Hello,

I am currently playing around with priors to decide which one makes most sense for the data I am expecting from an experiment that I want to preregister. My understanding about Cauchy priors is that they include larger effect sizes because of their heavy tails, whereas half normal does not. Here my questions:

1) I would have expected that a half normal is more sensitive to smaller effects compared to a Cauchy with default prior (0.707) because it puts no weight to these extreme effects. However, when I observe a relatively small effect, the Cauchy returns a larger BF than the half normal does, and vice versa when I observe a relatively large effect. Could someone explain this to me?

2) The Cauchy prior scaling "r" translates to 0.5 probability mass of effect sizes that one expects (e.g. for default r = 0.707, 50% fall in -0.707 to 0.707), whereas half normal priors are scaled by the (unstandardized) size of the effect under the alternative, (which is entered as the standard deviation of the distribution). Because of the shape of a normal, this thus should then translate to 0.68 probability mass?

3) Cauchy priors seems to be mostly used and I suppose this makes sense because they work in standardized (not native measurement units) and thus allow comparisons between studies. However, if a study acquires an internal validation measure against which learning effects can be compared, for example, it might make sense to test for effects using a (half) normal working with native units?

4) I guess one aspect to guide this decision is whether you are subjective or objective Bayesian. Besides this, is there anything else you think one should take into account?

Many thanks,

David