Bayes Formel

(Ω,A,P)(\Omega, \mathcal{A}, P) W-Raum und A,BA,B Ereignisse aus A\mathcal{A} und P(A)>0P(A)>0 und P(B)>0P(B)>0.

P(A∣B)=P(B∣A)P(A)P(B)P(A|B)=\frac{P(B|A)P(A)}{P(B)}
  • Priors are simple to compute / find
    • "diagnosis example" causal relation
      • robust and good to assess
        • cavity pandemic, one is stable the other changes
    • causal vs diagnostic
      • P(symptom∣cause)P(\text{symptom}\mid \text{cause}) → causal
      • P(cause∣symptom)P(\text{cause}\mid \text{symptom}) → diagnostic
      • causal easy to assess
      • diagnostic ones are actually needed
      • is A caused by B or B caused by A
        • diagnostic, liking food doesnt make you a dog
        • causal, liking food may be caused by being a dog