[20分] 數學勁人請答!!!(關於bayes theorem)

First of all P(B) = P(B1)*P(B2)*P(B3) if events B1, B2 and B3 are "independent", this is important because it won't work this way otherwise.

Secondly, Bayes theorem should be stated P(A|B) = P(B| A) * P(A) / P(B) not P(B n A) * P(A) / P(B) so be careful.

Are any of these events independent? you may need to know this before getting any further.

2007-09-28 03:01:04 補充：
No, Bayes theorem does not assume the events are independent. Dose the question say the events B1, B2 and B3 independent then??

2007-09-29 01:36:10 補充：
Naive bayes classifier, the "naive" conditional independence assumptions assumes that each feature Fi is "conditionally independent" of every other feature Fi for i not equal to j, meaning P(Fi|C,Fj) = P(Fi|C)So it does not assume B1, B2 and B3 are independent

其實最大既問題係你假設左D事件係Independent.
兩件事independent 即係:
P(A&B) = P(A) * P(B)

由於無人話過佢地係Independent,
所以 P(B|A) 未必等於P(B1|A) * ...*P(B3|A), 而 P(B)亦未必等於P(B1)*..P(B3)

即係除非你知道B1, B2, B3之間有幾多係重覆(即係知道 B1 & B2 & B3之類既Prob), 否則你計唔到的

不妨用個Venn Diagram, 考慮兩個既case (即得B1&B2), 你會發現A, B1, B2, A&B1, A&B2既面積即使不變, A&B1&B2同B1&B2既面積比, 係可以變的.