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class_09_14 - Statistical Data Mining ORIE 474 Fall 2007...

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Statistical Data Mining ORIE 474 Fall 2007 Tatiyana Apanasovich 09/14/07 Bayesian vs Frequentist

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Bayes’ theorem From the definition of conditional probability we have and but , so Bayes’ theorem First published (posthumously) by the Reverend Thomas Bayes (1702−1761) An essay towards solving a problem in the doctrine of chances , Philos. Trans. R. Soc. 53 (1763) 370; reprinted in Biometrika, 45 (1958) 293.
Conditional probability & trees. Example 5.3: How many girls? Family, 2 children D: Both are girls C: At least 1 girl P ( D | C ) = P ( C I D ) P ( C ) = P ( G1 I G2 ) P ( C ) = 1 / 4 3 / 4 = 1 3 G1 B1 2          1/4 G2 B2 G2 B2 1          1/4 1          1/4 0          1/4 3/4 First  child Second    child Number  of girls Prob.

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In contrast, condition on G2: How many girls? Family, 2 children D: Both are girls G2: Second is a girl G1 B1 2          1/4 G2 B2 G2 B2 1          1/4 1          1/4 0          1/4 1/2 First  child Second    child Number  of girls Prob.
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