The Turing Lectures: The Intersection of Mathematics, Statistics and Computation – Professor Mark Girolami: “Probabilistic Numerical Computation: A New Concept?”

Lecture blurb:

The vast amounts of data in many different forms becoming available to politicians, policy makers, technologists, and scientists of every hue presents tantalising opportunities for making advances never before considered feasible.

Yet with these apparent opportunities has come an increase in the complexity of the mathematics required to exploit this data. These sophisticated mathematical representations are much more challenging to analyse, and more and more computationally expensive to evaluate. This is a particularly acute problem for many tasks of interest, such as making predictions since these will require the extensive use of numerical solvers for linear algebra, optimization, integration or differential equations. These methods will tend to be slow, due to the complexity of the models, and this will potentially lead to solutions with high levels of uncertainty.

This talk will introduce our contributions to an emerging area of research defining a nexus of applied mathematics, statistical science and computer science, called “probabilistic numerics”. The aim is to consider numerical problems from a statistical viewpoint, and as such provide numerical methods for which numerical error can be quantified and controlled in a probabilistic manner. This philosophy will be illustrated on problems ranging from predictive policing via crime modelling to computer vision, where probabilistic numerical methods provide a rich and essential quantification of the uncertainty associated with such models and their computation.


After graduation from the University of Glasgow, Mark Girolami spent the first ten years of his career with IBM as an Engineer. After this he undertook, on a part time basis, a PhD in Statistical Signal Processing whilst working in a Scottish Technical College. He then went on rapidly to hold senior professorial positions at the University of Glasgow, and University College London.

He is an EPSRC Established Career Research Fellow (2012 – 2017) and previously an EPSRC Advanced Research Fellow (2007 – 2012). He is the Director of the EPSRC funded Research Network on Computational Statistics and Machine Learning and in 2011, was elected to the Fellowship of the Royal Society of Edinburgh, when he was also awarded a Royal Society Wolfson Research Merit Award. He has been nominated by the Institute of Mathematical Statistics to deliver a Medallion Lecture at the Joint Statistical Meeting in 2017. He is currently one of the founding Executive Directors of the Alan Turing Institute for Data Science.

His research and that of his group covers the development of advanced novel statistical methodology driven by applications in the life, clinical, physical, chemical, engineering and ecological sciences. He also works closely with industry where he has several patents leading from his work on e.g. activity profiling in telecommunications networks and developing statistical techniques for the machine based identification of counterfeit currency which is now an established technology used in current Automated Teller Machines. At present he works as a consultant for the Global Forecasting Team at Amazon in Seattle.

The Alan Turing Institute is the UK’s National Institute for Data Science.

The Institute’s mission is to: undertake data science research at the intersection of computer science, mathematics, statistics and systems engineering; provide technically informed advice to policy makers on the wider implications of algorithms; enable researchers from industry and academia to work together to undertake research with practical applications; and act as a magnet for leaders in academia and industry from around the world to engage with the UK in data science and its applications.

The Institute is headquartered at The British Library, at the heart of London’s knowledge quarter, and brings together leaders in advanced mathematics and computing science from the five founding universities and other partners. Its work is expected to encompass a wide range of scientific disciplines and be relevant to a large number of business sectors.

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