Re:Frequentist Statistics are Frequently Subjective
by yummyfajitas on Saturday December 05, 2009 @11:40AM
(#978213)
The argument is that Bayesian statistics are less subjective because while we won't come to the same conclusion, we will perform the same update to our prior probabilities.
An example: consider a medical diagnostic test with a 1% false positive rate and no false negatives.
If I understand him correctly, Eliezer is arguing that the scientist (i.e. the lab running the test) should present an update rule, not the posterior probability. I.e., the lab report should say: "Whatever your prior estimate of P(sick) is, your posterior should now be P(sick)/(0.01 P(not sick) + P(sick))" instead of saying "the patient has an x% chance of being sick".
Suppose before the test I believe the odds the patient is sick are 1% and you think they are 10%. Once the test comes out positive, I've updated my probability estimate to 50%, you to 92%.
The update rule provided by Bayesian statistics is objective, even if the posterior is subjective. The frequentists have nothing comparable which is objective.
An example: consider a medical diagnostic test with a 1% false positive rate and no false negatives.
If I understand him correctly, Eliezer is arguing that the scientist (i.e. the lab running the test) should present an update rule, not the posterior probability. I.e., the lab report should say: "Whatever your prior estimate of P(sick) is, your posterior should now be P(sick)/(0.01 P(not sick) + P(sick))" instead of saying "the patient has an x% chance of being sick".
Suppose before the test I believe the odds the patient is sick are 1% and you think they are 10%. Once the test comes out positive, I've updated my probability estimate to 50%, you to 92%.
The update rule provided by Bayesian statistics is objective, even if the posterior is subjective. The frequentists have nothing comparable which is objective.
See also this link:
http://www.overcomingbias.com/2009/02/share-likelihood-ratio...