Project partners


  1. TrainBayes (DFG)
  2. siMINT (BMBF)
  3. FEHLBa (DFG)



  1. Material from the project TrainBayes (DFG)

Simulation with a probability tree diagram

Here, you can see a probability tree diagram which represents a Bayesian situation in which people are tested with a medical diagnostic test. In the beginning it is assumed:
  • 8% of all people are ill.
  • 90% of the ill people are identified with the medical diagnostic test and hence test positive.
  • 15% of the healthy people are tested positive by mistake.

An interesting question in such a situation is: How likely is a person actually ill, if this person tests positive?
This probability is equivalent to the proportion of ill (and positively tested) people among all positively tested people. This proportion is represented in the fraction on the right-hand side and the paths, which are necessary for the calculation are highlighted in the probability tree diagram.

The given information in the Bayesian situation can vary. Hence, the question arises, how variations of the three given pieces of information affect the probability that a person is actually ill, if this person tests positive.

With this simulation you can visualize and analyse the effects of such variations in the probability tree diagram and the fraction, which represents the probability of interest.
Notation: • ill "I" vs. healthy "I" • test positive "+" vs. negative "−" health condition Test I I + + P(I) = P(I) = PI(+) = PI(−) = PI(+) = PI(−) = P(I ∩ +) = P(I ∩ −) = P(I ∩ +) = P(I ∩ −) =
P+(I) = + P(I ∩ +) P(I ∩ +) P(I ∩ +) = + =