Bayes Formel

$(\Omega ,\mathcal{A},P)$ W-Raum und $A,B$ Ereignisse aus $\mathcal{A}$ und $P(A)>0$ und $P(B)>0$. $P(A|B)=\frac{P(B|A)P(A)}{P(B)}$

• 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
    • $P(\text{symptom}\mid \text{cause})$ → causal
    • $P(\text{cause}\mid \text{symptom})$ → 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