What was on deck on Jason Collins blog through April and May
Your examples are nice theoretical illustrations of the effects, on statistical estimates, of failing to take ‘base rates’ into account. However, it seems to me that it w/d be impossible to arrive at rates which were sufficiently relevant/accurate to be applicable in practice. Consider the covid example: It w/d not be feasible to derive a natural frequency (“from observing cases that have been representatively sampled from a population”; or otherwise) that could realistically be applied to a self-selected individual undertaking a RAT test (because: symptoms, close contacts, occupation, location etc). Analogous issues (eg: age, family history, genes, race etc) would likely apply to the breast cancer example.