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WP56: Scientific Uncertainty: a User Guide The Munich Re Programme: Evaluating the Economics of Climate Risks and Opportunities in the Insurance Sector Scientific uncertainty: a user’s guide Seamus Bradley August 2011 Centre for Climate Change Economics and Policy Working Paper No. 65 Munich Re Programme Technical Paper No. 9 Grantham Research Institute on Climate Change and the Environment Working Paper No. 56 The Centre for Climate Change Economics and Policy (CCCEP) was established by the University of Leeds and the London School of Economics and Political Science in 2008 to advance public and private action on climate change through innovative, rigorous research. The Centre is funded by the UK Economic and Social Research Council and has five inter-linked research programmes: 1. Developing climate science and economics 2. Climate change governance for a new global deal 3. Adaptation to climate change and human development 4. Governments, markets and climate change mitigation 5. The Munich Re Programme - Evaluating the economics of climate risks and opportunities in the insurance sector (funded by Munich Re) More information about the Centre for Climate Change Economics and Policy can be found at: http://www.cccep.ac.uk. The Munich Re Programme is evaluating the economics of climate risks and opportunities in the insurance sector. It is a comprehensive research programme that focuses on the assessment of the risks from climate change and on the appropriate responses, to inform decision-making in the private and public sectors. The programme is exploring, from a risk management perspective, the implications of climate change across the world, in terms of both physical impacts and regulatory responses. The programme draws on both science and economics, particularly in interpreting and applying climate and impact information in decision-making for both the short and long term. The programme is also identifying and developing approaches that enable the financial services industries to support effectively climate change adaptation and mitigation, through for example, providing catastrophe insurance against extreme weather events and innovative financial products for carbon markets. This programme is funded by Munich Re and benefits from research collaborations across the industry and public sectors. The Grantham Research Institute on Climate Change and the Environment was established by the London School of Economics and Political Science in 2008 to bring together international expertise on economics, finance, geography, the environment, international development and political economy to create a world- leading centre for policy-relevant research and training in climate change and the environment. The Institute is funded by the Grantham Foundation for the Protection of the Environment, and has five research programmes: 1. Use of climate science in decision-making 2. Mitigation of climate change (including the roles of carbon markets and low- carbon technologies) 3. Impacts of, and adaptation to, climate change, and its effects on development 4. Governance of climate change 5. Management of forests and ecosystems More information about the Grantham Research Institute on Climate Change and the Environment can be found at: http://www.lse.ac.uk/grantham. This working paper is intended to stimulate discussion within the research community and among users of research, and its content may have been submitted for publication in academic journals. It has been reviewed by at least one internal referee before publication. The views expressed in this paper represent those of the author(s) and do not necessarily represent those of the host institutions or funders. Scientific Uncertainty: A User’s Guide Seamus Bradley Department of Philosophy, Logic and Scientific Method London School of Economics and Political Science Houghton Street WC2A 2AE London lse.ac.uk/philosophy seamusbradley.net August 9, 2011 b6c1703 v1.51 Abstract There are different kinds of uncertainty. I outline some of the various ways that uncertainty enters science, focusing on uncertainty in climate science and weather prediction. I then show how we cope with some of these sources of error through sophisticated modelling techniques. I show how we maintain confidence in the face of error. 3 Contents Contents4 1 Two motivating quotes ....................... 5 1.1 Laplace’s demon: ideal scientist.............. 5 1.2 On Exactitude in Science.................. 6 1.3 Characterisations of uncertainty.............. 7 1.4 Outline............................ 8 2 Data gathering............................ 8 2.1 Truncated data: imprecision................ 9 2.2 Noisy data: inaccuracy................... 9 2.3 Deeper errors ........................ 10 2.4 Meaningfulness of derived quantities........... 11 3 Model building ........................... 11 3.1 A toy example........................ 13 3.2 Curve fitting......................... 13 3.3 Structure error........................ 15 3.4 Missing physics....................... 15 3.5 Overfitting.......................... 15 3.6 Discretisation ........................ 17 3.7 Model resolution ...................... 18 3.8 Implementation....................... 18 4 Coping with uncertainty...................... 19 4.1 Make better measurements!................ 19 4.2 Derivation from theory................... 20 4.3 Interval predictions..................... 22 4.4 Ensemble forecasting.................... 23 4.5 Training and evaluation .................. 25 4.6 Robustness.......................... 27 4.7 Past success ......................... 29 5 Realism and the “True” model of the world ........... 29 6 Summary............................... 31 4 Scientific Uncertainty: A User’s Guide 5 On two occasions I have been asked, “Pray, Mr. Babbage, if you put into the machine wrong figures, will the right answers come out?” I am not able rightly to apprehend the kind of confusion of ideas that could provoke such a question Charles Babbage 1 Two motivating quotes How do error and uncertainty enter science? What can we do about it? This paper explores these questions in the context of scientific modelling, specifically climate modelling. While my main interest is in models of the climate, I think a lot of what I say will translate into other disciplines. I want to start this paper with two quotes that highlight two aspects of the modelling process. 1.1 Laplace’s demon: ideal scientist In trying to characterise what determinism was, Laplace described his famous “demon” who was a kind of ideal scientist. We may regard the present state of the universe as the effect of its past and the cause of its future. An intellect which at a certain moment would know all forces that set nature in motion, and all positions of all items of which nature is composed, if this intellect were also vast enough to submit these data to analysis, it would embrace in a single formula the movements of the greatest bodies of the universe and those of the tiniest atom; for such an intellect nothing would be uncertain and the future just like the past would be present before its eyes. The perfection that the human mind has been able to give to astronomy affords but a feeble outline of such an intelligence. Discoveries in mechanics and geometry, coupled with those in universal gravitation, have brought the mind within reach of comprehending in the same analytical formula the past and the future state of the system of the world. All of the mind’s efforts in the search for truth tend to approximate the intelligence we have just imagined, although it will forever remain infinitely remote from such an intelligence. Laplace (1951 [1816])1 This demon knows everything there is to know: for him, there is no uncer- tainty. We of course fall far short of Laplace’s ideal scientist, and our actual 1This is actually a slightly different translation to the one cited, given in Smith (2007). Scientific Uncertainty: A User’s Guide 6 science is full of uncertainties of various kinds. My aim here is to characterise what kinds of uncertainty arise in science, and point out some of the ways we cope with them. Laplace attributed three important capacities to his demon.2 First it must know “all the forces that set nature in motion”: it must be using the same equations as Nature is. Second, it must have perfect knowledge of the initial conditions: “all positions of which nature is composed”. Laplace makes reference only to positions, but let’s grant that he was aware his demon would need to know various other particulars of the initial conditions — momentum, charge. — let’s pretend Laplace was talking about position in state space. The third capacity that Laplace grants his demon is that it be “vast enough to submit these data to analysis”. This translates roughly as infinite computational power. I will have less to say about this third capacity, at least directly. Laplace was operating in a purely Newtonian world, without quantum effects, without relativistic worries. In this paper, I will do the same. On the whole, climate scientists make the assumption that it is safe to model the climate system as a Newtonian, deterministic system. 1.2 On Exactitude in Science My second motivating quote is pulling in the opposite direction. Laplace is thinking about the ultimate in accurate prediction, this story from Jorge Luis Borges points to the limits inherent in modelling. In that Empire, the Art of Cartography attained such Perfec- tion that the map of a single Province occupied the entirety of a City, and the map of the Empire, the entirety of a Province. In
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