Bayes TheoremIn Probability, if {Hk}\{H_k\}{Hk} partitions Ω\OmegaΩ then P(Hj∣E)=P(Hj∩E)P(E)=P(Hj)P(E∣Hj)∑kP(Hk)P(E∣Hk)P(H_j | E) = {P(H_j \cap E) \over P(E)} = {{P(H_j) P(E|H_j)} \over {\sum\limits_{k} P(H_k) P(E|H_k)}}P(Hj∣E)=P(E)P(Hj∩E)=k∑P(Hk)P(E∣Hk)P(Hj)P(E∣Hj) HjH_jHj is posterior in this case. The Odds form of Bayes Theorem is O(H∣E)=O(H)P(E∣H)P(E∣HC)O(H|E) = O(H) {P(E|H) \over P(E|H^C)}O(H∣E)=O(H)P(E∣HC)P(E∣H) If Hk{H_k}Hk partitions Ω\OmegaΩ then P(Hj∣E)=P(E∣Hk)P(Hk)∑jP(E∣Hj)P(Hj)P(H_j | E) = {{P(E|H_k) P(H_k)} \over {\sum\limits_{j} P(E|H_j) P(H_j)}}P(Hj∣E)=j∑P(E∣Hj)P(Hj)P(E∣Hk)P(Hk)Backlinks1230123Comments
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