Statistics

As artificial intelligence grows ever more prominent within public discourse, record levels of investment and political pressure been ploughed into applying these technologies in the healthcare space. Despite this, few AI innovations translate into the clinical setting or result in real-world patient benefit. In this talk Dr Zucker will provide an overview of the barriers to AI adoption within the UK healthcare system, offer practical advice to academics on how to maximise the impact of their work in health and describe some of the projects and opportunities that can support AI and data science researchers within the region.

Bayesian emulation, and more generally Gaussian process models, have been successfully applied across a wide variety of scientific disciplines. This is both in the context of efficiently analysing computationally intensive models, as well as general statistical models for inference and prediction of response for new predictors given a training dataset. In this talk, we introduce emulators as fast statistical approximators, providing a predicted value at any input, along with a corresponding measure of uncertainty. We then proceed to discuss developments of Known Boundary Emulation (KBE) strategies which utilise the fact that, for many computer models, there exist hyperplanes in the input parameter space for which the model output can be evaluated far more efficiently. For example, this may be because the response is known at such inputs; or in the context of a computer model, such inputs may yield an analytical solution or the potential for application of a much simpler, more efficient, numerical solver. We demonstrate how information on these known hyperplanes can be incorporated into the emulation process via analytical update, thus involving no additional computational cost, before illustrating our techniques on a scientifically relevant and high-dimensional systems biology model of hormonal crosstalk in the roots of an Arabidopsis plant. 

Dynamic covariance matrix models for multivariate normal data are a widely-applicable class of statistical models, meant to capture the covariate-dependent nature of the variance and dependence parameters. However, such models are rarely used in practice, partly due to the computational difficulties involved in model fitting. In particular, it is challenging to ensure the positive definiteness of the covariance matrix while guaranteeing computational scalability for even moderate dimension of the response vector. In this talk we will present methods for fitting multivariate Gaussian regression models where each parameter of the mean vector and of (an unconstrained parametrisation of) the covariance matrix can be modelled additively, via parametric or spline-based smooth effects. We will focus particularly on the modified Cholesky decomposition and we will show how the sparsity of the corresponding derivative system aids scalability w.r.t. the dimension of the response vector. The usefulness of the new models will be illustrated on a UK regional electrical net-demand forecasting application.

In this seminar, I will provide an insightful introduction to the fascinating world of Mixture of Experts (MoE) modelling, a versatile technique used across various fields. I will explore the fundamentals of MoE models, discussing their structure and practical applications. I will then highlight my contributions to this field, particularly in handling datasets with censored observations. Finally, I will conclude by sharing some current challenges I am passionate about, hoping to spark interest in potential collaborations within the school.

Human mortality patterns and trajectories in closely related populations are likely linked together and share similarities. It is always desirable to model them simultaneously while taking their heterogeneity into account. When a mortality model is applied to each population separately, they tend to result in divergent forecasts of life expectancy in the long term. We introduce a method for joint and coherent mortality modelling and forecasting of multiple subpopulations using the multivariate functional principal component analysis techniques, which ensures the non-divergent forecasting in the long run when several subpopulation groups have similar socio-economic conditions or common biological characteristics. We demonstrate the proposed methods by using sex-specific mortality data, and the forecast performances are compared with several existing models, including the independent functional data model and the Product-Ratio model.

Assuming X is a random vector and A a non-invertible matrix, one sometimes need to perform inference while only having access to samples of Y=AX. The corresponding likelihood is typically intractable. One may still be able to perform exact Bayesian inference using a pseudo-marginal sampler, but this requires an unbiased estimator of the intractable likelihood. We propose saddlepoint Monte Carlo, a method for obtaining an unbiased estimate of the density of Y with very low variance, for any model belonging to an exponential family. Our method relies on importance sampling and characteristic functions, with insights brought by the standard saddlepoint approximation scheme with exponential tilting.  We show that saddlepoint Monte Carlo makes it possible to perform exact inference on particularly challenging problems and datasets. We focus on the ecological inference problem, where one observes only aggregates at a fine level. We present in particular a study of the carryover of votes between the two rounds of various French elections, using the finest available data (number of votes for each candidate in about 60,000 polling stations over most of the French territory).

Joint work with Théo Voldoire, Nicolas Chopin, and Guillaume Rateau. Preprint: https://arxiv.org/abs/2410.18243