Element contents
Philosophy of Probability and Statistical Modelling
Published online by Cambridge University Press: 10 December 2020
Summary
This Element has two main aims. The first one (sections 1-7) is an historically informed review of the philosophy of probability. It describes recent historiography, lays out the distinction between subjective and objective notions, and concludes by applying the historical lessons to the main interpretations of probability. The second aim (sections 8-13) focuses entirely on objective probability, and advances a number of novel theses regarding its role in scientific practice. A distinction is drawn between traditional attempts to interpret chance, and a novel methodological study of its application. A radical form of pluralism is then introduced, advocating a tripartite distinction between propensities, probabilities and frequencies. Finally, a distinction is drawn between two different applications of chance in statistical modelling which, it is argued, vindicates the overall methodological approach. The ensuing conception of objective probability in practice is the 'complex nexus of chance'.
- Type
- Element
- Information
- Online ISBN: 9781108985826Publisher: Cambridge University PressPrint publication: 21 January 2021
References
Abrams, M. (2015). Equidynamics and reliable inference about frequencies. Metascience 24, 173–88.Google Scholar
Berkovitz, J. (2015). The propensity interpretation of probability: A re-evaluation. Erkenntnis 80, 1–83.Google Scholar
Bird, A. (Forthcoming). A simple introduction to epidemiological modelling – The SIR model. Available at: https://philosophyandmedicine.org/events/laypersons-guide-to-epidemiological-modelling/.Google Scholar
Blythe, R., and McKane, A. J. (2007). Stochastic models of evolution in genetics, ecology and linguistics. Journal of Statistical Mechanics: Theory and Experiment 7, P07018.Google Scholar
Bogen, J., and Woodward, J. (1988). Saving the phenomena. The Philosophical Review 97 (3), 303–52.Google Scholar
Bokulich, A. (2008). Explanatory fictions. In Suárez, M., ed., Fictions in Science: Philosophical Essays on Modelling and Idealization, Routledge, pp. 91–109.Google Scholar
Carnap, R. (1945). The two concepts of probability: The problem of probability. Philosophy and Phenomenological Research 5 (4), 513–32.Google Scholar
Carnap, R. (1950). Logical Foundations of Probability, Chicago: University of Chicago Press.Google Scholar
Cartwright, N. (1989). Nature’s Capacities and Their Measurement, Oxford: Oxford University Press.Google Scholar
Cartwright, N. (1999). The Dappled World: A Study of the Boundaries of Science, Cambridge: Cambridge University Press.Google Scholar
Cox, D. R. (2006). Principles of Statistical Inference, Cambridge: Cambridge University Press.CrossRefGoogle Scholar
Daston, L. (1988). Classical Probability in the Enlightenment, Princeton: Princeton University Press.CrossRefGoogle Scholar
De Finetti, B. (1937). ‘La prévision: ses lois logiques, ses sources subjectives.’ Annales de l’Institut Henri Poincaré, 7, 1–68Google Scholar
De Finetti, B. (2008). Philosophical Lectures on Probability, Mura, Alberto, ed., Dordrecht: Springer. (English version of De Finetti, B. (1995), Filosofia della Probabilitá, Milan: Il Saggiatore).Google Scholar
Diaconis, P., et al. (2007). Dynamical bias in the coin toss. Society for Industrial and Applied Mathematics (SIAM review) 49 (2), 211–35.Google Scholar
Eagle, A. (2004). Twenty-one arguments against propensity interpretations of probability. Erkenntnis 60 (3), 371–416.Google Scholar
Emery, N. (2015). Chance, possibility, and explanation. British Journal for the Philosophy of Science 66 (1), 95–120.Google Scholar
Emery, N. (2017). A naturalist guide to objective chance. Philosophy of Science 84 (3), 480–99.Google Scholar
Fetzer, J. (1993). Peirce and propensities. In Moore, , ed., Charles S. Peirce and the Philosophy of Science. Tuscaloosa:Alabama University Press, pp. 60–71.Google Scholar
Fisher, R. A. (1930). The Genetical Theory of Natural Selection, Oxford: Clarendon Press.Google Scholar
Frigg, R., and Hoefer, C. (2007). Probability in GRW theory. Studies in the History and Philosophy of Modern Physics 38 (2), 371–89.Google Scholar
Gelman, A., and Hennig, C. (2017). Beyond subjective and objective in statistics. J. R. Statist. Soc. A 180 (4), 967–1033.Google Scholar
Ghirardi, G. C., Rimini, A., and Weber, T. (1986). Unified dynamics for microscopic and macroscopic systems. Physical Review D 34 (2), 470–91.Google Scholar
Gigerenzer, G., et al. (1989). The Empire of Chance: How Probability Changed Science and Everyday Life, Cambridge: Cambridge University Press.Google Scholar
Gisin, N., and Percival, I. C. (1992). The quantum state diffusion model applied to open systems. Journal of Physics A: Math Gen 25, 5677.Google Scholar
Hacking, I. (1975). The Emergence of Probability, Cambridge: Cambridge University Press.Google Scholar
Hacking, I. (1990). The Taming of Chance, Cambridge: Cambridge University Press.CrossRefGoogle Scholar
Hájek, A. (1997). ‘Mises redux’ – redux: Fifteen arguments against finite frequentism. Erkenntnis 45 (2/3), 209–27.Google Scholar
Hájek, A. (2009). Fifteen arguments against hypothetical frequentism. Erkenntnis 70, 211–35.Google Scholar
Heesterbeek, J. A. P. (2002). A brief history of RO and a recipe for its calculation. Acta Biotheoretica 50, 189–204.Google Scholar
Hewitt, E., and Savage, L. J. (1955). Symmetric measures on Cartesian products. Trans. Amer. Math. Soc. 80, 470–501.CrossRefGoogle Scholar
Hoefer, C. (2018). Chance in the World: A Humean Guide to Objective Chance, Oxford: Oxford University Press.Google Scholar
Hopf, E. (1932). On causality, statistics and probability. Journal of Mathematics and Physics, 13, 51–102.Google Scholar
Howson, C., and Urbach, P. (2006). Scientific Reasoning: The Bayesian Approach, Open Court Publishing (3rd edition).Google Scholar
Humphreys, P. (1985). Why propensities cannot be probabilities. The Philosophical Review 94 (4), 557–70.Google Scholar
Humphreys, P. (1989). The Chances of Explanation, Princeton: Princeton University Press.Google Scholar
Ismael, J. (Forthcoming). On chance (or why I am only a half-Humean). In Kleinberg, S., ed., Time and Causation in the Sciences, Cambridge: Cambridge University Press.Google Scholar
Kermack, W. O., and McKendrick, A. G. (1927). A contribution to the mathematical theory of epidemics. Proceedings of the Royal Society of Medicine, 115A, 700–21.Google Scholar
Keynes, J. M. (1921). A Treatise on Probability, Cambridge: Cambridge University Press.Google Scholar
Kimura, M. (1968). The Neutral Theory of Molecular Evolution, Cambridge: Cambridge University Press.Google Scholar
Kolmogorov, A. N. (1933). Foundations of the Theory of Probability, London: Chelsea Books (2nd edition, 1956).Google Scholar
Kucharski, A. (2020). The Rules of Contagion: Why Things Spread and Why They Stop, London: Profile Books.Google Scholar
Laplace, P. S. (1814). A Philosophical Essay on Probabilities, trans. F. W. Truscott and F. L. Emory, New York: Dover.Google Scholar
Lewis, D. (1980). A subjectivist guide to objective chance. In Lewis, D. (1986), Philosophical Papers, vol. 2, Oxford: Oxford University Press, pp. 83–113.Google Scholar
Loewer, B. (2004). David Lewis’ Humean theory of objective chance. Philosophy of Science, 71, 1115–25.Google Scholar
Lyon, A. (2011). Deterministic probability: Neither chance nor credence. Synthese 182: 413–32.Google Scholar
Mayo, D. (1996). Error and the Growth of Experimental Knowledge, Chicago: University of Chicago Press.Google Scholar
Mayo, D. (2018). Statistical Inference as Severe Testing: How to Get beyond the Statistics Wars, Cambridge: Cambridge University Press.Google Scholar
McCullough, P. (2002). What is a statistical model? Annals of Statistics 30 (5), 1225–310.Google Scholar
Moran, P. (1959). Random processes in genetics. Proc. Cambridge Philos. Society, 54, 60–72.Google Scholar
Morgan, M., and Morrison, M. (1999). Mediating Models: Perspectives on Natural and Social Sciences, Cambridge: Cambridge University Press.Google Scholar
Myrvold, W. C. (2012). Deterministic laws and epistemic chances. In Ben-Menahem, M. Hemmo, (eds.), Probability in Physics, The Frontiers Collection. Berlin: Springer Verlag, pp. 73–85.CrossRefGoogle Scholar
Peirce, C. S. (1910). Note on the doctrine of chances. In Philosophical Writings of Peirce, New York: Dover.Google Scholar
Poincaré, H. (1912). Calcul de Probabilités, 2nd ed., Paris: Gauthier Villars (1st ed., 1898).Google Scholar
Popper, K. (1957), “The Propensity Interpretation of the Calculus of Probability and the Quantum Theory,” in Körner, Stephan, ed., Observation and Interpretation in the Philosophy of Physics, New York: Dover, pp. 65–70.Google Scholar
Ramsey, F. P. (1926). Truth and probability. In The Foundations of Mathematics and Other Logical Essays, Cambridge: Cambridge University Press.Google Scholar
Reichenbach, H. (1935/49). The Theory of Probability: An Inquiry into the Logical and Mathematical Foundations of the Calculus of Probability, Berkeley: University of California Press.Google Scholar
Renyi, A. (1955). On a new axiomatic theory of probability. Acta Mathematica Academiae Scientiae Hungaricae, vol. 6, 286–335.Google Scholar
Rice, S. H. (2008). A stochastic version of the Price equation reveals the interplay of deterministic and stochastic processes in evolution. BMC Evolutionary Biology, 8, 262.Google Scholar
Rowbottom, D. (2013), ‘Bertrand’s paradox revisited: Why Bertrand’s “solutions” are all inapplicable’, Philosophia Mathematica (III), 21, 110–14.Google Scholar
Skyrms, B. (1977). Resiliency, propensities, and causal necessity. The Journal of Philosophy, LXXIV (11), 704–13.Google Scholar
Sober, E. (2010). Evolutionary theory and the reality of macro-probabilities. In Eels, E. and Fetzer, J., eds., The Place or Probability in Science. Dordrecht: Springer, pp. 133–60.Google Scholar
Strevens, M. (2003). Bigger than Chaos: Understanding Complexity through Probability, Cambridge, MA: Harvard University Press.Google Scholar
Strevens, M. (2013). Tychomancy: Inferring Probability from Causal Structure. Cambridge, MA: Harvard University Press.Google Scholar
Strevens, M. (2016). The reference class problem in evolutionary biology: Distinguishing selection from drift. In Ramsey, G. and Pence, C., eds., Chance in Evolution, Chicago: University of Chicago Press, pp. 145–75.Google Scholar
Suárez, M. (2007). Quantum propensities. Studies in the History and Philosophy of Modern Physics 38 (2), 418–38.Google Scholar
Suárez, M. (2013). Propensities and pragmatism. The Journal of Philosophy, CX (2), 61–92.Google Scholar
Suárez, M. (2017a). Propensities, probabilities, and experimental statistics. In M. Massimi, J. W. Romeijn, and G. Schurz (eds.), EPSA15: Selected Papers: European Studies in Philosophy of Science, 5, pp. 335–45.Google Scholar
Suárez, M. (2017b). Comment on Gelman and Hennig, Journal of the Royal Statistical Society A, 180 (4), 1020–1.Google Scholar
Suárez, M. (2018). The chances of propensities. British Journal for the Philosophy of Science, 69, 1155–77.Google Scholar
Suppes, P. (1962). Models of data. In Nagel, E., Suppes, P., and Tarski, A. (eds.), Logic, Methodology and Philosophy of Science: Proceedings of the 1960 International Congress. Reprinted in Suppes, P. (1969), Studies in the Methodology and Foundations of Science: Selected Papers from 1951 to 1969, Dordrecht: Springer, pp. 24–35.Google Scholar
Van Fraassen, B. (1993). Quantum Mechanics: An Empiricist View, Oxford: Oxford University Press.Google Scholar
von Mises, R. (1928/1957). Probability, Statistics and Truth, 2nd ed. (1957), London: Allen & Unwin.Google Scholar
von Plato, J. (1985). The method of arbitrary functions. British Journal for the Philosophy of Science, 34 (1), 37–47.Google Scholar
Werndl, C. (2013). On choosing between deterministic and indeterministic models: Underdetermination and indirect evidence. Synthese, 190 (12), 2243–65.Google Scholar
Williamson, J. (2010). In Defence of Objective Bayesianism. Oxford: Oxford University Press.CrossRefGoogle Scholar
- 16
- Cited by