Statistics

TBA

TBA

TBA

De Fenetti’s Theorem states that all N-indexed exchangeable sequences of real-valued random variables are mixings of i.i.d sequences. For real-valued random processes with exchangeable increments on [0, 1], Kallenberg’s 1973 result provides a complete characterisation of these processes via another mixing relationship. This talk is about an analogue of Kallenberg’s Theorem for random trees. We will explore the connection between random trees and stochastic processes, leading to a conjecture by Aldous, Miermont and Pitman on a mixing relationship of continuum random trees, and a recent proof of the conjecture.

While powerful methods have been developed for high-dimensional hypothesis testing assuming orthogonal predictors, current approaches struggle to generalise to non-orthogonal designs. Procedures such as Generalised Higher Criticism and the Cauchy Combination Test pay a substantial price in reduced power for providing an approximate orthogonalisation.

I will be describing a novel paradigm for global null testing, Stable Distillation (SD), that introduces auxiliary randomisation -- in a way different from, but broadly analogous to established model-selection and post-selection procedures such as Knockoffs and Stable Algorithms -- with a focus on minimising the noise added. SD iteratively extracts independent p-values corresponding to hypotheses according to evolving expectations about the nature of the underlying signals. This allows rapid calculation of p-values deep into the tail, enabling us to identify rare signals on a background of large numbers of null predictors in large regression models.

While it is in principle a very general method, SD was created with the particular exigencies of genomic testing in mind, and we present two applications of this method: First, testing a whole gene for association with a phenotype by combining signals across its many genomic markers. Second, as one component of an omnibus test for inferred haplotype genealogies, it can identify rare haplotypes of strong effect, while more broadly distributed associations are measured by a more conventional quadratic-form-based test. This application has been implemented in the LOCATER procedure, achieving substantial power gains over traditional single marker testing and window-based testing in cases of allelic heterogeneity.

Preprint on Stable Distillation: https://arxiv.org/pdf/2212.12539

Paper on LOCATER: https://academic.oup.com/genetics/article/232/1/iyaf158/8226070

Power calculations, and variants thereof, are widely used to choose sample sizes for medical studies and scientific experiments. Since power is a conditional quantity, the quality of the sample size resulting from a power calculation is dependent on the values assumed for the inputs to the calculation. Mis-specification of inputs could result in substantially under- or over-powered studies. Assurance, also known as probability of success, is a Bayesian alternative to power which defines a prior distribution over the inputs, which allows us to integrate out our uncertainty in them. The result is an unconditional probability that the study will result in a successful outcome, which is a more direct quantity than power and less sensitive to mis-specification. In this talk I will introduce assurance in general, discuss how it might be evaluated, and then detail some of the specific contexts in which we have been applying it, including cluster randomised trials, diagnostic accuracy studies and reliability demonstration tests. I will also take the opportunity to consider the interpretation of the prior in a context in which there are two potentially different prior distributions over the same set of unknowns.

 

We introduce a new nonparametric methodology for estimating a directed acyclic graph (DAG) from observational data. Our method is nonparametric in nature: it does not impose any specific form on the joint distribution of the underlying DAG. Instead, it relies on a linear operator on reproducing kernel Hilbert spaces to evaluate conditional independence. However, a fully nonparametric

approach would involve conditioning on a large number of random variables, subjecting it to the curse of dimensionality. To solve this problem, we apply nonlinear sufficient dimension reduction to reduce the number of variables before evaluating the conditional independence. We develop an estimator for the DAG, based on a linear operator that characterizes conditional independence, and

establish the consistency and convergence rates of this estimator, as well as the uniform consistency of the estimated Markov equivalence class. We introduce a modified PC-algorithm to implement the estimating procedure efficiently such that the complexity depends on the sparseness of the underlying true DAG. We demonstrate the effectiveness of our methodology through simulations and a real data analysis.

Amyloid positron emission tomography (PET) supports the early diagnosis of Alzheimer’s disease by visualising beta-amyloid deposits in the cerebral cortex. However, patient head motion can degrade image quality and reduce confidence in clinical diagnosis. Existing motion correction relies on external optical cameras or data-driven change point detection. External cameras can be costly and disrupt clinical workflows, whereas change-point detection methods may require a prior value that is difficult to determine.

This work presents an automated motion detection, estimation, and correction pipeline for brain PET imaging. Motion was detected using change-point detection with automatic priors, motion estimation uses image registration, and motion correction uses the open-source Software for Tomographic Image Reconstruction (STIR). The pipeline was evaluated using simulated Derenzo and warm-in-hot contrast phantoms and patient scans acquired with fluorodeoxyglucose (FDG) and flutemetamol. Motion detection and estimation were assessed using root-mean-square error (RMSE) in detection when motion occurs, translation, and rotation. Clinical evaluation compared motion corrected and uncorrected images using mean region-of-interest (ROI) values and a double-blinded reader assessment of diagnostic agreement and confidence.

At full counts, automated change point detection detected all time point without false positives or false negatives, with a timing RMSE of 0.22 seconds. Motion estimated translation RMSE ≤1 mm and rotation RMSE <2°. The ROI values are closer relative to ground truth from −14.6% in motion corrupted images to −1.3% in motion corrected images. In patient scans, quantitative measurements from corrected images were significantly closer to those from the longest frame with no detectable motion than were measurements from uncorrected images. Clinical assessment showed greater unanimous agreement and significantly higher diagnostic confidence following motion correction.

These findings support the potential of automated motion correction to reduce quantitative deviations and improve confidence in brain PET interpretation without the need to expensive hardware.

Semi-supervised learning (SSL) is the problem of finding missing labels from a partially labelled data set. The heuristic one uses is that “similar feature vectors should have similar labels”. The notion of similarity between feature vectors explored in this talk comes from a graph-based geometry where an edge is placed between feature vectors that are closer than some connectivity radius. A natural variational solution to the SSL is to minimise a Dirichlet energy built from the graph topology. And a natural question is to ask what happens as the number of feature vectors goes to infinity? In this talk I will give results on the asymptotics of graph-based SSL using an optimal transport topology. The results will include a lower bound on the number of labels needed for consistency and, time permitting, some recent extensions to infinite dimensional settings.

Service contracts and manufacturer warranties are large short-duration liability books that are still commonly reserved with a single aggregate earning curve.

This talk describes a contract(or warranty)-level alternative: from point-of-sale data only, each contract is given a month-by-month probabilistic projection of expected claims, expected cancellations, and value emergence. Those streams define an Earned Contract schedule and roll up to revenue recognition, liability measurement, and a portfolio cash-flow file that can also be used for structured risk transfer.

The method was published in Risks (2026) with an additional paper available on SSRN and under peer review. I will outline the three modelling steps (exposure, GLM pure premium, projection), the accounting use under IFRS 17 / ASC 606 and the Solvency II best-estimate discussion for finite predictable risks, and what changes when the unit of account is the contract-month rather than the block.