Research
Recent projects
Donkeys!
Publications
Technical reports
Statistics & probability
Other science
Economics & finance
Books and book chapters
Other
Teaching
Theory of Inference
Miscellaneous
Presentations
Software
Cabot Institute
Contact:
Department of Mathematics,
University of Bristol,
University Walk,
Bristol BS8 1TW
tel: +44 (0)117 9287782
fax: +44 (0)117 9287999
j.c.rougier@bristol.ac.uk
Find me:
Room 4.12, left out of the lift on the fourth floor of the main Maths building.
Treat me: Coffee and (vegan) cake
at Cafe Kino, now on Stokes Croft.


Jonathan (Jonty) Rougier's homepage
Reader in Statistics
Summer School in risk and uncertainty in natural hazards
More details here.
Exciting new book!


J.C. Rougier, R.S.J. Sparks, and L.J. Hill (eds), 2013, Risk and
Uncertainty Assessment for Natural Hazards, Cambridge, UK: Cambridge
University Press.
"This is an invaluable compendium for academic researchers and
professionals working in the fields of natural hazards science, risk
assessment and management and environmental science and will be of interest to
anyone involved in natural hazards policy." I wrote that :)

Research
My research concerns the assessment of uncertainty in complex
systems, particularly environmental systems such as climate. Here is an
informal
summary. The main issues I think about are:
 How do we use scientific models? If they are to be used
quantatively to predict the behaviour of a system, e.g. the
climate, how do we represent the discrepancy between the model and
the system?
 Is there a general framework for combining modelevaluations,
system observations, and expert judgements, that is applicable
across different areas of science?
 What is the role of probability in representing our
uncertainty? What does a probability represent, and what are the
limitations of the probability calculus? What is the best way to
explain probabilistic concepts to nonstatisticians?
 How do we implement our inferential calculations with very
large models, that may take weeks or even months to evaluate?
What corners do we cut?
Some current and recent projects
 CREDIBLE: one
of the two NERCfunded consortia on uncertainty and risk assessment for
natural hazards; 20122015.
 RATES: NERCfunded project to quantify mass trends in Antarctica using a
synthesis of model evaluations and several different datasets; 20112013.
 PalaeoQUMP:
"PalaeoQUMP aims to constrain climate sensitivity [...] using a
wider range of derived climate observations from the geological
past (reconstructions from sediments and geomorphological changes
for the Last Glacial Maximum and the midHolocene period), to
evaluate climate model predictions generated using the same
series of simulations as QUMP produced for the modern climate."
Funded by NERC QUEST: 20072010, but we're still analysing the
model runs!
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Publications
Technical reports
 J.C. Rougier (2011), Monte Carlo methods for
Bayesian palaeoclimate reconstruction.
Abstract. In palaeoclimate reconstruction, the natural
modelling direction is forwards from climate to sensors to proxy
measurements. Statistical methods can be used to invert this
direction, making climate inferences from proxy measurements. Among
these methods, the Bayesian method would seem to deal best with the
substantial epistemic uncertainties about climate, and about its
impact on sensors. The main challenge is to perform this inference
efficiently within a simulation approach. This paper reviews the
Importance Sampling approach to Bayesian palaeoclimate
reconstruction, and then goes on to demonstrate the value of recent
advances in Markov chain Monte Carlo (MCMC) inference.
Available as a pdf file. This
paper was written as an addendum to the SUPRAnet report Studying
uncertainty in palaeoclimate reconstruction: A framework for
research (still under development).
 J.C. Rougier (2011), A representation theorem for stochastic
processes with separable covariance functions, and its implications
for emulation. Substantially revised, again, 12 Oct 2011. As
this paper gets longer, I hope it gets clearer.
Abstract.
Many applications require stochastic processes specified on two or
higherdimensional domains; spatial or spatialtemporal modelling,
for example. In these applications it is attractive, for conceptual
simplicity and computational tractability, to propose a covariance
function that is separable; e.g. the product of a covariance
function in space and one in time. This paper presents a
representation theorem for such a proposal, and shows that all
processes with continuous separable covariance functions are
secondorder identical to the product of secondorder uncorrelated
processes. It discusses the implications of separable or nearly
separable prior covariances for the statistical emulation of
complicated functions such as computer codes, and critically
reexamines the conventional wisdom concerning emulator structure,
and size of design.
Available as a pdf file.
 J.C. Rougier and M. Crucifix (2012),
Uncertainty in climate science and climate policy.
This is a book chapter for L. Lloyd and E. Winsberg, eds,
Conceptual Issues in Climate Modeling, University of Chicago Press,
forthcoming. Submitted draft chapter available as
a pdf file.
 J.C. Rougier, A. ZammitMangion and N. Schoen (2013), Computation and visualisation for largescale Gaussian updates.
In geostatistics, and also in other applications in science and
engineering, we are now performing updates on Gaussian process models
with many thousands or even millions of components. These largescale
inferences involve computational challenges, because the updating
equations cannot be solved as written, owing to the size and cost of
the matrix operations. They also involve representational challenges,
to account for judgements of heterogeneity concerning the underlying
fields, and diverse sources of observations.
Diagnostics are particularly valuable in this situation. We present
a diagnostic and visualisation tool for largescale Gaussian updates,
the `medal plot'. This shows the updated uncertainty for each
observation, and also summarises the sharing of information across
observations, as a proxy for the sharing of information across the
state vector. It allows us to `sanitycheck' the code implementing the
update, but it can also reveal unexpected features in our
modelling. We discuss computational issues for largescale updates,
and we illustrate with an application to assess mass trends in the
Antarctic Ice Sheet.
UPDATED! Available at http://arxiv.org/abs/1406.5005.
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Statistics and Probability
J.C. Rougier and M. Goldstein (2014), "Climate Simulators and
Climate Projections", Annual Review of Statistics and Its
Application, 1, 103123. Available
online, doi:10.1146/annurevstatistics022513115652
A. Zammit Mangion, J.C. Rougier, J.L. Bamber and N.W. Schoen
(2014), "Resolving the Antarctic contribution to sealevel rise: a
hierarchical modelling framework", Environmetrics, 25(4), 245264. Available
online, doi:10.1002/env.2247
J.C. Rougier, M. Goldstein, and L. House (2013), "Secondorder
exchangeability analysis for multimodel ensembles", Journal of the
American Statistical Association, 108, 852863. Available
online, doi:10.1080/01621459.2013.802963
I. Scheel, P.J. Green, and J.C. Rougier (2011), "A graphical diagnostic for
identifying influential model choices in Bayesian hierarchical
models", Scandinavian Journal of Statistics, 38(3),
529550. doi:10.1111/j.14679469.2010.00717.x
J.C. Rougier (2010), Discussion of "A statistical analysis of
multiple temperature proxies: Are reconstructions of surface
temperatures over the last 1000 years reliable?" by McShane and
Wyner, Annals of Applied Statistics, 5(1),
9698. doi:10.1214/10AOAS409
J.C. Rougier and M. Kern (2010), Predicting Snow Velocity in Large
Chute Flows Under Different Environmental Conditions. Applied
Statistics, 59(5), 737760. doi:10.1111/j.14679876.2010.00717.x
J.C. Rougier, S. Guillas, A. Maute, A.D. Richmond (2009), Expert
Knowledge and Multivariate Emulation: The ThermosphereIonosphere
Electrodynamics General Circulation Model
(TIEGCM), Technometrics, 51(4), 414424. doi:10.1198/TECH.2009.07123
M. Goldstein and J.C. Rougier (2009), Reified Bayesian Modelling
and Inference for Physical Systems, Journal of Statistical Planning
and Inference, 139(3), 12211239. doi:10.1016/j.jspi.2008.07.019
With discussion and rejoinder.
J.C. Rougier (2008), Efficient Emulators for Multivariate
Deterministic Functions, Journal of Computational and Graphical
Statistics, 17(4), 827843. doi:10.1198/106186008X384032. R package OPE_0.8.tar.gz.
J.C. Rougier (2008), Discussion of 'Inferring Climate System
Properties Using a Computer Model', by Sanso et al, Bayesian
Analysis, 3(1), 4556. DOI:10.1214/08BA301B
M. Goldstein and J.C. Rougier (2006), Bayes
Linear Calibrated Prediction for Complex Systems, Journal of the
American Statistical Association, 101 (no. 475), 11321143.
M. Goldstein and J.C. Rougier (2004), Probabilistic
Formulations for Transferring Inferences from Mathematical Models to
Physical Systems, SIAM Journal on Scientific
Computing, 26(2),
467487. doi:/10.1137/S106482750342670X
I. MacPhee, J.C. Rougier and G. Pollard (2004), Server Advantage
in Tennis Matches, Journal of Applied Probability,
41(4), 11821186.
J.C. Rougier and M. Goldstein (2001), A Bayesian Analysis of Fluid
Flow in Pipelines, Applied Statistics, 50(1), 7793.
P.S. Craig, M. Goldstein, J.C. Rougier and A.H. Seheult (2001),
Bayesian Forecasting for Complex Systems Using Computer Simulators,
Journal of the American Statistical Association, 96,
717729.
J.C. Rougier (2013), 'Intractable and unsolved': some thoughts on statistical data assimilation with uncertain static parameters, Phil. Trans R. Soc. A., 371, doi:10.1098/rsta.2012.0297
D.B. Stephenson, M. Collins, J.C. Rougier, and R.E. Chandler
(2012), Statistical problems in the probabilistic prediction of
climate change, Environmetrics, 23(5), 364372. doi: 10.1002/env.2153
M. Collins, R.E. Chandler, P.M. Cox, J.M. Huthnance, J.C. Rougier, and
D.B. Stephenson (2012), Quantifying future climate change, Nature Climate
Change, 2,
403409. doi:10.1038/nclimate1414
R.M. Gladstone, V. Lee, J.C. Rougier, A.J. Payne, H. Hellmer, A. Le
Brocq, A. Shepherd, T.L. Edwards, J. Gregory, and S.L. Cornford
(2012), Calibrated prediction of Pine Island Glacier retreat during
the 21st and 22nd centuries with a coupled flowline model, Earth
and Planetary Science Letters, 333334,
191199. doi:10.1016/j.epsl.2012.04.022
P.W. Fitzgerald, J.L. Bamber, J. Ridley and J.C. Rougier (2011),
Exploration of parametric uncertainty in a Surface Mass Balance Model
applied to the Greenland Ice Sheet, Journal of Geophysical Research,
in
press, doi:10.1029/2011JF002067
N.R. Edwards, D. Cameron, J.C. Rougier (2011), Precalibrating an
intermediate complexity climate model, Climate Dynamics, 37, 14691482.
S. Guillas, J.C. Rougier, A. Maute, A.D. Richmond, and
C.D. Linkletter (2009), Bayesian calibration of the
ThermosphereIonosphere Electrodynamics General Circulation Model
(TIEGCM), Geoscientific Model Development, 2,
137144. Available
online.
M. Crucifix and J.C. Rougier (2009), On the use of simple dynamical systems
for climate predictions: A Bayesian prediction of the next glacial
inception. The European Physics Journal  Special Topics, 174(1),
1131. DOI:10.1140/epjst/e2009010875
J.C. Rougier, D.M.H. Sexton, J.M. Murphy, and D. Stainforth (2009),
Analysing the climate sensitivity of the HadSM3 climate model using
ensembles from different but related experiments. Journal of
Climate, 22(13), 35403557. DOI:10.1175/2008JCLI2533.1
J.C. Rougier and D.M.H. Sexton (2007), Inference in Ensemble
Experiments, Philosophical Transactions of the Royal Society,
Series A, 365,
21332143. doi:10.1098/rsta.2007.2071
J.C. Rougier (2007), Probabilistic
Inference for Future Climate Using an Ensemble of Climate Model
Evaluations, Climatic Change, 81, 247264. DOI:10.1007/s1058400691569
J.C Rougier (2005), Probabilistic Leak Detection in Pipelines
Using the Mass Imbalance Approach. Journal of Hydraulic
Research, 43(5), 556566.
M. van Oijen, J.C. Rougier and R. Smith (2005), Bayesian
Calibration of ProcessBased Forest Models: Bridging the Gap Between
Models and Data, Tree Physiology, 25, 915927.
S.C. Parker and J.C. Rougier (2007), The Retirement Behaviour of
the SelfEmployed in Britain, Applied Economics, 39(6), 697713.
P.R. Holmes and J.C. Rougier (2005), Trading Volume and Contract
Rollover in Futures Contracts, Journal of Empirical Finance,
12(2), 317338.
S.C. Parker and J.C. Rougier (2001), Measuring Social Mobility as
Unpredictability, Economica, 68, 6376.
B. Hillier and J.C. Rougier (1999), Real Business Cycles,
Investment Finance and Multiple Equilibria, Journal of Economic
Theory, 86, 10022.
J.C. Rougier (1997), A Simple Necessary Condition for Negativity
in the Almost Ideal Demand System with the Stone Price Index,
Applied Economics Letters, 4, 979.
J.C. Rougier (1996), An Optimal Price Index for Stock Index
Futures Contracts, Journal of Futures Markets, 16,
18999.
J.C. Rougier (1993), The Impact of MarginTraders
on the Distribution of Daily Stock Returns: The London Stock Exchange,
Applied Financial Economics, 3, 3258.
J.C. Rougier, R.S.J. Sparks, and L.J. Hill (eds), 2013, Risk and
Uncertainty Assessment for Natural Hazards, Cambridge, UK: Cambridge
University Press.
 L.J. Hill, R.S.J. Sparks, and J.C. Rougier, Risk assessment and
uncertainty in natural hazards, ch 1, pp 118.
 J.C. Rougier, Quantifying hazard losses, ch 2, pp 1939.
 J.C. Rougier and K.J. Beven, Model and data limitations: the sources and
implications of epistemic uncertainty, ch 3, pp 4063.
Nonpeerreviewed
J. Murphy, R. Clark, M. Collins, C. Jackson, M. Rodwell,
J.C. Rougier, B. Sanderson, D. Sexton and T. Yokohata (2011),
Perturbed parameter ensembles as a tool for sampling model
uncertainties and making climate projections, Proceedings of ECMWF
Workshop on Model Uncertainty, 2024 June 2011,
183208. Available
online.
J.C. Rougier, T.L. Edwards, M. Collins and D.M.H. Sexton (2011),
Lownoise projections of complex simulator output: A useful tool when
checking for code errors, Proceedings of ECMWF Workshop on Model
Uncertainty, 2024 June 2011,
209220. Available
online.
J.C. Rougier and L. Chen (2010), Comment on the paper by Diggle et
al., Journal of the Royal Statistical Society, Series C, 59(2),
216.
R. Chandler, J.C. Rougier, and M. Collins (2010), Climate
change, Significance, 7(1), 912.
J.C. Rougier (2009), Notes on statistical modelling for complex
systems, ver. 0.5, unpublished. Available as a pdf file. Please note the version
number: this document is still evolving.
J.C. Rougier (2008), Climate change detection and attribution, ISBA
bulletin, 15(4), 36. Available online.
J.C. Rougier (2008), Formal Bayes Methods for Model Calibration
with Uncertainty, in K. Beven and J. Hall (eds), Applied Uncertainty
Analysis for Flood Risk Management, Imperial College Press / World
Scientific. Draft version available as a pdf
file.
J.C. Rougier (2006), Comment on the paper by Haslett et al.,
Journal of the Royal Statistical Society, Series A,
169(3), 432433.
J.C. Rougier (2005), Literate Programming for Creating and
Maintaining Packages. R News, 5(1), 3539.
J.C. Rougier (2004), Comment on the paper by Murphy et al. Nature did not
want to publish this comment, but I think it says some useful things.
Available as a pdf file.
J.C. Rougier (2001), Comment on the paper by Kennedy and
O'Hagan, Journal of the Royal Statistical Society, Series B,
63, page 453.
J.C. Rougier (2001), What's the Point of `tensor'?, R
News, 1(2), 2627.
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Miscellaneous
Selected presentations (since 2009)
 Server advantages in tennis matches, Iain MacPhee day,
Durham, April 2014. Slides available.
This is a blackboard presentation of MacPhee et al,
2004.
 "Intractable and unsolved": the challenge of data assimilation
with uncertain static parameters, Intractability workshop,
Bristol, April 2012. Slides available. This
is really a talk about longtimescale palaeoclimate reconstruction.
 Nomograms for visualising relationships between three
variables, UseR! 2011 invited talk. Slides
available. Here is some beta code for producing the parallel
scale nomograms used in the
talk: parallelNomo.R. This is the
picture you should get if you run the
example: nomogramBMI.pdf.
After the discussion at UseR! 2011 I appreciated that I had an
extra degree of freedom, which I could use to set the righthand axis
so that the typical donkey had a horizontal line on the nomogram.
Then I put all the donkeys' lines on the plot, and finished it off
with a couple of density functions, original and predicted. The
results is not exactly 'less is
more': donkDensity_19Aug.pdf.
After seeing that line at the top of the 'not less is more'
nomogram heading off to surprising lengths I created a parallel
coordinate plot of the donkey data,
using parallelCoord.R, which resulted
in parallelCoord_26Aug.pdf. As
Kate Milner noted, "that is an exceptionally long donkey" (128cm).
And in fact she checked her notebooks and this length had been
misrecorded: it was in fact 102cm. And what's
the UseR!
connection? it was over a beer at the mixer that David Nicolaides
made me understand the value of this plot for screening.
 Multivariate emulation for North American midHolocene
temperature reconstructions, MPIM, Hamburg, Mar
2011. Slides available. This is a longer
version of the talk given at the Liverpool Marine Symposium, with a
stronger focus on emulating large climate simulators (HadCM3, in our
case). Note that the reconstruction at the end is purely
illustrative.
 Calibration and hypothesis testing for a model of avalanche
behaviour, IHRR, Durham, Jan 2011. Slides
available. Please note that this is a preliminary analysis and we
are currently investigating a more sophisticated statistical model for
the relationship between the HB parameters and the measurements.
 Inference using large climate simulators: HadCM3 and North
American MidHolocene temperature anomalies, Liverpool Marine
Symposium, Jan 2011. Slides available. The
slides for the talk at the MPIM (Mar 2011) are more detailed.
 Accounting for the limitations of quantitative models,
SECaM, Exeter, Jan 2011. Slides
available.
 Stochastic dynamical modelling in Environmental Science,
AMSTAT, Warwick, Oct 2010. See the slides for the Exeter Jan 2011 seminar.
 What can pollen tell us about palaeoclimate?, ICAS, Leeds,
Oct 2010. Slides available (more
detailed).
 Is Building Bigger and 'Better' Climate Change Models a Poor
Investment?, CRASSH conference, Clare College Cambridge, 29 Sep
2010. text available, I was proposing
the motion. Watch
the debate.
 Probabilistic frameworks, INI CLP workshop on probabilistic
climate prediction, Exeter, Sep
2010. See
the
slide! Watch
the presentation (multiple formats).
 A new statistical framework for analysing multimodel
ensembles, IMS 2010, Gothenburg, Aug
2010. Slides available.
 A new statistical framework for analysing multimodel
ensembles, 11th IMSC, Edinburgh, July
2010. Slides available.
 What can pollen tell us about palaeobiomes?, 11th IMSC,
Edinburgh, July 2010. See the slides for the ICAS Oct 2010 seminar.
 Assessing model limitations, Governing Through Uncertainty
meeting, Bristol, May 2010. Slides available.
 Complex systems: Accounting for model limitations, Research Students' Conference 2010, Warwick, April 2010. slides available.
 Complex systems: Accounting for model limitations, St Andrews, Mar 2010. slides available.
 Model limitations: Sequential data assimilation with uncertain
static parameters, Edinburgh, Mar
2010. Slides available.
 Uncertainty and risk in natural hazards, Nottingham, Nov
2009. Slides available.
 Introduction to computer experiments, and the challenges of expensive
models, RSS Statistical Computing Section, Bath, October
2009. Slides available.
 Quantifying uncertainty in probability of exceedence (PE) curves,
NERC/KTN workshop on Catastrophe modelling for natural hazard impact, Lloyd's,
London, Oct 2009. Slides available and
also R code for the pictures.
 Emulatorbased simulator calibration for highdimensional data, JCGS session, JSM2009, Washington DC, Aug 2009. Slides available.
 The What, Why, and How of Multivariate Emulation, Spring
Research Conference On Statistics in Industry and Technology,
Vancouver, May 2009. Slides available.
 Simple models for glacial cycles, Bath Institute for Complex
Systems, Feb 2009. Slides available.
Software
R packages
 calibrate. A
package of useful functions for calibrating a computer simulator.
 paranomo. Draw
parallelscale nomograms. Also contains the 'donkeys' dataset
(see Donkeys).
 slice. General
purpose adaptive slice sampling, also contains mvqqplot, a
multivariate qqplot function.
Other resources
Donkeys!
Joint work with Kate Milner.
Donkeys are extremely hard to weigh, but easy to measure with a
measuring tape. Because weight is a important factor in health and in
veterinary care, statistical models are used to predict weight on the
basis of measured hearth girth and
height. The Donkey
Sanctuary sponsored Kate Milner to go to Kenya with a large
weighing scales and collect data on donkeys. Together we are
analysing the results, with the intention of producing an improved
'nomogram' (or similar) showing how to predict a Kenyan donkey's
weight on the basis of its height and heart girth, and also age and
condition.
Resources:
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