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Cyan comments on Dissenting Views - Less Wrong
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A prior is a probability distribution assigned prior to conditioning on some specific data. If I learn data1 today and data2 tomorrow, my overnight probability distribution is a posterior relative to data1 and a prior relative to data2.
The reason I nitpick this is because the priors we actually talk about here on LW condition on massive amounts of evidence.
More nitpicking: the data doesn't really have to be "specified" - at least, it can be presented in the form of a black box with contents that are not yet known, or perhaps not yet even measured.