Having been reading over the German Tank problem as an example of a serious statistical question which can be nicely answered using Bayesian methods (i.e., Pymc3), I was thinking about how intuitive it was to constrain the
DiscreteUniform likelihood to be at least
=1, because we know that the Germans made at least 1 tank during their war effort, when all of a sudden the though struck me, why should not the same assumption be baked into most regressions utilizing the Normal distribution?
For example, sometimes we want to estimate the price of something, which can never be negative, and many other examples of practical regression share this same exact restriction on the dependent variable, so shouldn’t, as a quick alternative, the log-normal distribution be used in most cases of regression?
I apologize if this question is incredibly naive or betrays some huge statistical misunderstanding; at least I want to find out if my newfound reasoning here checks out, and I would appreciate any comments on it.