14:00 – 15:00 – Adam Sykulski (Imperial):
Title: Lagrangian statistical modelling of ocean drifters
Abstract: This talk will study spatiotemporal data collected from ocean buoys known as drifters. These instruments are designed to freely float around our ocean, mimicking a particle of water, and regularly report their positions to passing satellites, allowing a global monitoring system of ocean flow observed as thousands of spatiotemporal trajectories. The statistical analysis of this trajectory data is non-trivial – the data is “Lagrangian” in that it is moving in both space and time, and the environment is sparsely sampled and highly spatially and temporally nonstationary.
In this talk I present some techniques from stochastic modelling that can answer questions such as: What is the most likely travel path of a particle in the ocean that connects two arbitrary points, and how long would this path take? What can we learn from drifters that are deployed very close together? How fast do particles diffusively spread in the ocean, and do they spread anisotropically? All of these questions are important for understanding pressing challenges such as oil spills, plastic pollution, and climate change. The focus is on data-driven statistical solutions, the presentation will not be too technical, and no prerequisite knowledge of oceanography is expected from the audience!
15:30 – 16:30 – Yanbo Tang (Imperial):
Title: Stochastic Convergence Rates and Applications of Adaptive Quadrature in Bayesian Inference
Abstract: We provide the first stochastic convergence rates for a family of adaptive quadrature rules used to normalize the posterior distribution in Bayesian models. Our results apply to the uniform relative error in the approximate posterior density, the coverage probabilities of approximate credible sets, and approximate moments and quantiles, therefore guaranteeing fast asymptotic convergence of approximate summary statistics used in practice. The family of quadrature rules includes adaptive Gauss-Hermite quadrature, and we apply this rule in two challenging low-dimensional examples. Further, we demonstrate how adaptive quadrature can be used as a crucial component of a modern approximate Bayesian inference procedure for high-dimensional additive models. The method is implemented and made publicly available in the aghq package for the R language, available on CRAN.
Refreshments available between 15:00 – 15:30