Harnessing the Power of Stein Discrepancies in Bayesian Computation

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Some of the most important applications in statistics, machine learning and artificial intelligence are currently gated by the computational technologies available to fit models to a dataset. Indeed, as researchers better understand a phenomenon of interest, increasingly sophisticated models for the phenomenon can be built; for example, detailed differential equation descriptions of physical laws, or bespoke agent-based models of animal movement. However, the correspondingly larger computational demand associated with these models imposes a practical limit on the number of times a model can be interrogated. This in turn presents a major challenge when attempting to fit a model to a dataset, since only by evaluating the model at different input parameters can those parameters that are compatible with a dataset be identified. As a result, in many important applications it is currently not possible to use the most suitable or most accurate model within a rigorous statistical framework.This project aims to accelerate the process of fitting models to data, by developing novel computational methodology that is more efficient than the current state-of-the-art. This will be achieved in the Bayesian framework, in which a "posterior" probability distribution is used to describe which parameters best represent the dataset. The major technical advance that underpins this research is "Stein discrepancy", which enables an optimisation-centric perspective on numerical approximation of the posterior distribution, to which powerful optimisation techniques can be employed. If successful, these methods will reduce the number of model evaluations required, enabling more appropriate and sophisticated models to be fitted to a dataset. This will, in turn, add value in the diverse application domains in which computational models, and the inferences and predictions that they produce, are employed. Two such applications are considered; developing patient-specific multi-physics models of the human heart, with a view to personalised treatment, and predicting the mechanical properties of structures built using novel techniques and novel materials.