This is totally backwards. I would phrase it, “Priors get out of the way once you have enough data.” That’s a good thing, that makes them useful, not useless. Its purpose is right there in the name—it’s your starting point. The evidence takes you on a journey, and you asymptotically approach your goal.
If priors were capable of skewing the conclusion after an unlimited amount of evidence, that would make them permanent, not simply a starting-point. That would be writing the bottom line first. That would be broken reasoning.
Yes, but that’s not the way the problem goes. You don’t fix your prior in response to the evidence in order to force the conclusion (if you’re doing it anything like right). So different people with different priors will have different amounts of evidence required: 1 bit of evidence for every bit of prior odds against, to bring it up to even odds, and then a few more to reach it as a (tentative, as always) conclusion.
This is totally backwards. I would phrase it, “Priors get out of the way once you have enough data.” That’s a good thing, that makes them useful, not useless. Its purpose is right there in the name—it’s your starting point. The evidence takes you on a journey, and you asymptotically approach your goal.
If priors were capable of skewing the conclusion after an unlimited amount of evidence, that would make them permanent, not simply a starting-point. That would be writing the bottom line first. That would be broken reasoning.
“A ladder you throw away once you have climbed up it”.
Where’s that from?
https://en.wikipedia.org/wiki/Wittgenstein%27s_ladder
But what exactly constitutes “enough data”? With any finite amount of data, couldn’t it be cancelled out if your prior probability is small enough?
Yes, but that’s not the way the problem goes. You don’t fix your prior in response to the evidence in order to force the conclusion (if you’re doing it anything like right). So different people with different priors will have different amounts of evidence required: 1 bit of evidence for every bit of prior odds against, to bring it up to even odds, and then a few more to reach it as a (tentative, as always) conclusion.