David Spiegelhalter's Personal Home Page
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Job
I am now Emeritus Professor of Statistics at the University of Cambridge.
From 2016 until 2023 I was Chair of the Winton Centre for Risk and Evidence Communication. This Centre, generously funded by the David and Claudia Harding Foundation, was based in the Department of Pure Mathematics and Mathematical Statistics in Cambridge, and was dedicated to improving the way that quantitative evidence is used in society.
From October 2007 until December 2018 I was the Winton Professor for the Public Understanding of Risk in the Statistical Laboratory, Centre for Mathematical Sciences, University of Cambridge. I worked with a small team comprising Mike Pearson (web and animation), and
Owen Smith (web), and our website was Understanding Uncertainty. This is an educational resource
featuring the use of probability and statistics in everyday life, and
makes extensive use of animations to help 'tell the story' of the data.
The Art of Statistics



The Art of Statistics is a Pelican book published by Penguin in March 2019 in the UK, and by Basic Books in the US in September 2019 - the books are identical apart from the subtitle and cover. The UK Pelican paperback was published in February 2020. This is its UK Amazon site, which is good for reviews (although you might want to buy from a different source so as to encourage diversity in book sales), and here is its US Amazon site.
It's had some good reviews from Nature, Evening Standard, Spectator, E and T magazine, Standpoint, Popular Science and particularly in the Financial Times.
There have been articles about it by Hannah Fry in the New Yorker , and by myself in Aeon Magazine and Scientific American .
I have done interviews for the Guardian podcast, RTE Business, Monocole radio.
Coincidences
The Cambridge Coincidence Collection started as part of filming for the BBC4 programme Tails you win: the science of chance , and since then over 5000 coincidences have been contributed to our website.
Immodest stuff
- See my Google Scholar page for the top citation-earners. I am among the many ISI Highly Cited Researchers.
- Google Scholar's list of top-cited statisticians in September 2020 had me about 26th in the world with around 126,000 citations (although there do seem to be some high-ranking 'statisticians' who seem more like particle physicists..) I hover around 8th when it lists biostatisticians. My citations include some medical papers in which I am one of many authors.
- 2017-2018: President of the Royal Statistical Society.
- 2015: I am the reigning (first and only) World Champion in Loop, the version of pool invented by Alex Bellos that is played on an elliptical table with a single pocket in the baize - more like a putting green than a pool table. Alex describes the principles in detail on the
official Loop page.
Me in action at the Port Eliot Festival where I won the Loop championship - this was done using a mixture of mathematical insight, a little skill arising from a mis-spent youth, and a huge dose of luck.
- 2014: Knight Bachelor in the Queen's Birthday Honours List
- 2013: Honorary Fellow of the Royal College of Physicians
- 2013: Fisher Memorial Lecture, St Andrews University.
- 2013: Honorary Doctorate of Science from the University of Bath.
- 2013: Honorary Doctorate of Science from the University of Heriot-Watt.
- 2011: Science Communication Award for Established Researchers from the Society of Biology
- 2011: My proudest achievement is doing moderately well in the first (and only) series of Winter Wipeout on BBC1 - I did this in the guise of 'Professor Risk', and felt it a professional obligation to tackle the Big Red Balls. You can see my 'performance' here
The full episode (Qualifier: 15:12 to 16:10, and Skilift starting 31:30 , my spectacular exit at 36:00) has been watched by over 5,500,000 people on Youtube, apart from the 8 million or so who saw it on TV. I wrote an article about this for the Times. - 2010: Weldon Medal from the University of Oxford
- 2010: Honorary Doctorate of Science from the University of Plymouth for services to statistical education
- 2009-10: President of the Mathematics Section of the British Science Association.
- 2009 Pinkerton Medal from the Association of Anaesthetists of Great Britain and Ireland
- 2009: Elected Fellow of the Institute of Mathematics and its Applications
- 2009: I gave the 2009 Distinguished Lecture Series in Statistical Sciences at the Fields Institute in Toronto
- 2008:
Spiegelhalter et al (2002) had the 3rd highest citations in the Mathematical Sciences in the last 10 years:
- 2008: Bernoulli Lecture at the 7th World Congress of Probability and Statistics (Institute of Mathematical Statistics) in Singapore
- 2006: Career Achievement Award, Society for Medical Decision Making
- 2006: OBE (Officer of the Order of the British Empire)
- 2006: Honorary Professor of Biostatistics, University of Cambridge
- 2005: Elected Fellow of the Royal Society
Media
Newspaper and magazine articles
I work closely with the Science Media Centre, receiving press releases under embargo on health stories with substantial statistical content, and having the opportunity for comments to be distributed to journalists. This leads to frequent quotes appearing in mainstream media, often on the topic of relative and absolute risks. Full articles include -- 2016: Observer article: Our nine-point guide to spotting a dodgy statistic
- Some older articles are listed here.
- I have been a guest columnist in the Times on the risks of ecstasy and horse-riding, swine flu, Paul the Octopus (all behind a paywall) and other topics, the Guardian on uncertainty in forecasting, and New Scientist on over-reaction to risk.
Online articles
I have also written popular articles and blogs, with some highlights including:- 2009: BBC Online Choose the yum and risk the yuk? ($>$ 300,000 hits)
- 2010: Guardian article: The myth of meaningful coincidence
- 2012: BBC Online Will I live longer than my cat? (which I did, the cat sadly having died soon after the article was published) ($>$ 300,000 hits)
- 2017: Medium article How dangerous is burnt toast?
- 2018: Medium article The risks of alcohol - again
Radio
- Numerous appearances on Radio 4 programmes such as Today, More or Less , You and Yours, The Investigation, Analysis, PM and many others.
- 2019: Co-scripted and voiced Radio 4 Archive on 4 The Risk Makers
- 2018: Co-scripted and voiced Radio 4 Archive on 4 Good Luck Professor Spiegelhalter
- 2018: I presented a one-hour BBC World Service documentary You Can Handle the Truth on teaching children to critically examine claims made on the media, involving travel to Uganda, California and Norway to conduct interviews.
- 2013-2019: Three appearances with Brian Cox and Robin Ince on Radio 4's The Infinite Monkey Cage still available on Iplayer., including the extraordinary 100th edition, which was also televised.
- June 2013: I featured in an episode of The Life Scientific hosted by Jim Al-Khalili, still available on Iplayer.
- November 2013: I fronted an investigation into the PISA statistics comparing education systems around the world, which is now available on Iplayer.
Television
- 2019: Extensive interview about The Art of Statistics with Christiane Amanpour on CNN's Amanpour
- 2019: On the panel for an edition of BBC1's Politics Live
- I was one of the three presenters for the BBC4 documentary Climate Change by Numbers first shown in March 2015, and repeated at odd times since.
- I fronted Tails you win: the science of chance produced by Wingspan Productions and first shown on BBC4 on 18th October 2012. You might be able to see it on Youtube here, unless it's been taken down. The details of the numbers in the programme are given here.
- As mentioned above, I was seventh in an episode of BBC1's Winter Wipeout , attracting my biggest ever audience in the millions. Possibly my greatest achievement.
- I also appeared on the BBC4 documentary The Joy of Stats fronted by the wonderful Hans Rosling, the brilliant BBC2 Horizon programme To Infinity and Beyond which featured the infinite monkey and typewriter problem, and discussing homeopathy on Professor Regan's Medicine Cabinet , Panorama Why are Gambling Machines Addictive? playing on a fixed-odds betting terminal,
- I've been live on Newsnight a few times, including facing Jeremy Paxman - he was charming.
- And there is a clip here of me appearing with David Meade and doing some nice coin flips.
- I also appeared in an episode of Morgan Freeman's Through the Wormhole , where I appear to have a very large object dropped on my head.
- I have a rather meagre page on IMDB.
Science Media Centre
I work with the Science Media Centre in providing frequent comments for journalists writing stories about risks. I was on the panel that drew up guidelines for press reporting of science stories requested by the Leveson InquiryVideos
There are numerous videos of my talks online - see later for a selection. Proper films include -- 2019: I co-scripted and voiced BBC Ideas animation What would Florence Nightingale make of Big Data?
- 2019: I co-scripted and voiced BBC Ideas animation Are you a hedgehog or a fox?
- 2018: Royal Society video People of Science with Brian Cox ($>$70K views)
- 2011: Explaining the risk of bacon sandwiches has had over 10K views.
- 2012: My Professor Risk video has been watched over 100,000 times
Engagement with newspapers
For example meetings with sub-editors at The Times and groups of reporters from the Guardian, Daily Mail and Daily Telegraph, and lecturing to trainee journalists and press officers.Education work:
- 2020- Member: Royal Society Mathematics Futures committee .
- 2016-2019 Member: Royal Society Advisory Committee for Mathematics Education (ACME)
- I was an advisor to the Department for Education on the new syllabus for GCSE Mathematics, and possibly helped to get 'expected frequencies' into the Programme of Study: see this blog for some background and suggested material:Using expected frequencies when teaching probability.
- Development of teaching materials on probability and risk for Key Stages 3 to 4 in conjunction with NRich (Jenny Gage) - this work was presented at the International Conference for Mathematic Education in Seoul, Korea in July 2012. Material is now available on NRich under the title Great Expectations: Probability through Problem Solving, and is currently being turned into a book to be published by Cambridge University Press.
- I was on the Advisory Board for an MEI project producing material for the future Core Mathematics qualification, intended for those who get Grade C or above in GCSE Mathematics but do not go on to A level Maths. The MEI project is based on on the proposals by Professor Tim Gowers' blog on the type of maths that would be genuinely useful to students - here is a BBC article on the project. Funded by the Department for Education.
- I was an advisor on the The Cambridge Mathematics Education Project (CMEP) which 'has the goal of helping to make sixth-form mathematics a rich, coherent and stimulating experience for students and teachers'. Funded by the Department for Education.
- Talks to young people, for example through the Millennium Mathematics Project , University of Cambridge Widening Participation, Royal Institution Masterclasses, Cambridge Science Week, as well as talks in individual schools and colleges. In particular, Maths Inspiration can attract audiences of 1,000 in major West End theatres.
- A column in Plus Magazine: see for example articles on the lottery, football premier league, surprises, how long you might live, and the probability that Obama would win the 2008 Presidential election.
Outreach collaborations:
- 2014-: Advisor for the Royal Statistical Society Ambassadors scheme, where 20 career-young statisticians have been selected to be trained for pubic engagement with statistics.
- On the Advisory Board for the new Science Museum Mathematics gallery.
- I was an advisor for the British Library's Beautiful Science exhibition, spoke at the opening ceremony and performed with Dame Sally Davies, Chief Medical Officer, at a public meeting on communicating health information.
- Judge on East Anglian heat for Famelab in 2013, 2015.
- I was joint curator of Risk Lab, an exciting exhibition combining art and experiments about risk hosted by the wonderful Science Gallery at Trinity College Dublin.
- On the Board of the Royal Statistical Society Getstats campaign for improvement of statistical literacy: this includes developing a syllabus and material for journalism training on statistics and risk
- Collaboration with the Met Office on an online randomised experiment of alternative ways of presenting probabilistic information on 5-day weather forecasts - over 8000 unique participants.
- Worked with BBC Lab UK on a mass psychology experiment on risk perception and attitude: the Big Risk Test. Over 100,000 participants.
Academic collaborations:
- Collaborator on a NIHR-funded project to research and improve the public understanding of surgical outcome data in congenital heart disease. This involves working with patient and media groups to test alternative presentation formats, and develop an animated web-site for the public and resulted in this wonderful website.
- I was one of the original investigators in the University of Cambridge Behaviour and Health Research Unit (BHRU) which had a 5-year 3M Department of Health grant to "contribute evidence to national and international efforts to achieve sustained behaviour change that improves health outcomes and reduces health inequalities".
- Jointly led a Mellon-Sawyer seminar throughout 2009-10 on Modelling Futures: Understanding Risk and Uncertainty. This ran through CRASSH and involved participants from History and Philosophy of Science, Geography, Judge Institute, Statistical Laboratory and many other Cambridge institutions from both the sciences and humanities, and was intended to shed light on the advantages and the limitations of formal models for prediction in the light of pervasive societal and scientific uncertainty.
Public and professional service:
- 2020- Non-Executive Director of the UK Statistics Authority.
- 2020- Attended one meeting of the SAGE group advising on COVID-19.
- 2019- Member: Board of Royal Society Mathematics Futures Programme
- 2017-18 President, Royal Statistical Society
- 2016-2019 Member: Royal Society Advisory Committee for Mathematics Education (ACME)
- 2015: Provided advice to the Cabinet Office on methods underlying the National Security Risk Assessment.
- 2015: Advising HQIP (Health Quality Improvement Partnership) on statistical methods for the Consultant Outcome Programme: HQIP is the national body responsible for clinical audits and the presentation of performance statistics to the public.
- 2015: Advisor to the BBC Trust's impartiality review of the BBC's reporting of statistics.
- 2014: I was part of a team working with the Government Chief Scientific Advisor, Sir Mark Walport, on his first annual report, on Innovation and Risk. I wrote Chapter 6 on communication.
- 2013-2016: Chair of Royal Society Partnership Grants Committee, giving grants to schools for collaborative projects.
- 2013-: Member of Royal Society Rosamund Franklin Award committee.
- 2013: JBS-3: I was part of the Joint British Societies team that developed revised guidelines for cardiovascular care. An interactive program and Heart Risk app based on our animations are now available here.
- 2013+ : Member of Scientific Advisory Board for AXA Research Fund, which commits around 20 million Euros a year on academic posts and projects concerning risk.
- 2013: Member of team that produced the re-analysis of child cardiac surgery mortality data following the temporary closure of the Leeds General Infirmary Unit in 2013 .
- 2012: I was part of a Department of Health Working Group on Uncertainty in Vaccine Evaluation and Procurement that drew up guidelines for how to deal with uncertainty about the cost-effectiveness of vaccines: the final guidance recommended checking that the best estimate of the incremental cost-effectiveness ratio (ICER) was less that 20,000 pounds a quality-adjusted life-year (QALY), and that there was 90% certainty that the iCER was less than 30,000 pounds a QALY. This guidance has now become the accepted method, and has been used, for example, in evaluating the meningococcal B immunization. See Annex 5 of the Code of Practice of Joint Committee on Vaccination and Immunisation (JCVI).
- 2012: Member of Expert panel on invitation support materials for NHS cancer screening, and presented to the Citizen's Jury on breast cancer screening leaflets .
- 2012: With Mike Pearson, we produced a video for the screening aneurysm screening programme (2nd video on web-page)
- 2012: Member responsible for statistical analysis on the Expert Advisory Group for breast implants that set government policy Poly Implant Prothese (PIP) breast implants: final report of the Expert Group .
- 2012: Member of Government Chief Scientific Advisor's Blackett Review group which reported on High Impact Low Probability events .
- 2010: Member of Royal Society working group that produced Climate change: A Summary of the Science .
- 2010: Member of the South Central Strategic Health Authority's Independent Review of Paediatric Cardiac Surgery and Clinical Governance at the Oxford Radcliffe Infirmary.
- 2010: Member of the Scientific Advisory Group for Emergencies (SAGE) for Volcanic Ash: Schools (Guy) Lecturer.
- 2010: Chair of the Trial Screening Committee of the Flexible Sigmoidoscopy trial.
Connections
- If documentaries are included, my Bacon Number is 3, through Jim Al-Khalili (Horizon), Jonathan Ross (A night with the stars) to Kevin Bacon (Film 72)
- My Erdos Number is 3 (through AFM Smith and Samuel James Taylor)
- So my Erdos-Bacon Number is 6. Wikipedia only reports 8 people with lower Erdos-Bacon numbers, but I don't think these include documentaries.
Teaching Probability

Sex by Numbers

The Norm Chronicles

The Norm Chronicles (with Michael Blastland) was published by Profile Books in June 2013. It has a promotional website.
Reviews (favourable!) have appeared in The Economist , Daily Mail , The Guardian , Sunday Times (Dominic Lawson) [paywall] , Bookbag , The Times , and a digested read in the Guardian .
Articles and interviews have appeared in Daily Telegraph , The Observer , The BIg Issue , Guardian Colour section , Pacific Standard , and an article by David Ropeik in the Big Think .
There is a video from the RSA featuring both the authors, and a Guardian podcast with an extensive interview with both of us.
Talks
I have given more than 500 talks on risk and statistics since 2007 to a huge range of audiences, including school students, university students, University of the Third Age, professional bodies, international conferences, and the civil service, including being a regular performer at science festivals (eg Cambridge, Cheltenham, New Scientist) and literary festivals (eg Hay, Glasgow, Oxford). Some recent highlights include:
- 2019 Office for Statistics Regulation conference: Upholding Trustworthiness, Quality and Value
- 2019 Government Economics and Social Science Annual Conference: Can we communicate uncertainty about facts, numbers and science without losing trust and credibility?
- 2019 Centre for Data Ethics and Innovation: Trustworthiness of algorithms
- 2018 ESCoE Conference: The effects of communicating uncertainty around numbers
- 2018 UNECE Annual Conference: Trustworthy communication of numbers and evidence
- 2018 European Food Safety Authority annual conference: Communicating uncertainty without losing trust and credibility
- 2018 Alan Turing Institute : Be prepared to show your working: what can statistical science contribute to transparent, validated and explainable algorithms?
- 2015: Cambridge, Edinburgh and Cheltenham Science Festivals.
- 2015: Cambridge and Glasgow Literary Festivals.
- April 2015: Plenary lecture: International Occupational Health Association..
- December 2014: The Morriston Davies Lecture, British Thoracic Society.
- November 2014: Wooldridge Lecture, British Veterinary Association.
- July 2014: Latitude festival, Suffolk.
- July 2014: Plenary Lecture, International Conference on Teaching Statistics (ICOTS), Arizona.
- March 2014: Oxford Literary Festival.
- November 2013: Annual Blackett Lecture, Operations Research Society.
- July 2013: Fisher Memorial Lecture, St Andrews University.
- June 2013: Jackson Rees Lecture for Association of Paediatric Anaesthetists, Cambridge.
- June 2013: Cheltenham Science Festival.
- May 2013: Society for Radiation Protection Schools Lecture.
- April 2013: Gillian Vaisey Memorial Lecture, Newnham College Cambridge
- November 2012: Seize the Day public event on death at Wellcome
- October 2012: Schorstein lecture at Barts William Harvey Day
- August 2012: SCIFOO camp hosted by Google
- June 2012: Hay Literary Festival
- May 2012: DEFRA Annual Dalton Lecture
- April 2012: Royal Institution Discourse
- March 2012: BAMC Annual public lecture
- Jan 2012: Annual Lecture of Medicines and Health Regulatory Agency (MHRA)
- Dec 2011: Annual Lecture of Institute of Risk Management
- Nov 2011: Annual Simonyi Public Understanding of Science lecture, Oxford
- Sep 2011: Plenary Lecture: EPICOH Occupational Health International Conference, Oxford
- Aug 2011: Plenary Lecture: International Statistical Institute conference, Dublin
- Jun 2011: Cheltenham Science Festival
- Mar 2011: Plenary Lecture: ACME Annual Conference, London
- Jun 2010: Cheltenham Science Festival
- Mar 2010: Royal Society meeting on Scientific Uncertainty
- Jan 2010: The Darwin Lectures, Cambridge the opening Lecture in this Series
Videos of talks
Many of my talks have appeared online, although I have not watched most of them and so can't comment on their quality. They can be found by putting my name into Youtube, but be warned that a lot of the material is repeated. Some more popular recent examples include
- 2019: LSE Events: Learning from Data: the art of statistics
- 2019 Alan Turing Institute. Be prepared to show your working!
- 2019 Surprising art of statistics at 5x15
- 2017: Public Health England Conference: Communicating for informed choice or for persuasion?
A sample of older talks is given below.
- November 2013: Coincidences. (12 mins) 5 x 15 talks
- September 2013: Risk, Chance and Choice. (22 mins) [with Michael Blastland, discussing The Norm Chronicles at the RSA (Royal Society of Arts]
- May 2013: The Upside of Risk. (60 mins) [public talk at opening of Risk Gallery in Dublin]
- Jan 2013: Probability and Statistics. (60 mins) [first of 14 lectures given at AIMS in 2012 - these were not delivered as talks to be videoed, and are a bit shambolic and they were accompanied with practical classes. But have been well edited (note: lecture 1 has > 3000 views, lecture 14 has 120!)]
- November 2012: talking at the Informed Choice About Cancer Screening Citizens' Jury . (20 mins)
- August 2012: Motorbikes, Terrorism, Heart Attacks, Sausages. TedX, Cambridge, (15 mins) [reasonable performance on Micromorts and Microlives]
- November 2011: Living with risk and uncertainty Ñ we're all going to die (sometime). Warwick, (60 mins)
- August 2011: Communicating Risk and Uncertainty. Madingley Lecture Series, Cambridge, (60 mins) [not bad but long]
- Jan 2010: Risk: Trying to Quantify Our Uncertainty. Darwin lecture in Cambridge (60 mins) [10,000 views so presumably not too bad]
- December 2009: Cambridge Ideas. (6 mins) [professional video, very good]
Recent Publications
Here is a list of publications since 2007: an earlier list is available here in a 2012 CV.
2020
- McConway, K., & Spiegelhalter, D. (2021). Sound human, steer clear of jargon, and be prepared. Significance 18(2) ; XX-XX DOI:10.1111/1740-9713.01508
- Finnikin, S., & Spiegelhalter, D. (2021). What is my covid risk? British Medical Journal 372 ; n637 DOI:10.1136/bmj.n637
- Dryhurst, S., Schneider, C. R., Kerr, J., Freeman, A. L., Recchia, G., Spiegelhalter, D. & Van der Linden, S. (2021) COVID-19 risk perception: A longitudinal analysis of its predictors and associations with health protective behaviours in the United Kingdom. Journal of Risk Research xx ; xx DOI:10.1080/13669877.2021.1890637
- Jackson, C., Freeman, A. L., Szlamka, Z., & Spiegelhalter, D. J. (2021). The adverse effects of bisphosphonates in breast cancer: A systematic review and network meta-analysis. PloS one 16(2) ; e0246441 DOI:10.1371/journal.pone.0246441
- Freeman, A. L. J., Kerr, J., Recchia, G., Schneider, C., Lawrence, A. C., Finikarides, L., Luoni, G., Dryhurst, S., & Spiegelhalter, D. J. (under review). Communicating personalised risks from COVID-19: guidelines from an empirical study medRxiv 16(2) ; e0246441 https://www.medrxiv.org/content/10.1101/2020.10.05.20206961v1
- Blastland, M., Freeman, A. L., van der Linden, S., Marteau, T. M., & Spiegelhalter, D. (2020). Five rules for evidence communication. Nature 587 ; 362-364 DOI:10.1038/d41586-020-03189-1
- G.D. Farmer, G.M. Pearson, W.J. Skylark, A.L.J. Freeman, D.J. Spiegelhalter (2020) Making prognostic algorithms useful in shared decision-making: Patients and cliniciansÕ requirements for the Predict:Breast Cancer interface MedRxiv 2020.11.16.20232348
- Clift AK, Coupland CA, Keogh RH, Diaz-Ordaz K, Williamson E, Harrison EM, Hayward A, Hemingway H, Horby P, Mehta N, Benger J., Khunti, K., Spiegelhalter, D., Sheikh, A., Valabhji, J., Lyons, R.A., Robson, J., Semple, M.G., Kee, F, Johnson, P., Jebb, S., Williams, T., Hippisley-Cox, J. (2020) Living risk prediction algorithm (QCOVID) for risk of hospital admission and mortality from coronavirus 19 in adults: national derivation and validation cohort study. BMJ 371; m3731 DOI:10.1136/bmj.m3731
- Freeman, A.L.J., Kerr J., Recchia G., Schneider, C.R., Lawrence, A.C.E., Finikarides L, Luoni G, Dryhurst S, Spiegelhalter DJ (2020) Communicating personalised risks from COVID-19: guidelines from an empirical study MedRxiv 2020.10.05.20206961
- Spiegelhalter, D. (2020). Use of "normal" risk to improve understanding of dangers of covid-19. BMJ 370; m3259 DOI:10.1136/bmj.m3259
- Spiegelhalter, D. (2020). No more damned lies .... New Scientist 245(3295); 48-51
- Smith, G. D., & Spiegelhalter, D. (2020). Shielding from COVID-19 should be stratified by risk. BMJ 369; m2063 DOI:10.1136/bmj.m2063
- van der Bles, A. M., van der Linden, S., Freeman, A. L. J., & Spiegelhalter, D. J. (2020). The effects of communicating uncertainty on public trust in facts and numbers. Proc Natl Acad Sci U S A 117(14); 7672-7683 DOI:10.1073/pnas.1913678117
- Spiegelhalter DJ (2020). Should We Trust Algorithms? Harvard Data Science Review 2.1 DOI:10.1162/99608f92.cb91a35a
- Dryhurst S, Schneider CR, Kerr J, Freeman ALJ, Recchia G, van der Bles AM, Spiegelhalter DJ and van der Linden S (2020). Risk perceptions of COVID-19 around the world Journal of Risk Research 2(2); 101-116 DOI:10.1080/13669877.2020.1758193
- Stephens EM, Spiegelhalter DJ, Mylne K and Harrison M. (2020). The Met Office Weather Game: investigating how different methods for presenting probabilistic weather forecasts influence decision-making Geoscience Communication 2(2); 101-116 DOI:10.5194/gc-2-101-2019
- Climent-Palmer M and Spiegelhalter D (2019). Hormone replacement therapy and the risk of breast cancer: How much should women worry about it? Post Reprod Health 25(4); 175-178 DOI:10.1177/2053369119898586
- van der Bles AM, van der Linden S, Freeman ALJ., Mitchell J, Galvao AB, Zaval L and Spiegelhalter DJ (2019). Communicating uncertainty about facts, numbers and science R Soc Open Sci 6(5); e170707 DOI:10.1098/rsos.181870
- Spiegelhalter, DJ (2019) The Art of Statistics Penguin UK and Basic Book US
- Devos Y, Elliott KC, Macdonald P, McComas K, Parrino L, Vrbos D, Robinson T, Spiegelhalter D, and Gallani B.(2019) Conducting fit-for-purpose food safety risk assessments. EFSA Journal 17(S1); :e170707 DOI:0.2903/j.efsa.2019.e170707
- Brick C, Spiegelhalter DJ (2019) Winners and Losers: Communicating the Potential Impacts of Policies: Commentary on Zeller. Nicotine Tob Res , 21; 336-337 DOI:10.1093/ntr/nty197
- Rakow T, Blackshaw E, Pagel C, Spiegelhalter D (2018). Comparing What to What, on What Scale? The Impact of Item Comparisons and Reference Points in Communicating Risk and Uncertainty Journal of Behavioural Decision Making, 31; 547-561 DOI:10.1002/bdm.2073
- Spiegelhalter D (2018) Commentary on Piumatti et al. 2018. J Public Health , 40; 312 DOI:10.1093/pubmed/fdy038
- Heard CL, Rakow T, Spiegelhalter D (2018) Comparing comprehension and perception for alternative speed-of-ageing and standard hazard ratio formats J Applied Cognitive Psychology, 32; 81-93 DOI:10.1002/acp.3381
- Brick C., Freeman A., Wooding S., Skylark W., Marteau T., & Spiegelhalter D. (2018). Winners and losers: communicating the potential impacts of policies. Palgrave Communications, 4; 81-93 DOI:10.1057/s41599-018-0121-9
- Freeman, A, Spiegelhalter, DJ (2018). Communicating health risks in science publications: time for everyone to take responsibility BMC Medicine, 16 DOI:10.1186/s12916-018-1194-4
- Spiegelhalter DJ (2017) Trust in Numbers J Roy Statist Soc Series A - Statistics in Society, 180: 948-965 DOI:10.1111/rssa.12302 (pdf)
- Freeman A, Marshall M, Treadwell J, Spiegelhalter D, Rafi I. (2017) Communicating risk in primary care: what the Academy of Medical Sciences' report means in practice. Br J Gen Pract, 67: 346-347 DOI:10.3399/bjgp17X691793
- Pagel C, Jesper E, Thomas J, Blackshaw E, Rakow T, Pearson M, Spiegelhalter D. (2017) Understanding Children's Heart Surgery Data: A Cross-Disciplinary Approach to Codevelop a Website. Ann Thorac Surg, 104: 342-352 DOI:doi.org/10.1016/j.athoracsur.2016.11.080 (link)
- Spiegelhalter DJ. (2017) Discussion of "The ASA's p-value statement, one year on" by Robert Matthews Significance, 14: 38-41 DOI:doi.org/10.1111/j.1740-9713.2017.01021.x (link)
- Spiegelhalter D. (2017) Risk and uncertainty communication Annual Review of Statistics and Its Application , 4: 31-60 DOI:doi.org/10.1146/annurev-statistics-010814-020148 (link)
- Grieve R, Abrams K, Claxton K, Goldacre B, James N, Nicholl J, Parmar M, Parker C, Sekhon JS, Smeeth L, Spiegelhalter D. (2016) Cancer Drugs Fund requires further reform British Medical Journal, 354: DOI: 10.1136/bmj.i5090 (link)
- Spiegelhalter DJ. (2016) David Spiegelhalter: Doesn't like Hunt's use of statistics British Medical Journal, 354: (link)
- Rhodes KM, Turner RM, White IR, Jackson D, Spiegelhalter DJ, Higgins JPT (2016) Implementing informative priors for heterogeneity in meta-analysis using meta-regression and pseudo data. Statistics in Medicine, 30: DOI: 10.1002/sim.7090
- Mamidanna R, Ni Z, Anderson O, Spiegelhalter SD, Bottle A, Aylin P, Faiz O, Hanna GB (2016) Surgeon Volume and Cancer Esophagectomy, Gastrectomy, and Pancreatectomy: A Population-based Study in England. Ann Surg, 263: 727-732, DOI: 10.1097/SLA.0000000000001490
- Spiegelhalter D (2016) How old are you, really? Communicating chronic risk through 'effective age' of your body and organs. BMC Med Inform Decis Mak, 263: 727-732, DOI: 10.1186/s12911-016-0342-z (link)
- Gage J and Spiegelhalter DJ (2016) Teaching Probability, Cambridge University Press; Cambridge (CUP page)
- Spiegelhalter DJ. (2015) Sex-rated statistics Significance, 12: 21-25, DOI: 10.1111/j.1740-9713.2015.00840.x (pdf)
- Rakow T, Wright RJ, Spiegelhalter DJ, Bull C (2015) The pros and cons of funnel plots as an aid to risk communication and patient decision making Br J Psychol 102: 327-348. DOI: 10.1111/bjop.12081
- Nolan T, Dack C, Pal K, Ross J, Stevenson FA, Peacock R, Pearson M, Spiegelhalter D, Sweeting M, Murray E (2015) Patient reactions to a web-based cardiovascular risk calculator in type 2 diabetes: a qualitative study in primary care. Br J Gen Pract 65: :e152-e160 DOI: 10.3399/bjgp15X683953
- Spiegelhalter DJ and Gage J (2015) What can education learn from real-world communication of risk and uncertainty? Mathematical Enthusiast 12: 4-10. (pdf)
- Spiegelhalter DJ (2015) Sex by Numbers: what statistics can tell us about sexual behaviour, Profile Books; London (Amazon)
- Spiegelhalter DJ (2014) The need for a common language. In Government Chief Scientific Adviser's Annual Report Innovation: managing risk, not avoiding it. Evidence and case studies. Chap 6: 71-78. (pdf)
- Spiegelhalter, D. J.(2014). The future lies in uncertainty. Science, 345: 264-265. DOI:10.1126/science.1251122 [pdf]
- Schmidli H, Gsteiger S, Roychoudhury S, O'Hagan A, Spiegelhalter D, Neuenschwander B (2014) Robust meta-analytic-predictive priors in clinical trials with historical control information Biometrics 70(4): 1023-1032 DOI:10.1111/biom.12242
- Spiegelhalter, D. J., Best, N. G., Carlin, B. P., & Van der Linde, A. (2014). The deviance information criterion: 12 years on. Journal of the Royal Statistical Society. Series B: Statistical Methodology, 76: 485-493. DOI:10.1111/rssb.12062
- Spiegelhalter, D. J. (2014). The power of the MicroMort. British Journal of Obstetrics and Gynaecology, 121: 662-663. doi:10.1111/1471-0528.12663
- McInerny, G. J., Chen, M., Freeman, R., Gavaghan, D., Meyer, M., Rowland, F., Spiegelhalter, D. J., Stefaner, S., Tessarolo, G., and Hortal, J. (2014). Information visualisation for science and policy: engaging users and avoiding bias. Trends Ecol Evol, 29: 148-157. doi:10.1016/j.tree.2014.01.003
- Boon, Nick, Roger Boyle, Kirsten Bradbury, John Buckley, Susan Connolly, Sonya Craig, John Deanfield et al.(2014) Joint British Societies' consensus recommendations for the prevention of cardiovascular disease (JBS3). Heart2, 100: ii1-ii67 doi:10.1136/heartjnl-2014-305693
- Sutherland WJ, Spiegelhalter D, Burgman MA. (2013) Twenty tips for interpreting scientific claims. Nature, 503: 335-337, (pdf) (8th most viewed story in Nature in 2013)
- Aberdein J, Spiegelhalter D. (2013) Have London's roads become more dangerous for cyclists? Significance, 10: 46-48, DOI: 10.1111/j.1740-9713.2013.00715.x
- Spiegelhalter DJ (2013) Are you 45% more likely to die in a UK hospital rather than a US hospital? British Medical Journal, , 347:f5775. DOI: 10.1136/bmj.f5775
- Spiegelhalter DJ (2013) Have there been 13 000 needless deaths at 14 NHS trusts? British Medical Journal, , 347:f4893. DOI: 10.1136/bmj.f4893
- Cooper NJ, Spiegelhalter D, Bujkiewicz S, Dequen P and Sutton AJ (2013) Use of implicit and explicit Bayesian methods in health technology assessment International Journal of Technology Assessment in Health Care, 29: 336-342 DOI: 10.1017/S0266462313000354
- Presanis AM, Ohlssen D, Spiegelhalter DJ and De Angelis D (2013) Conflict diagnostics in directed acyclic graphs, with applications in Bayesian evidence synthesis Statistical Science, 26: 376-397 doi:10.1214/13-STS426
- AT Booth, R. Choudhary, DJ Spiegelhalter (2013) A hierarchical Bayesian framework for calibrating micro-level models with macro-level data Journal of Building Performance Simulation, 6 : 293-318 DOI: 10.1080/19401493.2012.723750
- Blastland M, Spiegelhalter DJ (2013) The Norm Chronicles, Profile Books; London (Amazon)
- Blastland M, Spiegelhalter DJ (2013) Worrying times New Scientist, 218: 26-27.
- Goldacre B, Spiegelhalter DJ (2013) Bicycle helmets and the law British Medical Journal, , 346:f3817. DOI: 10.1136/bmj.f3817
- Pechey R, Spiegelhalter D and Marteau TM. (2013) Impact of plain packaging of tobacco products on smoking in adults and children: an elicitation of international experts' estimates BMC Public Health, 13:18. DOI: 10.1186/1471-2458-13-18 (pdf)
- Lunn D, Jackson C, Best N, Thomas A, Spiegelhalter D (2012) The BUGS Book: A Practical Introduction to Bayesian Analysis , Chapman and Hall; London (Amazon)
- Spiegelhalter D. (2012) Using speed of ageing and "microlives" to communicate the effects of lifetime habits and environment. British Medical Journal, 345:e8223. DOI: 10.1136/bmj.e8223 (pdf)
- Spiegelhalter D, Knight S, Sant T. (2012) Breast implants: The scandal, the outcry, and assessing the risks. Significance, 9(6)p 17-21. DOI: 10.1111/j.1740-9713.2012.00616.x
- McConway, K, Spiegelhalter D. (2012) Score and ignore: A radio listener's guide to ignoring health stories. Significance, 9(5)p 45-48. DOI: 10.1111/j.1740-9713.2012.00611.x (pdf)
- Rakow, T., Wright, R. J., Bull, C., & Spiegelhalter, D. J. (2012) Simple and multistate survival curves: can people learn to use them?. Med Decis Making , 32(6)p 792-804. DOI: 10.1177/0272989X12451057 (pdf)
- Sutherland WJ, Bellingan L, Bellingham JR, Blackstock JJ, Bloomfield RM, Bravo M, Cadman VM, Cleevely DD, Clements A, Cohen AS, Cope DR, Daemmrich AA, Devecchi C, Anadon LD, Denegri S, Doubleday R, Dusic NR, Evans RJ, Feng WY, Godfray HC, Harris P, Hartley SE, Hester AJ, Holmes J, Hughes A, Hulme M, Irwin C, Jennings RC, Kass GS, Littlejohns P, Marteau TM, McKee G, Millstone EP, Nuttall WJ, Owens S, Parker MM, Pearson S, Petts J, Ploszek R, Pullin AS, Reid G, Richards KS, Robinson JG, Shaxson L, Sierra L, Smith BG, Spiegelhalter DJ, Stilgoe J, Stirling A, Tyler CP, Winickoff DE, Zimmern RL. (2012). A collaboratively-derived science-policy research agenda. PLoS One, 7(3), e31824. DOI: 10.1371/journal.pone.0031824 (pdf)
- Turner RM, Lloyd-Jones M, Anumba DO, Smith GC, Spiegelhalter DJ, Squires H, Stevens JW, Sweeting MJ, Urbaniak SJ, Webster R, Thompson SG. (2012). Routine antenatal anti-D prophylaxis in women who are Rh(D) negative: meta-analyses adjusted for differences in study design and quality. PLoS One,7(2), e30711. DOI: 10.1371/journal.pone.0030711 (pdf)
- HE Jones and DJ Spiegelhalter. Improved probabilistic prediction of healthcare performance indicators using bidirectional smoothing models, (2012) J. Roy. Statist. Soc. Ser. A 175: 729-747, DOI: 10.1111/j.1467-985X.2011.01019.x (pdf)
- DJ Spiegelhalter, C Sherlaw-Johnson, M Bardsley, I Blunt, C Wood, C and O Grigg. (2012) Statistical methods for healthcare regulation: rating, screening and surveillance (with discussion). J. Roy. Statist. Soc. Ser. A 175:1-25, DOI: 10.1111/j.1467-985X.2011.01010.x
- HE Jones and DJ Spiegelhalter. The identification of `unusual' health-care providers from a hierarchical model American Statistician, 65 : 154-163, 2011. DOI: 10.1198/tast.2011.10190
- AT Booth, R. Choudhary, DJ Spiegelhalter. Handling uncertainty in housing stock models Building and Environment, 48 : 35-47, 2011. DOI: 10.1016/j.buildenv.2011.08.016
- DJ Spiegelhalter, H Riesch. Don't know, can't know: embracing deeper uncertainties when analysing risks. Phil Trans Roy Soc A , 369 4730-4750, 2011. DOI: 10.1098/rsta.2011.0163
- DJ Spiegelhalter, I Short, M Pearson. Visualizing uncertainty about the future. Science , 333: 1393-1400, 2011 DOI: 10.1126/science.1191181
- DJ Spiegelhalter. Fear and numbers in Fukushima. Significance , 8 : 100-103, 2011 DOI: 10.1111/j.1740-9713.2011.00501.x
- T Miron-Shatz, I Muhlhauser, B Bower, M Diefenbach, B Goldacre, RSW Smith, D Spiegelhalter and O Wegwarth Barriers to health information and building solutions. Pages 191-214 In Better Doctors, Better Patients, Better Decisions: Envisioning Health Care 2020 Eds. G Gigerenzer and JA Muir Gray MIT Press, Cambridge MA 2011
- D Spiegelhalter. Quantifying uncertainty Pages 17-33 In RIsk (Darwin College Lectures) Eds. L Skinns, M Scott, T Cox CUP, Cambridge 2011
- S Bujkiewicz, HE Jones, MC Lai, NJ Cooper, N Hawkins, H Squires, KR Abrams, DJ Spiegelhalter, AJ Sutton. Development of a transparent interactive decision interrogator to facilitate the decision-making process in health care. Value in Health , 14 : 768-76, 2011 DOI:10.1016/j.jval.2010.12.002
- Rodgers M, Epstein D, Bojke L, Yang H, Craig D, Fonseca T, Myers L, Bruce I, Chalmers R, Bujkiewicz S, Lai M, Cooper N, Abrams K, Spiegelhalter D, Sutton A, Sculpher M, Woolacott N (2011, February). Etanercept, infliximab and adalimumab for the treatment of psoriatic arthritis: a systematic review and economic evaluation. Health Technology Assessment , 15(10) , i-329. 2011 DOI:10.3310/hta15100
- NJ Cooper, J Peters, MC Lai, P Juni, S Wandel, S Palmer, M Paulden, S Conti, N Welton, KR Abrams, S Bujkiewicz, DJ Spiegelhalter, AJ Sutton. How Valuable are Multiple Treatment Comparison Methods in Evidence-Based Health-Care Evaluation? Value in Health , 14 : 371-380, 2011 DOI: 10.1016/j.jval.2010.09.001
- H Riesch DJ Spiegelhalter. 'Careless pork costs lives': risk stories from science to press release to media. Health, Risk & Society , 13: 47-64, 2011 DOI: 10.1080/13698575.2010.540645
- G-C Manzi, DJ Spiegelhalter, RM Turner, J Flowers, SG Thompson. Modelling bias in combining small-area prevalence estimates from multiple surveys' J. Royal Statistical Soc. Series A - Statistics in Soc., 174:31-50, 2011. DOI: 10.1111/j.1467-985X.2010.00648.x
- B Neuenschwander, G Capkun-Niggli, M Branson and DJ Spiegelhalter. Summarizing historical information on controls in clinical trials. Clinical Trials, 7:5-18, 2010 DOI: 10.1177/1740774509356002
- O Grigg and DJ Spiegelhalter. Clinical surveillance and patient safety. In Performance Measurement for Health System Improvement: Experiences, Challenges and Prospects. Eds PC Smith, E Mossialos, I Papanicolas and S Leatherman. Cambridge University Press, Cambridge. pp 286-310, 2009
- D J Spiegelhalter and Y-L Ng. One match to go! Significance, 6:151-153, 2009. DOI: 10.1111/j.1740-9713.2009.00387.x
- B Neuenschwander, M Branson and D J Spiegelhalter. A note on the power prior. Statistics in Medicine, 28: 3562-3566, 2009.DOI: 10.1002/sim.3722
- D Lunn, D Spiegelhalter, A Thomas and N Best . The BUGS project: Evolution, critique and future directions. Statistics in Medicine, 28: 3049 - 3067, 2009.DOI: 10.1002/sim.3680
- D J Spiegelhalter and K Rice. Bayesian Statistics. Scholarpedia, 4(8): 5230, 2009.http://www.scholarpedia.org/article/Bayesian_statistics
- H E Jones and D J Spiegelhalter. Accounting for regression-to-the-mean in tests for recent changes in institutional performance: analysis and power. Statistics in Medicine, 28: 1645-1667, 2009.DOI: 10.1002/sim.3583
- D J Spiegelhalter and A Barnett. London murders: a predictable pattern?. Significance, 6:5-8, 2009.DOI: 10.1111/j.1740-9713.2009.00334.x
- D Lunn, N G Best, D J Spiegelhalter, G Graham, and B Neuenschwander. Combining MCMC and `sequential' PK-PD modelling. Journal Pharmaceutical Statistics, 36: 19-38, 2009.DOI: 10.1007/s10928-008-9109-1.
- M Bardsley, C Sherlaw-Johnson, I Blunt, and D J Spiegelhalter. Using routine intelligence to target inspection of healthcare providers in England Quality and Safety in Health Care, 18: 189-194, 2009.DOI: 10.1136/qshc.2007.024802.
- J P T Higgins, S G Thompson, and D J Spiegelhalter. A re-evaluation of random-effects meta-analysis . J. Royal Statistical Soc. Series A - Statistics in Soc., 172:137-159, 2009.DOI: 10.1111/j.1467-985X.2008.00552.x
- O A Grigg, D J Spiegelhalter, and H E Jones. Local and marginal control charts applied to MRSA bacteraemia reports in UK acute NHS Trusts. J. Royal Statistical Soc. Series A - Statistics in Soc., , 172:49:66, 2009.DOI: 10.1111/j.1467-985X.2008.00553.x
- R M Turner, D J Spiegelhalter, G C S Smith, and S G Thompson. Bias modelling in evidence synthesis. J. Royal Statistical Soc. Series A - Statistics in Soc., 172:23-47, 2009.DOI: 10.1111/j.1467-985X.2008.00547.x
- DJ Spiegelhalter and H Goldstein. Comment: Citation statistics. Statistical Science , 24(1): 21-24, 2009
- O Grigg and D J Spiegelhalter. An empirical approximation to the null unbounded steady-state distribution of the CUSUM statistic. Technometrics, 50: 501-511, 2008.DOI: 10.1198/004017008000000299
- A S Walker, D J Spiegelhalter, D W Crook, D Wyllie, J Morris, and T E A Peto. Fairness of financial penalties to improve control of Clostridium difficile. British Medical Journal, 337:1385-1387, 2008.
- J Schulman, D J Spiegelhalter, and G Parry. How to interpret your dot: Decoding the message of clinical performance indicators. J. Perinatology, 28:588-596, 2008.DOI: 10.1038/jp.2008.67
- A. M. Presanis, D. De Angelis, D. J. Spiegelhalter, S. Seaman, A. Goubar, and A. E. Ades. Conflicting evidence in a Bayesian synthesis of surveillance data to estimate human immunodefficiency virus prevalence. J. Royal Statistical Soc. Series A-statistics In Soc., 171:915-937, 2008. DOI: 10.1111/j.1467-985X.2008.00543.x
- J Suckling, D Ohlssen, C Andrew, J Johnson, SC Williams, M Graves, CH Chen, D Spiegelhalter, and E Bullmore. Components of variance in a multicentre functional MRI study and implications for calculation of statistical power. Human Brain Mapping, 29:1111-1122, 2008. DOI: 10.1002/hbm.20451
- HE Jones, DI Ohlssen, and DJ Spiegelhalter. Use of the false discovery rate when comparing multiple health care providers. J Clin Epidemiol, 61:232-240, 2008 DOI: 10.1016/j.jclinepi.2007.04.017.
- AL Kinmonth, NJ Wareham, W Hardeman, S Sutton, AT Prevost, T Fanshawe, KM Williams, U Ekelund, D Spiegelhalter, and SJ Griffin. Efficacy of a theory-based behavioural intervention to increase physical activity in an at-risk group in primary care (ProActive UK): a randomised trial. Lancet, 371:41-48, 2008.DOI: 10.1016/S0140-6736(08)60070-7
- D. J. Spiegelhalter. Understanding uncertainty. Annals Family Medicine, 6(3):196-197, 2008.DOI: 10.1370/afm.848
- D J Spiegelhalter and H Riesch. Risk, middle-class drinking, and bacon sandwiches. Significance, 5:30-33, 2008.DOI: 10.1111/j.1740-9713.2008.00277.x
- O J Arthurs, T Donovan, D J Spiegelhalter, J D Pickard, and S J Boniface. Intracortically distributed neurovascular coupling relationships within and between human somatosensory cortices. Cerebral Cortex, 17:661-668, 2007.DOI: 10.1093/cercor/bhk014
- A Gorst-Rasmussen, D J Spiegelhalter, and C Bull. Monitoring the introduction of a surgical intervention with long-term consequences. Statistics in Medicine, 26:512-531, 2007.DOI: 10.1002/sim.2548
- O Grigg and D J Spiegelhalter. A simple risk-adjusted exponentially weighted moving average. Journal of American Statistical Association, 102:140-152, 2007.DOI: 10.1198/016214506000001121
- D Ohlssen, L D Sharples, and D J Spiegelhalter. Flexible random- effects models using Bayesian semi-parametric models: applications in institutional comparisons. Statistics in Medicine, 26:2088-2112, 2007.DOI: 10.1002/sim.2666
- D Ohlssen, L D Sharples, and D J Spiegelhalter. A hierarchical modelling framework for identifying unusual performance in health care providers. J Roy Statist Soc A, 170:865-890, 2007.DOI: 10.1111/j.1467-985X.2007.00487.x
- E C Marshall and D J Spiegelhalter. Simulation-based tests for divergent behaviour in hierarchical models. Bayesian Analysis, 2:409-444, 2007.DOI: 10.1214/07-BA218
- C Weir, A Grieve, and D J Spiegelhalter. Likelihood-based posterior updating for optimal dose allocation in a normal dynamic linear model. Journal of Biopharmaceutical Statistics, 17:1033-1050, 2007.DOI: 10.1080/10543400701643947
- T Ring and D J Spiegelhalter. Risk of intracranial aneurysm bleeding in autosomal-dominant polycystic kidney disease. Kidney International, 72:1400-2, 2007.DOI: 10.1038/sj.ki.5002488
- AT Prevost, D Mason, S Griffin, AL Kinmonth, S Sutton, and D Spiegelhalter. Allowing for correlations between correlations in random-effects meta-analysis of correlation matrices. Psychological Methods, 12:434-450, 2007.DOI: 10.1037/1082-989X.12.4.434
- In 2017 and previous years I taught Part 1B Statistics - this is my teaching page.
- I have previously taught Applied Bayesian Statistics in the Lent Term to Part III students.
- In 2012 and 2013 I taught a 3-week graduate course on probability and statistics at the African Institute for Mathematical Sciences (AIMS) in Muizenberg, South Africa. The 2012 lectures were nicely edited to try and make them more coherent, and can be viewed here.