I’ve been tempted to do this sometime, but I fear the prior is performing one very important role you are not making explicit: defining the universe of possible hypothesis you consider.
In turn, defining that universe of probabilities defines how bayesian updates look like. Here is a problem that arises when you ignore this: https://www.lesswrong.com/posts/R28ppqby8zftndDAM/a-bayesian-aggregation-paradox
I’ve been tempted to do this sometime, but I fear the prior is performing one very important role you are not making explicit: defining the universe of possible hypothesis you consider.
In turn, defining that universe of probabilities defines how bayesian updates look like. Here is a problem that arises when you ignore this: https://www.lesswrong.com/posts/R28ppqby8zftndDAM/a-bayesian-aggregation-paradox