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.
cracki•6d ago
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.
lsaferite•6d ago