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The black hole article shows that there are formal procedures one can take to manage and mitigate, if not eliminate, the influence of groupthink, in that case from prior expectations or knowledge.
While I have to study those examples more closely, I think the fundamental issue is the appropriate language for model uncertainty (ie. probabilities about models that output probabilities)
For a Bayesian, it is probabilities all the way down, as Frank’s post shows. Philosopher Richard Jeffreys also held that view.
Others, like Arthur Dempster and Glen Shafer, are not convinced that all uncertainty can be expressed by a single probability number. Their work lead to Dempster-Shafer theory, also known as the “Mathematical theory of Evidence” and is closely related to the notion of “imprecise” (aka interval) probabilities.
The work in this area is more likely to be published in symbolic logic journals than applied stats, but the tools developed there are likely (IMO) to productively resolve these philosophical disputes and lead to rigorous “statistical thinking” vs. the too common statistical rituals now at epidemic proportions.
Here are some interesting papers for the philosophically inclined. I’d start with the first one, and then the others for more formal development and justification.
- Crane, H. (2018) Imprecise probabilities as a semantics for intuitive probabilistic reasoning (link)
- Crane, H; Isaac, W (2018) Logic of Typicality (link)
- Crane, H. (2018) Logic of Probability and Conjecture (link)
For applications the following are interesting; 2 is a mathematical formalization of the argument made by @Sander in numerous threads about Bayesian probabilities being too optimistic, to accept the idea that these models capture all uncertainty. Martin turns the absence of any truly “non-informative” prior to prove any additive system of representing beliefs runs the risk of false confidence. Formal discussion at the meta-level (ie. model criticism) can be productively done in the realm of non–additive beliefs.
- Martin, R (2021) An imprecise-probabilistic characterization of frequentist statistical inference (link)
- Martin, R (2019) False confidence, non-additive beliefs, and valid statistical inference (link)
- Martin, R (2021) Valid and efficient imprecise-probabilistic inference across a spectrum of partial prior information (link)
- Balch, M, Martin R. Scott, F. (2019) Satellite conjunction analysis and the false confidence theorem (link)
Christian P. Robert gives his opinion here: