De Finetti on the dangers of mathematization

3 Aug, 2022 at 14:41 | Posted in Statistics & Econometrics | 2 Comments

Theory of Probability eBook by Bruno de Finetti - 9781119286295 | Rakuten  Kobo GreeceLet us bear in mind … that everything is based on distinctions which are themselves uncertain and vague, and which we conventionally translate into terms of certainty only because of the logical formulation … In the mathematical formulation of any problem it is necessary to base oneself on some appropriate idealizations and simplification. This is, however, a disadvantage; it is a distorting factor which one should always try to keep in check, and to approach circumspectly. It is unfortunate that the reverse often happens. One loses sight of the original nature of the problem, falls in love with the idealization, and then blames reality for not conforming to it.

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  1. Wonderful quote. For a comment built around it that ascribes much of the problem to failure to ground statistical models and inferences in real-world causal mechanisms, see p. 616-618 of
    Greenland, S. (2022). The causal foundations of applied probability and statistics. Ch. 31 in: Dechter, R., Halpern, J., and Geffner, H., eds. Probabilistic and Causal Inference: The Works of Judea Pearl. ACM Books, no. 36, 605-624,
    https://dl.acm.org/doi/10.1145/3501714.3501747,
    or p. 13-15 of the corrected version at https://arxiv.org/abs/2011.02677

    • Yours truly certainly encourages people to read your chapter in that Pearl book, Sander! I especially appreciate the following passage in it:

      “Given the causal nature of data generation, calling causal models “extra-statistical” is a misleading characterization of both causality and statistics: Valid statistical analysis is causal to the core; hence, realistic statistical analysis is a subset of causal analysis. Not even “extradistributional” is correct, because the core problem is about factors producing (causing) differences in distributions of those targeted (e.g., voters; patients with a given indication for treatment) and those observed (e.g., survey responders; patients in a trial). Without a causal model for deducing the assumed data distribution from the entire physical data generator, we have no basis for claiming our probability calculations are connected to our target or the world beyond our immediate data.”


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