Bayesian data analysis: Difference between revisions

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Bayesian data analysis is based on [[:Wikipedia:Bayesian inference|Bayesian inference]].
Bayesian data analysis is based on [[:Wikipedia:Bayesian inference|Bayesian inference]].
<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 [[:Wikipedia:conditional probability|conditional probability]] of observing ''x'', given ''y''. Then, by definition
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>