Selection of Priors for Bayes (Logistic)

hlsmith

Omega Contributor
#1
Well I am working on slowly incorporating a more Bayesian approach in order to get away from NHST. I am running a Bayesian logistic model with one binary predictor. Literature states (I believe) my intercept and independent variable should have a normal prior.


The non-informative (flat) prior is mean = 0 and variance = 1,000ish, which to my knowledge when I apply the logistic function they translate to mean = 0.5 and var = 1.


Now for my informative prior: mean = 1 and var = 0.5, as an example, which translate to mean = 0.7 and var = 0.62.


Am I correct in presuming these are the equivalent of the beta coefficient values or are they on the probability scale now (which seems more likely), so not log odds yet. Thus if I exponeniate them I get a mean odds ratio of 2 and precision of 1.87 or do I p/(1-p) and then exponentiate? I am just trying to make sure I am using the priors that I thought I was!!


Thanks you.


Does my above thoughts seem correct or am I missing anything?
 

Dason

Ambassador to the humans
#2
The non-informative (flat) prior is mean = 0 and variance = 1,000ish, which to my knowledge when I apply the logistic function they translate to mean = 0.5 and var = 1.
Nit-picky but I wouldn't call a non-informative high-variance normal prior "flat". It's non-informative but I reserve "flat" for true uniform priors.
 

hlsmith

Omega Contributor
#3
No, I agree. I thought the same thing when I wrote that word. I felt like I was just throwing it out there because I had seen it so many times.


"Weak" was likely the term I was thinking of!
 

hlsmith

Omega Contributor
#4
Just saw this in a Gelman et al. paper I am reading:


"Setting the scale s to infinity corresponds to a flat prior distribution"