Bayesianized p-Value
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In the example provided for equation (3.3), given the prior odds of 6, is it correct to infer that the researcher has put only a 14% probability of success on the factor being researched?
Odds of 6 = 0.86/(1-0.86), where probability p = 0.86, is the prior of the researcher of an 86% chance that the null holds (thus reject the hypothesis of a significant factor).
This translates to a 14% Bayesian prior for a successful factor?
Yes I think this is correct.
I strongly recommend reading the article of Harvey (The Scientific Outlook in Financial Economics).
It's one of the best I have read in the past 5 years.
In the paper, he uses a 4:1 ratio for prior odds, which translates in a belief that the effect is true 20% of the time (Section 8, p23).