Good if make prior after data instead of before(lesswrong.com)
lesswrong.com
Good if make prior after data instead of before
https://www.lesswrong.com/posts/JAA2cLFH7rLGNCeCo/good-if-make-prior-after-data-instead-of-before
9 comments
This article reveals a fundamental misunderstanding of Bayesian statistics by the author, when they say "for the sake of simplicity, let's call it a wash and assume the odds are the same". Because the odds ratio is key in statistics.
You cannot just go "this chance is very small and so is this chance therefore we can assume them to be similar". That's just wrong. The chance that the data we see happens if there are aliens is a lot smaller than the chance of the data given that are none. Yes, both are very small but that does not mean the odds ratio can be assumed to be 1. As the author illustrates, this incorrect reasoning breaks the usefulness of Bayesian statistics.
As for an example let's say that you claim to be using magic to win the lottery, which I don't believe. Now, the lottery happens and the winning number is 4529640, which is not yours. The probability of that number winning is small regardless of these initial hypotheses. If we follow the reasoning in the article we may say that that means because both chances are small this gives us no information on these hypotheses, which is clearly wrong.
You cannot just go "this chance is very small and so is this chance therefore we can assume them to be similar". That's just wrong. The chance that the data we see happens if there are aliens is a lot smaller than the chance of the data given that are none. Yes, both are very small but that does not mean the odds ratio can be assumed to be 1. As the author illustrates, this incorrect reasoning breaks the usefulness of Bayesian statistics.
As for an example let's say that you claim to be using magic to win the lottery, which I don't believe. Now, the lottery happens and the winning number is 4529640, which is not yours. The probability of that number winning is small regardless of these initial hypotheses. If we follow the reasoning in the article we may say that that means because both chances are small this gives us no information on these hypotheses, which is clearly wrong.
I know that this is a great discussion on Bayesian reasoning, but, honestly, I'm probably just going to use it to rebuff my friends who occasionally bring up aliens.
"Prior" is an adjective.
In math it's a well-known shorthand for "prior distribution", a noun. https://en.wikipedia.org/wiki/Prior_probability
Terrible title but good article.
The title certainly made me wonder if I was having a stroke. I am now sure I didn't.
Feel free to turn my statements into a bunch of probabilities.