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Bayesian data analysis: Difference between revisions
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<ref>D.S. Sivia, ''Data Analysis: A Bayesian Tutorial'', Oxford University Press, USA (1996) ISBN 0198518897</ref> | <ref>D.S. Sivia, ''Data Analysis: A Bayesian Tutorial'', Oxford University Press, USA (1996) ISBN 0198518897</ref> | ||
<ref>P. Gregory, ''Bayesian Logical Data Analysis for the Physical Sciences'', Cambridge University Press, Cambridge (2005) ISBN 052184150X</ref> | <ref>P. Gregory, ''Bayesian Logical Data Analysis for the Physical Sciences'', Cambridge University Press, Cambridge (2005) ISBN 052184150X</ref> | ||
Briefly, this approach is based on the following straightforward property of probability distributions. Let ''p(x,y)'' be the joint probability of observing ''x'' and ''y'' simultaneously. Let ''p(x|y)'' be the | Briefly, this approach is based on the following straightforward property of probability distributions. Let ''p(x,y)'' be the joint probability of observing ''x'' and ''y'' simultaneously. Let ''p(x|y)'' be the [[:Wikipedia:conditional probability|conditional probability]] of observing ''x'', given ''y''. Then, by definition | ||
:<math>p(x|y)p(y) = p(x,y) = p(y|x)p(x)\,</math> | :<math>p(x|y)p(y) = p(x,y) = p(y|x)p(x)\,</math> | ||
from which follows ''Bayes' theorem'': | from which follows ''Bayes' theorem'': | ||