I’m not saying not to use Bayes’ theorem, I’m saying to consider very carefully what to plug into “E”. In the election example, your evidence is “A guy on a website said that there was a 999,999,999 in a billion chance that the incumbent would win.” You need to compute the probability of the incumbent winning given this actual evidence (the evidence that a guy on a website said something), not given the evidence that there really is a 999,999,999/billion chance. In the cosmic ray example, your evidence would be “There’s an argument that looks like it should make a less than 10^20 chance of apocalypse”, which may have different evidence value depending on how well your brain judges the way arguments look.
I think this amounts to saying: real-world considerations force an upper bound on abs(log(P(E | H) / P(E))). I’m on board with that, but can we think about how to compute and increase this bound?
I’m not saying not to use Bayes’ theorem, I’m saying to consider very carefully what to plug into “E”. In the election example, your evidence is “A guy on a website said that there was a 999,999,999 in a billion chance that the incumbent would win.” You need to compute the probability of the incumbent winning given this actual evidence (the evidence that a guy on a website said something), not given the evidence that there really is a 999,999,999/billion chance. In the cosmic ray example, your evidence would be “There’s an argument that looks like it should make a less than 10^20 chance of apocalypse”, which may have different evidence value depending on how well your brain judges the way arguments look.
EDIT: Or what nerzhin said.
I think this amounts to saying: real-world considerations force an upper bound on abs(log(P(E | H) / P(E))). I’m on board with that, but can we think about how to compute and increase this bound?
Yes.