bayes_theorem
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| bayes_theorem [2025/09/21 18:55] – hkimscil | bayes_theorem [2025/09/21 22:35] (current) – hkimscil | ||
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| \text{heance } | \text{heance } | ||
| P(A \cap B) & = & P(A \mid B) * P(B) \;\; \text{ and | P(A \cap B) & = & P(A \mid B) * P(B) \;\; \text{ and | ||
| - | P(B \cap A) & = & P(B \mid A) * P(A) \qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad (1) \\ | + | P(B \cap A) & = & P(B \mid A) * P(A) \qquad\qquad\qquad\qquad\qquad\qquad\qquad (1) \\ |
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| P(B) & = & P(A \cap B) + P(\neg A \cap B) \nonumber \\ | P(B) & = & P(A \cap B) + P(\neg A \cap B) \nonumber \\ | ||
| & = & P(B \cap A) + P(B \cap \neg A) \nonumber \\ | & = & P(B \cap A) + P(B \cap \neg A) \nonumber \\ | ||
| - | & = & P(B \mid A) * P(A) + P(B \mid \neg A) * P(\neg A) \qquad\qquad\qquad\qquad\qquad (2) \\ | + | & = & P(B \mid A) * P(A) + P(B \mid \neg A) * P(\neg A) \qquad\qquad (2) \\ |
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| & = & \dfrac{P(B \cap A)}{P(B)} \;\;\; \text{ from (1) and (2) } \nonumber | & = & \dfrac{P(B \cap A)}{P(B)} \;\;\; \text{ from (1) and (2) } \nonumber | ||
| & = & \dfrac {(1)} {(2)} \nonumber \\ | & = & \dfrac {(1)} {(2)} \nonumber \\ | ||
| - | & = & \dfrac {P(B \mid A) * P(A)} {P(B \mid A) * P(A) + P(B \mid \neg A) * P(\neg A)} \qquad\qquad\qquad\qquad\qquad (3) \\ | + | & = & \dfrac {P(B \mid A) * P(A)} {P(B \mid A) * P(A) + P(B \mid \neg A) * P(\neg A)} \qquad\qquad (3) \\ |
bayes_theorem.1758448501.txt.gz · Last modified: by hkimscil