Abstract
Foretelling the future is an age-old human desire. Among the methods to pursue this goal mathematical modelling has gained prominence. Many mathematical models promise to make probabilistic forecasts. This raises the question of exactly what these models deliver: can they provide the results as advertised? The aim of this paper is to urge some caution. Using the example of the logistic map, we argue that if a model is non-linear and if there is only the slightest model imperfection, then treating model outputs as decision relevant probabilistic forecasts can be seriously misleading. This casts doubt on the trustworthiness of model results. This is nothing short of a methodological disaster: probabilistic forecasts are used in many places all the time and the realisation that probabilistic forecasts cannot be trusted pulls the rug from underneath many modelling endeavours.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Notes
- 1.
UKCP uses the IPCC A1B scenario. This is a kind of “optimistic” scenario of rapid growth and then a levelling off of the population by 2050 and a balance of renewable and fossil fuel energy. Total cumulative emissions amount to roughly twice what cumulative emissions were in 1990.
- 2.
http://www.ukcip.org.uk/wordpress/wp-content/UKCP09/Summ_Pmean_med_2080s.png; retrieved on 12 October 2011.
- 3.
For a general introduction to climate modelling see Kendal McGuffie and Ann Henderson-Sellers, A Climate Modelling Primer. 3rd ed. New Jersey: Wiley 2005; a discussion of the specific models used in UKCP can be found at http://ukcp09.defra.gov.uk/.
- 4.
For a discussion of different kinds of uncertainty and their sources see Seamus Bradley, “Scientific Uncertainty: A User’s Guide”, in: Grantham Institute on Climate Change Discussion Paper 56, 2011 (available at http://www2.lse.ac.uk/GranthamInstitute/publications/WorkingPapers/Abstracts/50-59/scientific-uncertainty-users-guide.aspx), and Leonard A. Smith and Nicholas Stern, “Uncertainty in Science and its Role in Climate Policy” Philosophical Transactions of the Royal Society A 369, 2011, pp. 1-24.
- 5.
We use square brackets to indicate that φ t [ p 0(x)] is the propagating forward in time of the initial distribution p 0(x). The flow of distribution derives from the flow of a state as follows: p t (x) := φ t [ p 0(x)] = ∑ i p 0(z i ), where the sum of z i reflects each of the states in X which are mapped onto x under the flow φ t (i.e. φ t ( z i ) = x for all i); if the flow is invertible this reduces to p t (x) = p 0 (φ –t (x)).
- 6.
UKCP09 probabilities are formed in a more complicated manner, combining outputs from multiple (imperfect) models using Bayesian methods (see http://ukclimateprojections.defra.gov.uk/23239 and http://ukclimateprojections.defra.gov.uk/23210). However, it is unclear why combining the outputs of several structurally imperfect models should make the problems we describe in the following section go away.
- 7.
Equation (1) is of course just the well-known logistic map. The rationale for choosing this equation is that it is one of the simplest non-linear maps and that it has originally been proposed as a population model; see Robert May, “A Simple Mathematical Equation with very Complicated Dynamics”, in: Nature 261, 1976, pp. 459-469. For the ease of presentation we assume that a new generation of fish is born once a week.
- 8.
We use so-called odds-for, which give the ratio of payout to stake. These are convenient because they are reciprocals of probabilities; i.e. if p(A) is the probability of A, then o (A) = 1/p(A) are the odds on A.
- 9.
Notice that our argument does not trade on worries about p 0 (x). We assume that the initial distribution gives us the correct initial probabilities and that setting ones degrees of belief in accordance with these probabilities would be rational. The core of our concern is what happens with these probabilities under the time evolution of the system.
- 10.
See Leonard Smith, “What Might We Learn from Climate Forecasts?”, in: Proceedings of the National Academy of Science USA 4, 99, 2002, pp. 2487-2492.
- 11.
See Robert May, “A Simple Mathematical Equation with very Complicated Dynamics”, loc. cit. and Leonard Smith, Chaos. A Very Short Introduction. Oxford: Oxford University Press 2007.
- 12.
By ‘random properties’ we mean, for instance, properties belonging to the ergodic hierarchy such as being mixing or Bernoulli; for a discussion of these see Joseph Berkovitz, Roman Frigg, and Fred Kronz, “The Ergodic Hierarchy, Randomness and Chaos”, in: Studies in History and Philosophy of Modern Physics 37, 2006, pp. 661-691. An example of a system that becomes increasingly random as the perturbation parameter is turned up is the Hénon-Heiles system; see John Argyris, Gunter Faust, and Maria Haase, An Exploration of Chaos. Amsterdam: Elsevier 1994. For a discussion of systems that become more random as the number of particles increases see Roman Frigg and Charlotte Werndl, “Explaining Thermodynamic-Like Behaviour in Terms of Epsion-Ergodicity”, in: Philosophy of Science 78, 3, 2011, pp. 628–652.
Acknowledgments
We would like to thank audiences in Athens, Bristol, Ghent, London, Paris, and Toronto for valuable discussions. This research was supported by the Centre for Climate Change Economics and Policy, funded by the Economic and Social Research Council and Munich Re. Smith would also like to acknowledge support from Pembroke College Oxford. Frigg would like to acknowledge support from the the Spanish Ministry of Science and Innovation through the project FFI2008-01580. Machete had financial support from RCUK Digital Economy Programme via EPSRC grant EP/G065802/1.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2013 Springer Science+Business Media Dordrecht
About this chapter
Cite this chapter
Frigg, R., Bradley, S., Machete, R.L., Smith, L.A. (2013). Probabilistic Forecasting: Why Model Imperfection Is a Poison Pill. In: Andersen, H., Dieks, D., Gonzalez, W., Uebel, T., Wheeler, G. (eds) New Challenges to Philosophy of Science. The Philosophy of Science in a European Perspective, vol 4. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-5845-2_39
Download citation
DOI: https://doi.org/10.1007/978-94-007-5845-2_39
Published:
Publisher Name: Springer, Dordrecht
Print ISBN: 978-94-007-5844-5
Online ISBN: 978-94-007-5845-2
eBook Packages: Humanities, Social Sciences and LawPhilosophy and Religion (R0)