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text: '"Prior [1rf probability]", "prior [1rb odds]", or just "prior" refers to a state of belief that obtained before seeing a piece of new evidence. Suppose there are two suspects in a murder, Colonel Mustard and Miss Scarlet. After determining that the victim was poisoned, you think Mustard and Scarlet are respectively 25% and 75% likely to have committed the murder. *Before* determining that the victim was poisoned, perhaps, you thought Mustard and Scarlet were equally likely to have committed the murder (50% and 50%). In this case, your "prior probability" of Miss Scarlet committing the murder was 50%, and your "posterior probability" after seeing the evidence was 75%.\n\nThe prior probability of a hypothesis $H$ is often being written with the unconditioned notation $\\mathbb P(H)$, while the posterior after seeing the evidence $e$ is often being denoted by the [1rj conditional probability] $\\mathbb P(H\\mid e).$%%note: [E. T. Jaynes](http://bayes.wustl.edu/) was known to insist on using the explicit notation $\\mathbb P (H\\mid I_0)$ to denote the prior probability of $H$, with $I_0$ denoting the prior, and never trying to write any entirely unconditional probability $\\mathbb P(X)$. Since, said Jaynes, we always have *some* prior information.%% %%knows-requisite([1r6]): This however is a heuristic rather than a law, and might be false inside some complicated problems. If we've already seen $e_0$ and are now updating on $e_1$, then in this new problem the new prior will be $\\mathbb P(H\\mid e_0)$ and the new posterior will be $\\mathbb P(H\\mid e_1 \\wedge e_0).$ %%\n\nFor questions about how priors are "ultimately" determined, see [11w].',
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Summary: '"Prior [1rf probability]", "prior [1rb odds]", or just "prior" refers to a state of belief that obtained before seeing a piece of new evidence. Suppose there are two suspects in a murder, Colonel Mustard and Miss Scarlet. After determining that the victim was poisoned, you think Mustard and Scarlet are respectively 25% and 75% likely to have committed the murder. *Before* determining that the victim was poisoned, perhaps, you thought Mustard and Scarlet were equally likely to have committed the murder (50% and 50%). In this case, your "prior probability" of Miss Scarlet committing the murder was 50%, and your "posterior probability" after seeing the evidence was 75%.'
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