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# Some questions regarding the prior

Hello!

I am new too Bayesian thinking and therefore I have several questions regaring the prior:

• Is it right when I say the predefined Cauchy prior defines the probability of the effect size (.707) for H1?
• Can somebody give me another interpretation of the Cauchy prior of .707 (t-test)? Does it e.g., mean that the score of the average person in the experimental group is .707 standard deviations above the average person in the control group?
• Is the “Cauchy prior” in the e.g. t-test the same as the “r scale covariates” in the e.g. Bayesian regression?
• What should I do when I have no prior knowledge? Should I set the prior to 0 (.5?) or should I use the “normal” e.g., t-test?
• When I have several other articles with effect sizes (e.g., d, eta²) around e.g. .3 can I also set the Cauchy prior to .3 or do I have to transform e.g., d, delta etc. into the Cauchy prior?
• Is there a minimum amount of evidence I should have (e.g. at least 5 articles) before I change the default prior of .707? For instance, I read the following on “http://willgervais.com/blog/2015/11/20/playing-with-bayes-factors”: “Within social psychology, for example, the median effect size is something like .36. And only around 20% of effects are larger than d = .7. So the JASP and BayesFactor default setting just might not be a good fit for social psychology. But it's super-easy to change. For my money, .36 is probably a better default than .707 for social psychology, because that's where our effects are actually centered”.

Best,
) Markus

• Hi Markus,

For the Cauchy, the prior width r equals the interquartile range. So if r=0.707, there is a 50% chance that the true value of effect size lies in the interval from -0.707 to +0.707. I encourage you to read the papers on Bayesian inference (part I and II) here: https://osf.io/m6bi8/

Finally, people who argue for a lower value of r fail to understand that lowering the width r but keeping the location fixed at 0 has undesirable consequences, as this just makes H1 very similar to H0. If you feel that your effect sizes are around .36, you should have a prior that peaks around .36. Right now the only parameter to adjust is the width (we are working on this). Bottom-line: just use the default.

Cheers,
E.J.

• Thank you very much!
Markus