Journal Article

What are conditional probabilities conditional upon?

K Hutchison

in The British Journal for the Philosophy of Science

Published on behalf of British Society for the Philosophy of Science

Volume 50, issue 4, pages 665-695
Published in print December 1999 | ISSN: 0007-0882
Published online December 1999 | e-ISSN: 1464-3537 | DOI: http://dx.doi.org/10.1093/bjps/50.4.665
What are conditional probabilities conditional upon?

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This paper rejects a traditional epistemic interpretation of conditional probability. Suppose some chance process produces outcomes X, Y,..., with probabilities P(X), P(Y),... If later observation reveals that outcome Y has in fact been achieved, then the probability of outcome X cannot normally be revised to P(X|Y) [≡'P&Y)/P(Y)]. This can only be done in exceptional circumstances - when more than just knowledge of Y-ness has been attained.

The primary reason for this is that the weight of a piece of evidence varies with the means by which it is provided, so knowledge of Y-ness does not have uniform impact on the probability of X. A better updating of the probability of X is provided by P(X|Y*), where Y* is not an outcome of the chance process being observed, but the sentence 'the outcome Y has been observed', an 'outcome' of the subsequent observation process.

This alternative formula is widely endorsed in practice, but not well recognized in theory, where the oversight has generated some unsatisfactory consequences.

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Subjects: Philosophy of Science ; Science and Mathematics

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