Proposal Description

AI is creating a paradigm shift across several scientific disciplines; the fields of spatial/spatio-temporal statistics and time series are no exception. This session involves leading experts exploring how deep learning and other AI-driven methodologies are being harnessed to solve long-standing statistical challenges characterised by complex dependencies, high dimensionality, and computational intractability. The presentations collectively showcase a move away from traditional models and methods that rely on simplifying assumptions toward highly flexible, scalable, and data-driven frameworks. The session will cover recent state-of-the-art work in simulation-based inference, dynamic forecasting, and nonstationary process modelling.

Prof. Raphael Huser from the King Abdullah University of Science and Technology (KAUST) will present a framework for making inference with a class of computationally intractable time series models known as trawl processes. The proposed approach is a Markov chain Monte Carlo (MCMC)-free framework that first learns the posterior density sequentially using telescoping density ratio estimation, and that then uses Chebyshev polynomial approximations to generate independent samples from the posterior distribution. The method ensures accurate and reliable inference, even in scenarios where traditional MCMC methods fail to perform adequately.

Building on the theme of simulation-based inference, Prof. Mikael Kuusela from Carnegie Mellon University (CMU) will introduce a novel neural simulation-based inference (SBI) approach for estimating and conditionally simulating with models that have computationally intractable likelihood functions. Neural networks are used in two ways: first, to construct an accurate surrogate of the likelihood function from a model's simulated output and, second, in a diffusion model for conditional simulation. The entire workflow is amortised, in the sense that the neural networks do not need to be re-trained for different data or parameters, and requires only unconditional simulations for neural-network training.

Prof. Andrew Zammit-Mangion from the University of New South Wales, Australia, will show how AI-based methods can be used for modelling nonstationary spatial processes. The proposed modelling framework is based on neural autoregressive flows (NAFs), which are used to warp the spatial domain upon which a traditional spatial process model is then defined. The modelling framework is applied to a 3D oceanographic dataset, where it is seen that the NAF-based model has superior representational capacity than traditional spatial process models.

Finally, Prof. Noel Cressie from the University of Wollongong, Australia, will discuss forecasting complex spatio-temporal phenomena using Fourier neural operators (FNOs). Traditional spatio-temporal models often fail to capture the nonlinear interactions and environmental heterogeneity seen in climate and biological systems. Here, FNOs, which are designed to approximate solutions to nonlinear partial differential equations, are embedded within a hierarchical statistical framework for modelling spatio-temporal dynamics. The FNO-based model is applied to real-world datasets, including Atlantic sea surface temperatures and European precipitation, and is seen to be able to provide accurate, valid probabilistic forecasts.

Collectively, these talks demonstrate how specific, state-of-the-art AI architectures provide powerful, scalable, and flexible approaches for statistical modelling, inference and prediction with spatial, temporal, and spatio-temporal data.