measures, the convergence rate is known to change from polynomial to exponential to uniform as the temperature rises through a critical value. We explain this transition by the tails of the marginal laws of the norm of the TLD, up to a second, larger critical temperature beyond which the TLD explodes. As the temperature increases, these tails change from stretched-exponential, through super-polynomial at the first critical temperature, to polynomial, mirroring the transition in the convergence rate. Moreover, this tail analysis gives a complete quantification of the convergence rates throughout the non-explosive regime, in both f-variation and Wasserstein distances.
Title: Mildly Overparameterized ReLU Networks on Orthogonal Data: Incremental Learning and Implicit Bias
Neural networks trained by gradient-based methods often exhibit incremental learning in which features are acquired one at a time, with long plateaus in the loss separated by sudden drops. We discuss recent work proving that, for two-layer ReLU networks trained from small initialisation on orthogonal data, this behaviour arises from saddle-to-saddle dynamics, with a new neuron activating at each saddle. We then explain how this incremental mechanism produces a favourable implicit bias: with only logarithmic network width, the learned interpolator has near-optimal norm.
Title: The criticality parameter T_eff for the tritium fuel cycle in nuclear fusion
It is broadly believed that future fusion reactors will be running on tritium and deuterium as fuels. Whereas the latter is naturally abundant, tritium has a half-life of roughly 12.3 years hence there is no natural reservoir from which it may be gathered at scale. A sequence of physical processes, themselves ignited by deuterium-tritium reactions leads to a closed-loop cycle within the reactor, known in the literature as the Inner-Outer Fuel Cycle (FC). In this talk, we will see how one may model the FC as a Crump-Mode-Jagers branching process, which will allow us to measure a FC鈥檚 capability of being self-sustainable over time by quantifying the rate at which Tritium is produced. A quantity which we call T_eff gives the classic subcriticality-criticality-supercriticality trichotomy seen in nuclear fission. Moreover, we derive from our model known quantities that have appeared in the fusion-engineering literature over the years.
This is joint work with Prof. David Foster (UKAEA) and with Prof. Andreas Kyprianou (Warwick).
Title: Inference on Counterfactual Distributions Using Martingale Posteriors
Causal inference is often focused on average effects, which can hide important aspects of the effect distributions. We propose a methodology for inference on entire counterfactual distributions, building upon the martingale posterior framework. This provides a highly flexible approach to estimating interventional densities, distribution functions, and derived quantities such as quantiles, which coherently quantifies the epistemic uncertainty on many causal estimands of interest. As the predictive recursions are based on an underlying nonparametric model, our method naturally inherits robustness with respect to restrictive parametric assumptions. In addition, implementation of our method is typically very fast. This approach can be applied to marginal or conditional counterfactual distributions and is easily extended to an instrumental variables setup. We prove convergence of the martingale posterior inference on the counterfactual outcome distributions for the causal models considered in the paper. We illustrate our approach on the effect of a job training program on earnings.
As part of the social activities within the Statistics Department, Football Social sessions take place every Tuesday at 5pm in Term 1, organised by Peter Matthews.
Anyone among PhD students, PostDocs and staff from the Statistics Department is welcome to participate, no prior experience needed. If you wish to get involved or if you have any questions, please contact Peter.
