[SEQ RERUN] Priors as Mathematical Objects
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.
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This post is part of the Rerunning the Sequences series, where we’ll be going through Eliezer Yudkowsky’s old posts in order so that people who are interested can (re-)read and discuss them. The previous post was Marginally Zero-Sum Efforts, and you can use the sequence_reruns tag or rss feed to follow the rest of the series.
Sequence reruns are a community-driven effort. You can participate by re-reading the sequence post, discussing it here, posting the next day’s sequence reruns post, or summarizing forthcoming articles on the wiki. Go here for more details, or to have meta discussions about the Rerunning the Sequences series.