How do I input my informed priors for regression?

Scribe42

Mostly new to Bayesian approach and totally new to JASP. Trying to leverage Bayes regression (or ANOVA) to tighten up the CI (from my in-market test) into a "credible interval" for parameter estimation. I don't conceptually have a null here, I just want an interval around my estimation of sales lift from a test treatment.

Frequentist regression/anova is:

sales = f((test vs control market (1 or 0), post vs pre time period (1 or 0), test/post interaction (1 or 0)).

The test/post interaction is my treatment and what I am interested in. I have a solid prior based on previous analysis.

What confuses me is that I would expect to somewhere input my prior distribution (presumably via a mean estimate and standard deviation), but I don't see anywhere to do that. JASP just seems to default to an uninformed prior.

Any help getting in the right direction greatly appreciated!

EJ

Hi Scribe42,

The priors can be set under "Advanced options" (linear regression) or "additional options" (ANOVA). The default options are not uninformed in the sense that they are not uniform, but they are fairly spread out and centered on 0. Adding more informed priors for regression/ANOVA is a worthwhile endeavor but things quickly get complicated. Zoltan Dienes has worked a lot with these kinds of problems - -I'd encourage you to check out his work!

Cheers,

E.J.

Scribe42

Appreciate the response!

As mentioned I'm fairly new to Bayes, but if I can't enter an informed prior I'm unclear on what the benefit of Bayesian analysis is to begin with. Apparently there's some analytical benefit to making the null hypothesis the prior, though I don't see (yet) how there's any advantage to that. Perhaps there's a benefit to accepting or rejecting the null, but how can this help with parameter estimation?

EJ

Hi Scribe42,

In many scenarios, the inference is very robust to the type of prior that is used. The primary Bayesian movement in statistics right now is "objective Bayes" and it uses general-purpose priors that meet specific desiderata. My own preference is to start with objective Bayes and then insert more specific information whenever it is available. Two recent papers that lists Bayesian advantages:

1. https://osf.io/3tdh9/
2. https://link.springer.com/article/10.3758/s13423-017-1343-3

Cheers,

E.J.