PhilGoetz comments on Bayes' rule =/= Bayesian inference - Less Wrong

37 Post author: neq1 16 September 2010 06:34AM

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Comment author: PhilGoetz 16 September 2010 08:09:23PM *  1 point [-]

THANK YOU! That's the best explanation I've ever seen of the difference. I don't know if it's right; but at least it's making a coherent claim.

Can you spell out how the computation is done with the priors in the Bayesian case?

Quibble:

However, we should expect the test to do at least as good as guessing (guessing would mean randomly selecting 1% of people and calling them T+).

Guessing that everyone is T- would have a lower error rate.

Comment author: datadataeverywhere 17 September 2010 05:32:35AM 0 points [-]

Guessing that everyone is T- results in a 100% false negative rate, which although not much better than a 99% false negative rate, might more than make up for a 1% decrease in the false positive rate.

If this is a real cancer test, and the researcher is optimizing a balance between false positives and false negatives, where would you prefer that he or she place that balance? A lot of medical tests have intentionally very low false negative rates even if that means they have proportionally much higher false positive rates (than they would if they were optimizing for a different balance).