Today I am thankful that Bayes’ Rule is unintuitive.
Much ink has been spilled complaining that Bayes’ Rule can yield surprising results. As anyone who has taken an introductory statistics class knows, it is difficult to solve a problem that requires an application of Bayes’ Rule without plugging values into the formula, at least for a beginner. Eventually, the student of Bayes may gain an intuition for the Rule (perhaps in odds form), but at that point they can be trusted to wield their intuition responsibly because it was won through disciplined practice.
This unintuitiveness is a feature, not a bug because it discourages motivated reasoning. If Bayes’ Rule were more intuitive, it would be simple to back out what P(A), P(B), and P(B|A) must be to justify your preferred posterior belief, and then argue for these quantities. It would also be simple to work backwards to select your prediction A from a favorable hypothesis space. Because Bayes’ Rule is unintuitive, these are challenging moves, and formally updating your beliefs is less vulnerable to motivated reasoning.
Today I am thankful that Bayes’ Rule is unintuitive.
Much ink has been spilled complaining that Bayes’ Rule can yield surprising results. As anyone who has taken an introductory statistics class knows, it is difficult to solve a problem that requires an application of Bayes’ Rule without plugging values into the formula, at least for a beginner. Eventually, the student of Bayes may gain an intuition for the Rule (perhaps in odds form), but at that point they can be trusted to wield their intuition responsibly because it was won through disciplined practice.
This unintuitiveness is a feature, not a bug because it discourages motivated reasoning. If Bayes’ Rule were more intuitive, it would be simple to back out what P(A), P(B), and P(B|A) must be to justify your preferred posterior belief, and then argue for these quantities. It would also be simple to work backwards to select your prediction A from a favorable hypothesis space. Because Bayes’ Rule is unintuitive, these are challenging moves, and formally updating your beliefs is less vulnerable to motivated reasoning.
Happy Thanksgiving!