Event trees | Vose Software

# Event trees

Event trees offer a way to describe a sequence of probabilistic events, together with their probabilities and impacts. They are perhaps the most useful of all the methods for depicting a probabilistic sequence, because they are very intuitive and the mathematics to combine probabilities is simple.

Event trees are built out of nodes (boxes) and arcs (arrows). For example, a typical event tree from animal health risk modeling:

The tree starts from the left with a node (here Select Animal to denote the random selection of an animal from some population), and arrows to the right indicated possible outcomes (here whether the animal is infected with some particular disease agent, or not) and their probabilities (p, which would be the prevalence of infected animals in the population, and (1-p)).  Branching out from these boxes are arrows to the next probability event (the testing of an animal for the disease), and attached to these arrows are the conditional probabilities of the next level of event occurring. The conditional nature of the probabilities in an event tree are extremely important to underline. In this example:

Se = P(Test positive for disease given the animal is infected); and

Sp = P(Test negative for disease given the animal is not infected)

Thus, following the rules of conditional probability algebra, we can say, for example:

P(animal is infected and tests positive) = p*Se

P(animal is infected and tests negative) = p*(1-Se)

P(animal tests positive) = p*Se + (1-p)*(1-Sp)

Event trees also provide us with a very intuitive way of understanding Bayes Theorem.