As many readers may note, we at Margin of Error tend to think of the world within a Bayesian framework. That’s not exactly unique: most of the prominent forecasters think of probability more as Bayesians than as Frequentists.
This morning, XKCD decided to wade into the debate:
I know which bet I would take. How about you?
Category: Probability & Statistics
Luke Muehlhauser says:
People often pretend like there wasn’t a long battle between frequentists and Bayesians during the 20th century, but Sharon McGrayne’s history of Bayesian thinking proves otherwise:
http://lesswrong.com/lw/774/a_history_of_bayes_theorem/
Joe Mudge says:
If the frequentist had have used the optimal alpha approach ( dx.doi.org/10.1371/journal.pone.0032734 ) and calculated an optimal alpha for a scenario of unequal prior probabilities of null and alternate hypotheses, he/she would have agreed with the Bayesian.
The optimal alpha approach using unequal relative costs of error would have also resulted in the frequentist agreeing with the Bayesian. The cost of error Type I error (falsely concluding the sun has gone nova) would be $50 because he/she would have lost the bet. The cost of Type II error (falsely concluding the sun has not gone nova) is negligible because there’s really no advantage to knowing the sun has just exploded since we’d soon all be dead. If Type I errors are more serious than Type II errors, the resulting optimal alpha that minimizes costs of errors would be much smaller than 0.05, leading the frequentist to the conclusion that the sun hasn’t gone nova.