Stochastic simulation

Stochastic simulation generates possible trajectories of a random biological model rather than only one deterministic path.

CTMC event simulation

If the current state has total event rate \(a_0\), the waiting time to the next event is

\[\tau\sim\operatorname{Exp}(a_0).\]

An event type is then selected with probability proportional to its rate. Repeating these steps gives a Gillespie trajectory.

outcomes = []
for run in range(1000):
    outcome = simulate_model(rng)
    outcomes.append(outcome)

Many independent trajectories can estimate probabilities, expectations, variances and distributions of outcomes.

Key idea. One stochastic simulation is one possible history; repeated simulations reveal the distribution of possible biological outcomes.