I am Assistant Professor in Predictive Modelling in the Mathematics Institute and School of Engineering at the University of Warwick. I have wide interests in uncertainty quantification the broad sense, understood as the meeting point of numerical analysis, applied probability and statistics, and scientific computation. On this site you will find information about how to contact me, my research, publications, and teaching activities.
The paper “Optimality criteria for probabilistic numerical methods” by Chris Oates, Jon Cockayne, Dennis Prangle, Mark Girolami, and myself has just appeared in print:
C. J. Oates, J. Cockayne, D. Prangle, T. J. Sullivan, and M. Girolami. “Optimality criteria for probabilistic numerical methods” in Multivariate Algorithms and Information-Based Complexity, ed. F. J. Hickernell and P. Kritzer. Radon Series on Computational and Applied Mathematics 27:65–88, 2020.
Abstract. It is well understood that Bayesian decision theory and average case analysis are essentially identical. However, if one is interested in performing uncertainty quantification for a numerical task, it can be argued that standard approaches from the decision-theoretic framework are neither appropriate nor sufficient. Instead, we consider a particular optimality criterion from Bayesian experimental design and study its implied optimal information in the numerical context. This information is demonstrated to differ, in general, from the information that would be used in an average-case-optimal numerical method. The explicit connection to Bayesian experimental design suggests several distinct regimes, in which optimal probabilistic numerical methods can be developed.
Like many international conferences, the SIAM Conference on Uncertainty Quantification planned for 24–27 March 2020 had to be postponed indefinitely in view of the Covid-19 pandemic. Undeterred by this, the speakers of four minisymposia on the theme of Probabilistic Numerical Methods have generously taken the time to adapt their talks for a new medium and record them for general distribution. The talks can be found at http://probabilistic-numerics.org/meetings/SIAMUQ2020/.
We hope that these talks will be of general interest. Furthermore, the speakers have declared themselves ready to answer questions in written form. If you would like to ask any questions or contribute to the discussion, then please submit your question via this form by 10 May 2020.
There is an opening for a PhD student to work with me and co-PIs Jon Cockayne and James Kermode on the project “Adaptive probabilistic meshless methods for evolutionary systems” as part of the EPSRC Centre for Doctoral Training in Modelling of Heterogeneous Systems at the University of Warwick.
This project will develop and implement a new class of numerical solvers for evolving systems such as interacting fluid-structure flows. To cope with extreme strain rates and large deformations these new solvers will be adaptive and meshless, and they will also implicitly represent their own solution uncertainty, thus enabling optimal design and uncertainty quantification. This exciting project brings together aspects of continuum mechanics, numerical methods for partial differential equations, and statistical machine learning.
Interested students should contact me and the other PIs with informal queries. Formal applications should use the HetSys application page.
It is a pleasure to announce that I have accepted an Assistant Professorship in Predictive Modelling at the University of Warwick, to be held jointly between the Mathematics Institute and the School of Engineering.
This position will also involve collaborative work in a number of interdisciplinary research centres and centres for doctoral training, in particular the Warwick Centre for Predictive Modelling and the EPSRC Centre for Doctoral Training in Modelling of Heterogeneous Systems.
It is a pleasure to announce that Birzhan Ayanbayev will join the UQ research group as a postdoctoral researcher with effect from 28 February 2020. He will be working on the DFG-funded project “Analysis of maximum a posteriori estimators: Common convergence theories for Bayesian and variational inverse problems”.