Decide the posterior for the coming data.

CSC

Dear all,

My question is either conceptual or practical. The critical effect was separately tested in three experimental sessions. I am investigating if the effect would increase session after session. My idea is to run the Bayesian t-test for each session, and the prior of the second session is the posterior of the first session. In this case, may I set the multiplication of Bayes factor and prior of the first session as the prior of second session? For example, the first prior is 0.707 and the first Bayes Factor is 1.1. The posterior of first prior is 0.778. Could this posterior be the prior of the second session?

thanks!

Sau-Chin Chen

EJ

Hi Sau-Chin,
If you want to test whether the effect increases, I think I'd suggest a linear contrast or perhaps just an ordinal constraint. I think Richard once wrote a blogpost on how to do that with the BayesFactor R package. Basically you take the standard results and then "correct" for the restrictions using the Hoijtink encompassing method.
In general, you can always use updating in the Bayesian framework, but you have to update everything. So after the first session you have a posterior distribution, and that posterior distribution needs to become the prior distribution for the next session (and this won't be centered on zero). Just multiplying BFs almost never works, because session 1 and 2 are not independent.

Cheers,
E.J.