Dr Daniel Williamson

Senior Lecturer


Telephone: 01392 725514

Extension: (Streatham) 5514

I am a Bayesian statistician and EPSRC fellow with a principal interest in Bayesian modelling, Subjectivism, uncertainty quantification (UQ) and decision making under uncertainty. 

In many diverse areas of science, complex physical systems are studied through the use of computer models. I am interested in how one draws inference regarding the past and future behaviour of the actual system by combining model runs, past observations of the system and expert judgement. UQ is important, usually because decision makers require information to make decisions under uncertainty. I am interested in how one combines information from computer models, data and expert judgement in order to provide policy support for decision makers, and my PhD thesis was written on this subject.

Quantifying the uncertainty in climate change predictions and projections is a high-profile example of a discipline in which each of these strands of evidence (climate models, climate data and expert judgement) must be combined, and I am active in this application area. The main focus of my work in this application is in the ways that the GCMs submitted to CMIP experiments are tuned, methods to assist in automatic tuning that account for relevant sources of uncertainty and combine simpler models with complex models, and the impact that tuning may have on subsequent analyses.

I am also interested in what uncertainty statements mean. As a subjective Bayesian, I view uncertainty statements as judgements that must belong to someone in order to have meaning. I am therefore interested in prior elicitation, the role of the expert in statistical modelling and in the interpretation of Bayesian analyses.

Finally, I am interested in general Bayesian modelling in applications and am currently working with scientists from the medical school on Bayesian modelling for dementia diagnosis and from the department of geography on Bayesian modelling of social science survey data in sustainable transport. I am also working on Bayesian dynamic linear models to improve seasonal forecasting for climate and identify drivers of weather persistence on seasonal timescales.

Active Research Grants/Areas:

EPSRC fellowship: Uncertainty quantification for the linking of spatio-temporal computer model hierarchies with the real world. 

The goal of this work is to develop methods in UQ for emulating the output of spatio-temporal computer models such as climate models and to do it across hierarchies of different models, where each model in the chain is perhaps more like reality (what climate scientists might refer to as more "physical") but where the price of this more physical behaviour is a model that cannot be run as much and hence a poorer quantification of uncertainty for that model. The hierarchy of models can help as the models are related through our belief that they each tell us something about the reality they describe, and because we can run lower resolution models a great deal more. The idea is that a lot of information lower down the chain of models can propagate up the chain and provide better uncertainty quantification for reality. I have been particularly exploring the idea that the highest resolution models are tuned by modelling centres using observations and are hence linked to reality in this way. By exploring new methods for tuning, particularly for spatio-temporal data, we can begin to bridge the gap to reality through, perhaps, multi-model ensemble approaches that account for the design of the tuning experiments. I work with PhD students James Salter and Victoria Volodina on topics in this area. James is interested in methods for calibrating models using spatial field data, in particular basis selection for projection-based methods. Victoria is working on linked emulators for model hierarchies and is currently looking at developing model prediction under a general non-RCP forcing scenario using only RCP runs on the model in question and a large ensemble of alternatives at lower resolution. Active collaborators for this work include Dr Adam Blaker from the National Oceanography Centre in Southampton UK, where we have been applying some of our methods to the NEMO ocean model at multiple resolutions; and Dr John Scinocca from the Canadian Centre for Climate Modelling and Analysis, where we are looking to use some of the methods to assist in tuning the Canadian climate model.

InnovateUK: Engaged Smart Travel

Working with a large consortium of industrial partners including NttData, Imtech, Vaisala, Black Swan, Exeter City Council and Devon County Coucil, we aim to investigate factors affecting congestion in and around the city of Exeter at commuting times and design interventions using smart technologies to improve congestion. The particular focus of the work at the university is on the travel behaviour of individual commuters and how it is influenced by factors such as weather conditions and traffic information. We will then use that information along with information gathered on individual's attitudes to change in order to design real time strategies for improving congestion in Exeter. So far, we have conducted a large survey of peoples commuting behaviour and attitudes in Exeter and are developing Bayesian models to analyse this survey ready for the next phase of the project. This is work joint with Dr Laura Dawkins a PDRA in statistical science, and with Prof Stewart Barr and Dr Sal Lampkin of the department of Geography. 

NERC: Euroclim

Led by overall PI Mark Baldwin and working with the Met Office, Euroclim looks to identify drivers of persistence in climate on seasonal timescales in order to improve seasonal forecasting. Victoria Volodina is working with myself and Geoff Vallis to develop emulators for a hierarchy of idealised climate models that Geoff and his team within Euroclim are developing. These emulators may be used later in the project to understand the relationship between different models and the effects of introducing, for example, improved radiation schemes on model output and optimal parameterisation. My main role in Euroclim is working with Prof David Stephenson and Dr Phillip Sansom a PDRA in statistical science, on developing Bayesian dynamic linear models for climate variables that can be used to identify unusual seasonal behaviour, characterise it in terms of its correlation structure in space and time, and to find drivers of this persistence using model selection.

EPSRC Recover: A decision theortic approach to developing early warning systems for tipping points. 

Led by Tim Lenton in CLES and also involving Dr Andrew Jarvis from Lancaster University, I am working with PDRA Dr Chris Bouton on using Bayesian models and sequential decision making to look at optimal decision making for climate change mitigation under the presence of damage caused by tipping points and the benefits of deciding whether to install early warning systems for tipping points that might help reduce this damage. The aim is to quantify tipping point uncertainty and to see how that uncertainty changes using various tipping points early warning fingerprints. The probabilities we derive from these Bayesian models can then be used in a sequential decision theoretic framework to explore the optimality of various mitigation strategies in the presence of potential tipping points and the value of early warning systems that will give us information on the fingerprints.

Published and Accepted Papers can be viewed on my publications page. The following papers are either submitted on in preparation:

Hourdin, F., Mauritsen, T., Gettleman, A., Golaz, J.C., Balaji, V., Duan, Q., Folini, D., Ji, D., Klocke, D., Qian, Y., Rauser, F., Rio, C., Tomassini, L., Watanabe, M., Williamson, D. (2015) The art and science of climate model tuning, BAMS, Revised Once.

Salter, J., Williamson, D. (2016) A comparison of statistical emulation methodologies for multi-wave calibration of environmental models, Environmetircs, In Revision.

Guidolin, M., Gebreslassie, M.G., Williamson, D., Tabor, G.R., Belmont, M.R., Savic, D. (2016) Toward the optimal design of a tidal farm layout using a surrogate model, Journal of Renewable Energy, In submission.

Williamson, D., Blaker, A.T., Sinha, B. (2016) Tuning without over-tuning: parametric uncertainty quantification for the NEMO ocean model. Geophysical Model Development, In Prep.

Williamson, D., Vernon, I.R. (2016) Desiging for tiny, arbitrarily shaped input spaces: efficient and optimal design in multi-wave computer experiments. In Prep. arXiv:1309.3520

Williamson, D. (2016) Climate models and the science-policy interface: Roles and challenges for Bayesian statistics. In Prep.