Centre for Statistics

The Statistical Consultancy Unit

Furnished by the Centre for Statistics with a talented core team, and given the freedom to tap into specialist expertise from the wider School of Mathematics, the Statistical Consultancy Unit is prepared for any challenge the world can throw at it.


Since the Centre for Statistics (CfS) formed the Statistical Consultancy Unit (SCU) to act ‘as an interface between external clients and the expertise within the CfS’, the SCU team has worked on a wide range of challenging and interesting projects. One of these asked: Can we find a way to predict when your trusty smartphone or laptop battery all of a sudden only gives you 30 minutes charge instead of its usual hours on end?

Like the performance of Formula 1 tyres that Pirelli purposefully designs to ‘fall off a cliff’, a lithium-ion battery will eventually hit a ‘knee’ in performance, rapidly deteriorating away from its design specifications. But unlike the Pirelli F1 tyres, this deterioration is neither wanted nor predictable in terms of when it will happen.

Given Li-ion batteries’ ubiquity and importance, accurate and early predictions of future capacity loss are essential to advance the state of the art and battery management, so that Li-ion batteries – to quote a well-known TV advert involving a speedy pink rabbit – “keep going on and on and on…”  

SCU researchers collaborated with Edinburgh-based battery technology firm Dukosi Ltd and the University of Edinburgh’s School of Engineering to address this problem. They engineered and trained machine learning algorithms on cell degradation data to provide early warning of when Li-ion cell performance is likely to hit this knee transition.

After just 3–5 cycles, they used their method to classify different cells’ lives as short, medium or long with 88–90% accuracy. Moreover, they could predict after 50 cycles the knee-point and knee-onset – the latter a new concept marking the juncture at which cell performance goes from a linear deterioration to a nonlinear one – with 9.4% error.

“The models provide a tool for cell manufacturers to speed up the validation of cell production techniques, and risk criteria that insurers and manufacturers of energy storage applications can use for battery warranties,” explains SCU Statistical Consultant Michael Allerhand.


Battery Life Figures


Ready for anything

The battery degradation project is just one example of the type of high-impact work that forms the SCU’s bread and butter. Working closely with the University of Edinburgh commercialisation service Edinburgh Innovations and the Bayes Centre, the University’s innovation hub for Data Science and Artificial Intelligence, as well as collaborating with other schools, and external industrial, third sector and government clients, the Unit is primed to solve interesting statistics and data science challenges.

Projects have ranged from research with the Mental Welfare Commission for Scotland examining the duration of hospital stays, to developing graphical models for comparing evidence in a real-world drug trafficking case, or from estimating the number of houses in Scotland with internal lead piping for the Drinking Water Quality Regulator for Scotland, to evaluating a new smartphone-based instrument developed at Edinburgh Royal Infirmary that assesses delirium in intensive care patients.

How they can provide meaningful input into such different and challenging topics can be summed up in one word: flexibility. Steered by Co-Director Chris Dent – whose long history of linking collaborators to challenges in the context of statistical modelling is invaluable – the team brings rich and diverse expertise in a range of statistical methodologies.

Allerhand has immensely broad technical knowledge from his many years’ experience in applied university research, covering the full gamut of the sciences. Coming from an ecological and medical sciences background, fellow Statistical Consultant Gail Robertson has an equally wide range of statistical skills, and offers specific expertise required for projects involving spatially-explicit data. Finally, Deputy Director Amy Wilson’s statistics experience in public policy, criminal justice (see, for example, Cocaine Crime Stats), and energy and infrastructure, adds further strings to the SCU’s statistical consultancy bow.


The Statistical Consultancy Unit Team
The SCU Team (from left): Dr. Mike Allerhand, Dr. Gail Robertson, Prof. Chris Dent, Dr. Amy Wilson


“Part of the idea is that the Unit provides a mechanism by which the expertise of anyone in the School of Mathematics can be deployed on consulting projects,” says Dent. This has meant the SCU team has been able to lean on specialist methodology knowledge from other academics within the Statistics group, as well as leading experts from the Operational Research and Applied Mathematics groups when needed.

With this flexibility, and provided with the freedom to contribute to any topics and any type of research activity of any duration, the SCU helps the School of Mathematics get involved in a wider range of interesting projects than mathematics schools historically have, and thereby play a greater role in both the University and wider society.

It also makes the School more agile. For example, one ongoing project Allerhand is involved in is applying classical and machine learning methods to evaluate outcome risks for patients with Covid-19 in intensive care who have underlying health conditions, such as chronic obstructive pulmonary disease – hoping to provide a valuable contribution to the current pandemic response.

Plugging statistical skills gaps

At the same time as consulting on important projects like these, the SCU is engaged in wider efforts to boost statistical skills. Allerhand offers his Continuing Professional Development (CPD) ‘Introduction to R’ training programme that has been running for a number of years. The three-day course provides absolute beginners with the tools they need to wield the R programming language for data manipulation and statistical analyses. Similarly, Robertson trains PhD students at the School of Biological Sciences through her course ‘Introduction to Statistics using R’.

And both Statistical Consultants dedicate time to providing the skills students will need in the real world. They supervise and run one summer project each for students undertaking a Statistics with Data Science MSc. “Their experience is extremely valuable in helping to create the challenges for these projects that are introduced by external companies,” says Dent. “Both in terms of creating the projects and teaching, this really builds on our consulting experience.”  

With the SCU now well-established, the team having completed numerous projects and training programmes for a diverse range of clients, Dent is excited by what the future may hold: “I hope the Unit will continue to involve the School of Mathematics in such a range of exciting work for many years to come, and that it can be an example to other research organisations of how they too can broaden their scope of activities.”



School of Mathematics alumnus Benjamin Skuse is a freelance science writer based in Somerset, UK. https://benjaminskuse.wordpress.com