Risk probabilities
Risk can be expressed as the probability that a biologically important event occurs within a specified time or under specified conditions.
If \(Y\) is an outcome and \(C\) a critical level, a useful quantity is
\[P(Y>C).\]Examples include the probability of an epidemic exceeding a given size, a population falling below a viability threshold or hospital demand exceeding capacity.
Estimating risk
For stochastic simulation, if \(m\) of \(M\) independent simulations exceed the threshold,
\[\hat p=\frac{m}{M}\]estimates the exceedance probability.
Key idea. Risk probabilities convert a distribution of possible outcomes into the probability of a decision-relevant event.