I’m wondering what pjeby has realised, which turns this naive yet straightforward understanding into wrongthought worth commenting on.
Consider a hypothesis, H1. If a piece of evidence E1 is consistent with H, the naive interpretation is that E1 is an argument in favor of H1.
In truth, this isn’t an argument in favor of H1 -- it’s merely the absence of an argument against H1.
That, in a nutshell, is the difference between Bayesian reasoning and naive argumentation—also known as “confirmation bias”.
To really prove H1, you need to show that E1 wouldn’t happen under H2, H3, etc., and you need to look for disconfirmations D1, D2, etc. that would invalidate H1, to make sure they’re not there.
Before I really grokked Bayesianism, the above all made logical sense to me, but it didn’t seem as important as Eliezer claimed. It seemed like just another degree of rigor, rather than reasoning of a different quality.
Now that I “get it”, the other sort of evidence seems more-obviously inadequate—not just lower-quality evidence, but non-evidence.
ISTM that this is a good way to test at least one level of how well you grasp Bayes: does simple supporting evidence still feel like evidence to you? If so, you probably haven’t “gotten” it yet.
Consider a hypothesis, H1. If a piece of evidence E1 is consistent with H, the naive interpretation is that E1 is an argument in favor of H1.
In truth, this isn’t an argument in favor of H1 -- it’s merely the absence of an argument against H1.
That, in a nutshell, is the difference between Bayesian reasoning and naive argumentation—also known as “confirmation bias”.
To really prove H1, you need to show that E1 wouldn’t happen under H2, H3, etc., and you need to look for disconfirmations D1, D2, etc. that would invalidate H1, to make sure they’re not there.
Before I really grokked Bayesianism, the above all made logical sense to me, but it didn’t seem as important as Eliezer claimed. It seemed like just another degree of rigor, rather than reasoning of a different quality.
Now that I “get it”, the other sort of evidence seems more-obviously inadequate—not just lower-quality evidence, but non-evidence.
ISTM that this is a good way to test at least one level of how well you grasp Bayes: does simple supporting evidence still feel like evidence to you? If so, you probably haven’t “gotten” it yet.
That is from ‘You can’t prove the null by not rejecting it’.