I have a supply chain model, where our historical data are sales from a store, S(t). We do not know how much inventory the store had at any given time, so we cannot compute the demand D(t) (which is what we want), we only know that D(t) >= S(t) for all t. Note, we do NOT know which of the sales were censored.
I was wondering: could I use a horseshoe prior on each point, denoting if it was censored? I guess my prior for them would be the belief that there wasn’t enough inventory to fulfill the demand on that day.
I think the actual prior would be time based: given that the previous sales were censored, there is a higher probability that the current sales would be, but that is another topic.