p4wnc6 comments on Priors as Mathematical Objects - Less Wrong
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Eliezer may not approve of it, but almost all of the literature uses the phrase "updating a prior" to mean exactly the type of sequential learning from evidence that Eliezer discusses. I prefer to think of it as 'updating a prior'. Bayes' theorem tells you that data is an operator on the space of probability distributions, converting prior information into posterior information. I think it's helpful to think of that process as 'updating' so that my prior actually changes to something new before the next piece of information comes my way.