What is it about?

Cromwell's principle requires that the prior probability that one's assumptions are incorrect is greater than 0. The idealized Cromwell's principle barely complies, stipulating that the probability of making incorrect assumptions is arbitrarily small. Enforcing that principle under large deviations theory leads to revising Bayesian models by maximum entropy in wide generality.

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Why is it important?

The idealized Cromwell's principle is relevant to Bayesian model checking since diagnostics often reveal that prior distributions require revision, which would be impossible under Bayes's theorem if those priors were 100% probable. Compliance with Bayes's theorem is important for mutually consistent inferences and decisions before and after the insight from diagnostics or other sources.

Perspectives

In this paper, the idealized Cromwell's principle is presented under standard analysis. A similar principle had been proposed in terms of nonstandard analysis in the philosophy literature.

David R. Bickel
University of North Carolina at Greensboro

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This page is a summary of: Bayesian revision of a prior given prior-data conflict, expert opinion, or a similar insight: a large-deviation approach, Statistics, January 2018, Taylor & Francis, DOI: 10.1080/02331888.2018.1427752.
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