Necessary/recommended level of theory for developing statistical intuition

As I prepare to take one of the entry level actuarial exams later in the year (ie. Probability) I wonder where these professionals would fit in? A significant amount of effort is devoted to modelling those uncertanties via extreme value theory, for example. Because the organizations that employ them bear the cost of errors when setting prices, the silliness seen in a typical social science applications are absent.

They would epitomize what Taleb and Harry Crane describe as having “skin in the game.” Crane in particular has proposed the radical notion that reported probabilities from models aren’t “real”, unless someone who makes such a claim is willing to make a wager at those implied odds. When looked at from an information theoretic standpoint, this is only taking JL Kelly’s 1956 paper “An Alternative Interpretation of the Information Rate” literally. I find substantial value in that point of view.

Crane, Harry (2018) The Fundamental Principle of Probability (preprint).

Crane, Harry (2018) Is Statistics Meeting the Needs of Science (preprint)

Crane, Harry (2020) Naive Probabilism (preprint)

Shafer, Glenn (2021) Testing by betting: A strategy for statistical and scientific communication (link)

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