In trying to understand how Bayesian probability is used, I’m curious to know what wouldn’t have been possible without it. how important was it in the course of human discovery, and in turn, how it effected history.
I don’t demand rigorous answers, feel free to speculate and throw possibilities as you like.
Bonus question: if Bayes didn’t discover it, when would it have to be discovered? (full speculation mode)
I’m tempted to speculate about a “harder” version of this question: what if we lived in a universe where Bayes’ theorem not only hand’t been discovered but wasn’t true? Like a universe with different physics of causality. But I digress.
I don’t have a direct answer for you, but it might be constructive to reflect that Bayes’ theorem is a particular mathematical understanding of a pattern people understand and use implicitly and pops up all over the place because Bayes’ is a view onto the mechanisms of causation. This suggests that even without Bayes’ theorem formally stated by anyone in any way, we’d still see it pop up all over the place, only no one would have identified it as a common pattern.
I’d have to say the harder version is quite cool as well.
Yes, it’s a good point, that it’s a pattern that will pop up all over the place regardless. so the question is, if no one formally stated it (i.e identified it as a common pattern), how would it look? what scientific discoveries wouldn’t have been made? what wouldn’t have been invented? what would we have believed to be true that’s actually false? what bad decisions would we make? what good decision have we made because of it that we would have been able to make without it?
all examples would do, though the more impactful the better :)
No speculation needed: Laplace would have discovered it, publishing in 1774, nine years after Bayes’ Essay appeared.
There’s no way it wouldn’t have been discovered. The mathematics is simple, and “inverse probability” (as it was called then) is a major part of what is done with probability and statistics.