Our (potentially rich or complex) state of knowledge and propensity to learn, before seeing the evidence, expressed as a probability function. This is a deeper and more general concept than 'Prior probability'. A prior probability is like guessing the chance that it will be cloudy outside, in advance of looking out a window. The more general notion of a Bayesian prior would include probability distributions that answered the question, "Suppose I saw the Sun rising on 999 successive days; would I afterwards think the probability of the Sun rising on the next day was more like 1000/1001, 1/2, or 1 - 10^-6?" In a sense, a baby can be said to have a 'prior' before it opens its eyes, and then to develop a model of the world by updating on the evidence it sees after that point. The baby's 'prior' expresses not just its current ignorance, but the different kinds of worlds the baby would end up believing in, depending on what sensory evidence they saw over the rest of their lives. Key subconcepts include ignorance priors and inductive priors, and key examples are Laplace's Rule of Succession and Solomonoff induction.
Comments
Alexei Andreev
Seems pretty odd for this to rely on Bayes Rule. Is that just a temporary thing?
Eliezer Yudkowsky
"Prior probability" doesn't rely on Bayes's Theorem, but the notion of a Bayesian prior does - it's a deeper concept and to understand it requires things like understanding the prior probability of sequences or prior probability functions. It's definitely not a concept you could acquire without Bayes's Theorem.
Alexei Andreev
So then should the title of the page be "Bayesian prior"?