Vignette should explain that `BayesFactor::anovaBF()` moves to using a Cauchy prior

[jhmaindonald]

Under 'Comparison with JASP', the vignette the Bayes factors vignette moves to use 'BayesFactor::anovaBF()', with no mention of the fact (unless there is magic under the hood that I have missed) that this involves a move to use a Cauchy prior, with the 'BayesFactor' default settings.

Also, it would be helpful to have comment on how the various outputs from BF_inclusion() relate to the four items returned by summary(BF_ToothGrowth).

[mattansb]

At that point, the vignette is comparing the bayesfactor_inclusion function with the similar functionality provided by JASP. To do this (in a new example), the BayesFactor pkg is used as it is what JASP uses. So I don't see the problem here.

If we were to list all the difference between the defaults of rstanarm and BayesFactor the use Cauchy priors would be second to the completely different parameterization used by both packages, which has come under some scrutiny recently. However, the aim of the vignette is to introduce users to main concepts and terms relating to Bayes factors and the related functions. So any such discussion is outside the scope of the vignette(s). This does not mean we do not encourage such discussions - we have a discussions section here on GitHub for just these things. If you want to start a discussion there about the design differences between the packages and how they affect results, you are welcome to do so 🤓

[mattansb]

Also, it would be helpful to have comment on how the various outputs from BF_inclusion() relate to the four items returned by summary(BF_ToothGrowth).

The functionality is explained in the context of the previous (main) example. Feel free to open a PR if you think some clarification is missing!

[jhmaindonald]

A major difference from the analyses that have appeared earlier, as I see it, is that there is now a move to use of a Cauchy prior. Why not say this, rather than assuming that the reader knows about the the BayesFactor settings? My sense, from my limited investigations, is that this is of more consequence than the details of scaling etc. Precisely because there are so many different choices of prior and associated parameters, some attempt to separate what makes a large difference from what is of less consequence is I think needed. Maybe, as you say, this is a subject for discusson.