Display likelihood function in Bayesian tests?
There most probably will be a very simple answer to this, but just asking for a friend (i.e., my med/bio undergrads)...
In JASP's Bayesian analysis output, plots show the prior and posterior parameter distributions. Why is the likelihood not shown? I think this would be great for educational purposes: the posterior distribution is between the prior and likelihood and can be closer to the former or the latter.
This would illustrate nicely a basic idea of Bayesian analysis: the update of a prior belief by observed data. The closer the posterior to the likelihood, the stronger the evidence the data provide. It also gives a complete picture of Bayes' equation: posterior = likelihood x prior.
Thanks for your input!
Peter
Comments
Hi Peter,
Good point. I noticed that in the Learn Bayes module, this is not present either; I think that would be the place for it. I'll attend Frantisek (who has programmed the relevant part of the Learn Bayes module) to this.
Cheers,
E.J.
Hi E.J.,
I think the likelihood can have a place in the regular analytical modules as well. The Learn Bayes module does not contain all of the NHSTs that JASP offers. Including likelihoods in the Bayesian analyses would be very instructive and insightul, even for seasoned Bayesians, maybe.
Perhaps at least a mention of what likelihood function was used in a Bayesian analysis? I find it instructive when students can recalculate computer output (for simple scenarios) manually. All to demystify statistical procedures and to open the black box a bit.
Cheers!
Peter