> Priors is just an explicit encoding of some of that knowledge.
A classic example is analyzing data on mind reading or ghost detection. Your experiment shows you that your ghost detector has detected a haunting with p < .001. What is the probability the house is haunted?
Well, something could count as evidence that ghosts or ESP exist, but the evidence better be really strong.
A person getting 50.1% accuracy on an ESP experiment with a p-value less than some threshold doesn't cut it. But that doesn't mean the prior is insurmountable.
The closing down of loopholes in Bell inequality tests is a good example of a pretty aggressive prior being overridden by increasingly compelling evidence.
The fact that you are designing an experiment and not trusting it is bonkers. The experiment concludes that the house is haunted and you've already agreed that it would be so before the experiment.
A classic example is analyzing data on mind reading or ghost detection. Your experiment shows you that your ghost detector has detected a haunting with p < .001. What is the probability the house is haunted?