Hi there,
I’m doing Bayesian A/B Testing using Pymc3. My dependent variable is exponentially distributed and I’m using the Gamma distribution as it’s prior.
I want to make the Gamma uninformative - what alpha/beta parameter settings would I choose to make this the case?
Ben Lambert’s distribution zoo is a nice tool for figuring out what parameters make sense for different distributions.
Unlike something like beta or normal, the gamma doesn’t have a natural uninformative parameter setting (I guess you know that, that’s why you’re here). So you’re going to have to rely a bit more on domain knowledge to figure out what “uninformative” means in your context – how much mass should be near 0, what should 95% of the CDF be less than, how much tail, etc. What values are impossibly large, things like this.
One thing I like about the gamma is that when beta is 1, the mean and variance are both alpha. That helps me to reason about the distribution a bit.
A complementary strategy is to use prior predictive checks to make the consequences of your prior concrete. If you don’t like what your model thinks is plausible before updating (i.e., conditional on your priors), then your model isn’t reflecting your priors.