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University of Exeter Business School

Professor Daniel Williamson

Professor Daniel Williamson




I am a Bayesian statistician and Professor of Uncertainty Quantification in the Land Environment Economics and Policy Institute. I suppose I could also be called "Professor of Bayesian Statistics" or "Professor of Data Science", but you have to settle on one title in the end. I have always been interested in decision making under uncertainty, with a particular focus on what uncertainty means (to analyst and decision maker), how to quantify it, how to use it to guide decision makers and when it is ethical to do so. A feature in the vast majority of my work has been the presence of one or more expensive computer simulators (or "models") of the aspects of reality we are uncertain about, and most of my application work has been with environmental models (e.g. atmosphere, ocean, land ice, coupled GCMs, land surface, crop growth). I am a subjectivist, so I think uncertainty is nothing more than a property of individuals, probability is one possible calculus for its quantification and communication, and “true randomness” may or may not exist, but it doesn’t really matter. I am also a Dad, a chess player, a cyclist, a (beginner) sea-kayaker and I play fantasy football (without any statistical modelling at all).


I have an MMATH and a PhD in Statistics from Durham University. My 2010 PhD thesis was titled: “Policy making using computer simulators for complex physical systems: Bayesian decision support for the development of adaptive strategies.”


  • 2010-2013: Post-Doctoral Research Associate at Durham University.
  • 2013-2016: EPSRC fellow and Lecturer: Department of Mathematics, University of Exeter.
  • 2016 – 2020: Senior Lecturer and Director of Impact, Department of Mathematics, University of Exeter. 
  • 2020 – 2023: Associate Professor of Bayesian Statistics, Director of Impact, Department of Mathematics and Statistics, University of Exeter.
  • 2023 – Present: Professor of Uncertainty Quantification, Land Environment Economics and Policy Institute, Department of Economics, University of Exeter. 


  • International Society for Bayesian Analysis Savage Award (for outstanding methodological PhD thesis) 2011
  • EPSRC Fellow 2013-2016.
  • International Society for Bayesian Analysis Lindley Prize 2014
  • Alan Turing Institute Fellow 2019-2023

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Research interests

The study and implementation of methods for quantifying uncertainty about the real-world using computer models (referred to in the literature as "Uncertainty Quantification (UQ)"), is my principle methodological interest, and I have mainly worked in environmental applications of these ideas. The “emulation” of computer models, so that they can be interrogated in real time, calibrated to observations and even coupled within efficient decision support tools is a core area of UQ. I have contributed to this area, particularly for environmental models, with extensions to Gaussian processes for non-stationarity, spatial output (via dimension reduction and kernel methods), and deep and linked Gaussian processes for coupling. I have made contributions to the topic of calibrating models to observations whilst managing structural error, in particular, using History matching, with extensions particularly for spatio-temporal data. I have developed and demonstrated these techniques in application to “climate model tuning”. 

I am interested in the development of digital twins, particularly the embedding of UQ to deliver real-time interrogation, coupling and calibration of models to data streams for digital twins to be used in decision support. I’m also interested in Ethical AI from a foundational perspective: how can the uncertainty used or reported by AI systems be understood and ethically used by decision makers, particularly where multiple competing models/frameworks can be deployed and may give different responses. Recently I have been considering Land Use Change problems, and in particular for delivering Net Zero, within the context of the all of the above (UQ, digital twinning and ethical AI). 

Research projects

PI for ADD-TREES an EPSRC AI for Net Zero project with full title AI-elevated Decision-support via Digital Twins for Restoring and Enhancing Ecosystem Services.

AI lead for Net Zero Plus, A Greenhouse Gas Removal Demonstrator focused on tree planting.

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Journal articles

Williamson D, Dawkins L, Barr S, Lampkin S (In Press). "What drives commuter behaviour?": a Bayesian clustering approach for understanding opposing behaviours in social surveys. Journal of the Royal Statistical Society: Series A
JM Salter, Williamson D (In Press). A comparison of statistical emulation methodologies for multi-wave calibration of environmental models. Environmetrics Abstract.
Williamson D, Astfalck L, Gandy N, Gregoire L, Ivanovic R (In Press). Coexchangeable process modelling for uncertainty quantification in joint climate reconstruction. Journal of the American Statistical Association
Mohammadi H, Challenor P, Williamson D, Goodfellow M (In Press). Cross-validation based adaptive sampling for Gaussian process models. SIAM/ASA Journal on Uncertainty Quantification Abstract.
Salter J, Williamson D (In Press). Efficient calibration for high-dimensional computer model output using basis methods. International Journal for Uncertainty Quantification Abstract.
Williamson D, Sansom PG (In Press). How are emergent constraints quantifying uncertainty and what do they leave behind?. Bulletin of the American Meteorological Society
Screen JA, williamson D (In Press). Ice-free at 1.5°C?. Nature Climate Change
Dawkins L, Williamson D, Barr S, Lampkin S (In Press). Influencing Transport Behaviour: a Bayesian Modelling Approach for Segmentation of Social Surveys. Journal of Transport Geography
Villefranque N, Blanco S, Couvreux F, Fournier R, Gautrais J, Hogan RJ, Hourdin F, Volodina V, Williamson D (In Press). Process-based climate model development harnessing machine learning III: the Representation of Cumulus Geometry and their 3D Radiative Effects. Journal of Advances in Modeling Earth Systems
Salter J, Williamson D, Gregoire L, Edwards T (In Press). Quantifying Spatio-temporal Boundary Condition Uncertainty for the North American Deglaciation. SIAM/ASA Journal on Uncertainty Quantification
Barr S, Lampkin S, Dawkins L, Williamson D (In Press). Shared Space: negotiating sites of (un)sustainable mobility. Geoforum Abstract.
Barr S, Lampkin S, Dawkins L, Williamson D (In Press). Smart Cities and Behavioural Change: (un)sustainable mobilities in the neo-liberal city. Geoforum
Barr S, Lampkin S, Dawkins L, Williamson D (In Press). ‘I feel the weather and you just know’. Narrating the dynamics of commuter mobility choices. Journal of Transport Geography
Bateman IJ, Anderson K, Argles A, Belcher C, Betts RA, Binner A, Brazier RE, Cho FHT, Collins RM, Day BH, et al (2023). A review of planting principles to identify the right place for the right tree for ‘net zero plus’ woodlands: Applying a place-based natural capital framework for sustainable, efficient and equitable (SEE) decisions. People and Nature, 5(2), 271-301. Abstract.
Gandy N, Astfalck LC, Gregoire LJ, Ivanovic RF, Patterson VL, Sherriff-Tadano S, Smith RS, Williamson D, Rigby R (2023). De-Tuning Albedo Parameters in a Coupled Climate Ice Sheet Model to Simulate the North American Ice Sheet at the Last Glacial Maximum. Journal of Geophysical Research: Earth Surface, 128(8). Abstract.
Ming D, Williamson D, Guillas S (2023). Deep Gaussian Process Emulation using Stochastic Imputation. Technometrics, 65(2), 150-161. Abstract.
Lampkin SR, Barr S, Williamson DB, Dawkins LC (2023). Engaging publics in the transition to smart mobilities. GeoJournal, 88(5), 4953-4970. Abstract.
Hourdin F, Ferster B, Deshayes J, Mignot J, Musat I, Williamson D (2023). Toward machine-assisted tuning avoiding the underestimation of uncertainty in climate change projections. Sci Adv, 9(29). Abstract.  Author URL.
Baker E, Harper AB, Williamson D, Challenor P (2022). Emulation of high-resolution land surface models using sparse Gaussian processes with application to JULES. Geoscientific Model Development, 15(5), 1913-1929. Abstract.
Baker E, Harper A, Williamson D, Challenor P (2021). Emulation of high-resolution land surface models using sparse Gaussian processes with application to JULES.  Abstract.
Xu W, Williamson DB, Challenor P (2021). LOCAL VORONOI TESSELLATIONS FOR ROBUST MULTIWAVE CALIBRATION OF COMPUTER MODELS. International Journal for Uncertainty Quantification, 11(5), 1-17.
Audouin O, Roehrig R, Couvreux F, Williamson D (2021). Modeling the GABLS4 Strongly‐Stable Boundary Layer with a GCM Turbulence Parameterization: Parametric Sensitivity or Intrinsic Limits?. Journal of Advances in Modeling Earth Systems, 13(3). Abstract.
Couvreux F, Hourdin F, Williamson D, Roehrig R, Volodina V, Villefranque N, Rio C, Audouin O, Salter J, Bazile E, et al (2021). Process‐Based Climate Model Development Harnessing Machine Learning: I. A Calibration Tool for Parameterization Improvement. Journal of Advances in Modeling Earth Systems, 13(3). Abstract.
Hourdin F, Williamson D, Rio C, Couvreux F, Roehrig R, Villefranque N, Musat I, Fairhead L, Diallo FB, Volodina V, et al (2021). Process‐Based Climate Model Development Harnessing Machine Learning: II. Model Calibration from Single Column to Global. Journal of Advances in Modeling Earth Systems, 13(6). Abstract.
Baker E, Harper A, Williamson D, Challenor P (2021). Supplementary material to "Emulation of high-resolution land surface models using sparse Gaussian processes with application to JULES".
Dawkins LC, Williamson DB, Mengersen KL, Morawska L, Jayaratne R, Shaddick G (2021). Where is the Clean Air? a Bayesian Decision Framework for Personalised Cyclist Route Selection Using R-INLA. Bayesian Analysis, 16(1).
Kimpton L, Challenor P, Williamson D (2020). Classification of Computer Models with Labelled Outputs.  Abstract.  Author URL.
Volodina V, Williamson D (2020). Diagnostics-driven nonstationary emulators using kernel mixtures. SIAM-ASA Journal on Uncertainty Quantification, 8(1), 1-26. Abstract.
Kimpton L, Challenor P, Williamson D (2019). Modelling Numerical Systems with Two Distinct Labelled Output Classes.  Abstract.  Author URL.
Sansom PG, Williamson DB, Stephenson DB (2019). State space models for non‐stationary intermittently coupled systems: an application to the North Atlantic oscillation. Journal of the Royal Statistical Society: Series C (Applied Statistics)
Sansom PG, Stephenson DB, Williamson DB (2018). State-space modeling of intra-seasonal persistence in daily climate. indices: a data-driven approach for seasonal forecasting.  Abstract.  Author URL.
Salter JM, Williamson D, Scinocca J, Kharin V (2018). Uncertainty quantification for computer models with spatial output using calibration-optimal bases. Journal of the American Statistical Association
Screen JA, Williamson D (2017). Ice-free Arctic at 1.5 °C?. NATURE CLIMATE CHANGE, 7(4), 230-231. Author URL.
Sansom PG, Williamson DB, Stephenson DB (2017). State space models for non-stationary intermittently coupled systems: an. application to the North Atlantic Oscillation.  Abstract.  Author URL.
Hourdin F, Mauritsen T, Gettelman A, Golaz J-C, Balaji V, Duan Q, Folini D, Ji D, Klocke D, Qian Y, et al (2017). The Art and Science of Climate Model Tuning. Bulletin of the American Meteorological Society, 98(3), 589-602. Abstract.
Williamson DB, Blaker AT, Sinha B (2017). Tuning without over-tuning: Parametric uncertainty quantification for the NEMO ocean model. Geoscientific Model Development, 10(4), 1789-1816. Abstract.
Williamson D, Blaker AT, Sinha B (2017). Tuning without over-tuning: parametric uncertainty quantification for the NEMO ocean model. Geoscientific Model Development Discussions, 1-41.
Williamson D (2015). Exploratory ensemble designs for environmental models using k-extended Latin Hypercubes. Environmetrics, 26(4), 268-268.
Williamson D, Goldstein M (2015). Posterior belief assessment: Extracting meaningful subjective judgements from bayesian analyses with complex statistical models. Bayesian Analysis, 10(4), 877-908. Abstract.
Williamson D, Blaker AT (2014). Evolving Bayesian Emulators for Structured Chaotic Time Series, with application to large climate models. SIAM Journal on Uncertainty Quantification, 2, 1-28. Abstract.
Williamson D, Blaker AT, Hampton C, Salter JM (2014). Identifying and removing structural biases in climate models with history matching. Climate Dynamics: observational, theoretical and computational research on the climate system
Williamson D, Vernon IR (2013). Efficient uniform designs for multi-wave computer experiments. arXiv Abstract. Web link.
Williamson D, Goldstein M, Allison L, Blaker A, Challenor P, Jackson L, Yamazaki K (2013). History matching for exploring and reducing climate model parameter space using observations and a large perturbed physics ensemble. Climate Dynamics, 41(7-8), 1703-1729. Abstract.
Yamazaki K, Rowlands DJ, Aina T, Blaker AT, Bowery A, Massey N, Miller J, Rye C, Tett SFB, Williamson D, et al (2013). Obtaining diverse behaviors in a climate model without the use of flux adjustments. Journal of Geophysical Research Atmospheres, 118(7), 2781-2793. Abstract.
Williamson D, Goldstein M (2012). Bayesian policy support for adaptive strategies using computer models for complex physical systems. Journal of the Operational Research Society, 63(8), 1021-1033. Abstract.
Williamson D, Goldstein M, Blaker A (2012). Fast linked analyses for scenario-based hierarchies. Journal of the Royal Statistical Society. Series C: Applied Statistics, 61(5), 665-691. Abstract.


Mohammadi H, Challenor P, Goodfellow M, Williamson D (2019). Emulating computer models with step-discontinuous outputs using Gaussian. processes. Abstract.  Author URL.

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Supervision / Group

Postdoctoral researchers

  • Muhammad Hasan Hasan
  • Bertrand Nortier

Postgraduate researchers

  • Cassandra Bird
  • Hollie Calley
  • Chris Parton-Fenton

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