Herleitung des Bayes-Theorems

Also leiten wir “The Key to the Universe” mal her:

Für ne vollständige Erklärung geht lieber auf Lesswrong.com oder yudkowsky.net.

Das ist rein mathematisch.

Gesucht: P(H/E)

Gegeben: P(H); P(E/H), P(E/non-H)

P(H&E) = P(H/E)*P(E)=P(E/H)*P(H)

-> P(H/E)=P(H&E) / P(E)

->P(H/E)= P(E/H)*P(H) / P(E)

P(E) = P(H&E) + P(Non-H&E)

-> P(H/E) = P(E/H)*P(H) / (P(H&E) + P(Non-H&E) )

-> P(H/E) = P(E/H)*P(H) / ( P(E/H)*P(H)  + P(E/non-H)*P(non-H) )

Tada!

 

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