Today's post, Priors as Mathematical Objects, was originally published on 12 April 2007. A summary (taken from the LW wiki):

As a mathematical object, a Bayesian "prior" is a probability distribution over sequences of observations. That is, the prior assigns a probability to every possible sequence of observations. In principle, you could then use the prior to compute the probability of any event by summing the probabilities of all observation-sequences in which that event occurs. Formally, the prior is just a giant look-up table. However, an actual Bayesian reasoner wouldn't literally implement a giant look-up table. Nonetheless, the formal definition of a prior is sometimes convenient. For example, if you are uncertain about which distribution to use, you can just use a weighted sum of distributions, which directly gives another distribution.

Discuss the post here (rather than in the comments to the original post).

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