I mean, there is something of a free parameter which is how strong your prior is over ‘hypotheses’ vs how much of a likelihood ratio you get from observing ‘evidence’ if there’s a difference between hypotheses and evidence, and you can set your prior joint distribution over hypotheses and evidence however you want.
Maybe this is what you meant by “What you can have is some parameter controlling the prior itself (so that the prior can be less or more confident about certain things).”
Yes, I think we are talking about the same thing. If you change your distribution over hypotheses, or the distribution over evidence implied by each hypothesis, then it means you’re changing the prior.
I mean, there is something of a free parameter which is how strong your prior is over ‘hypotheses’ vs how much of a likelihood ratio you get from observing ‘evidence’ if there’s a difference between hypotheses and evidence, and you can set your prior joint distribution over hypotheses and evidence however you want.
Maybe this is what you meant by “What you can have is some parameter controlling the prior itself (so that the prior can be less or more confident about certain things).”
Yes, I think we are talking about the same thing. If you change your distribution over hypotheses, or the distribution over evidence implied by each hypothesis, then it means you’re changing the prior.