Note you can still get massive updates if B’ is pretty independent of B. So if someone brings in camera footage of the crime, that has no connection with the previous witness’s trustworthiness, and can throw the odds strongly in one direction or another (in equation, independence means that P(B’|H,B)/P(B’|¬H,B) = P(B’|H)/P(B’|¬H)).
Thanks, I think this is the crucial point for me. I was implicitly operating under the assumption that the evidence is uncorrelated which is of course not warranted in most cases.
So if we have already updated on a lot of evidence, it is often reasonable to expect that part of what future evidence can tell us is already included in these updates. I think I wouldn’t say that the likelihood ratio is independent of the prior anymore. In most cases, they have a common dependency on past evidence.
Yep, that seems to be right. One minor caveat; instead of
it is often reasonable to expect that part of what future evidence can tell us is already included in these updates.
I’d say something like:
“Past evidence affects how we interpret future evidence, sometimes weakening its impact.”
Thinking of the untrustworthy witness example, I wouldn’t say that “the witness’s testimony is already included in the fact that they are untrustworthy” (=”part of B’ already included in B”), but I would say “the fact they are untrustworthy affects how we interpret their testimony” (=”B affects how we interpret B’ ”).
Thanks, I think this is the crucial point for me. I was implicitly operating under the assumption that the evidence is uncorrelated which is of course not warranted in most cases.
So if we have already updated on a lot of evidence, it is often reasonable to expect that part of what future evidence can tell us is already included in these updates. I think I wouldn’t say that the likelihood ratio is independent of the prior anymore. In most cases, they have a common dependency on past evidence.
Yep, that seems to be right. One minor caveat; instead of
I’d say something like:
“Past evidence affects how we interpret future evidence, sometimes weakening its impact.”
Thinking of the untrustworthy witness example, I wouldn’t say that “the witness’s testimony is already included in the fact that they are untrustworthy” (=”part of B’ already included in B”), but I would say “the fact they are untrustworthy affects how we interpret their testimony” (=”B affects how we interpret B’ ”).
But that’s a minor caveat.