for a statistic to be an unbiased estimate of a population parameter, the data values used in calculating the statistic are random variables, identically and independently distributed (iid), inter alia. so the sample mean is an unbiased estimate of the population mean only if the data used are random variables, iid, etc. the central limit thm also requires random variables. you know why?
because random error can be dealt with in statistical models but systematic error cannot, as systematic error is evidence of bias. and anecdotes are wrought with systematic error which you refuse to deal with. in your bayes examples, you're using anecdotes in both your prior and likelihood. again, if all the data you're looking at is biased, your result will be biased. if you include any biased data in the likelihood (prior is where it goes) then you are introducing bias in your posterior estimates.
well, you did offer a counter-example (anecdote) of how people discovered cures in the stone age. you claim they didn't use clinical trials as if this was a counter-arguemnt to whether clinical trials are the gold standard (they didn't use bayes either, btw). but your anecdote suffers from the same fatal flaw that you've been avoiding responding to, repeatedly. in fact they actually did do trials in those days. it was called 'trial and error.' someone with a cold may have accidentally walked by a burning eucalyptus grove and realized he felt better. someone else may have done the same near a burning poison oak bush and had a different outcome. others may have walked by something inert burning but believed they felt better for reasons not associated with what they were breathing. but we only hear the eucalyptus anecdote so you think there's no need for any controlled trial. no double-blinding. no control for a placebo effect. so if 1000 people got sick or died trying stuff to cure their cold they're not taking into account. it's that one that worked we all focus on to show clinical trials are not needed.
so now you're promoting stone-age methods like trial and error over clinical trials? you may as well drop bayes while your at it. and computers. and... all these things have added nothing to drug discovery, right?
and no answer for any of this except to self proclaim your statistical superiority, repeatedly. proclaiming and demonstrating are two different things. you're aware of what an ad homonym argument is? 2+2 is not 534 even if Einstein tells you so.
and by the way, what's your understanding of bias in statistics?