A different kind of non-central hypergeometric distribution?

[martinmodrak]

@mathDR

I thought by trying to “aggregate” my data (and not having individual sales) I would “help” the sampling.

That’s the “fun” with modern computers - quite often doing a clever thing will have worse performance than doing a simple thing. Doing a lot of identical simple operations is something the modern hardware is just very good at. ¯_(ツ)_/¯

@mathDR

An issue I am encountering though: there are some T-shirts that are basically never chosen, and no prior that I have come up with (as yet) will set the omegas for these T-shirts small enough. (since they are never selected, their prior weight is basically not updated, and that pulls all of the other probabilities down).

That sounds weird - not being selected should IMHO pull the weights down pretty quickly. If we look at just a binary model where either a specific t-short is selected or any other t-shirt is selected and ignore any covariates, we have a model that has analytical solution (Beta distribution - Wikipedia). Assuming a uniform prior, the posterior for the probability of being selected after never being selected in k trials should be \mathrm{Beta}(1, k + 1), i.e. it should go down relatively rapidly with increasing k.

So maybe there is something problematic going on in your model. One way to diagnose would be to just use no predictors and two t-shirt categories where both are always available and see if that matches the analytic solutions (moduolo any differences in priors) - but that probably warrants a new forum thread.

Best of luck with your model!