Stochastic System Dynamics — Probabilistic Stock-Flow Simulation

A deterministic sensitivity analysis varies one parameter at a time (or a small number) around a point estimate and observes how the output changes. SSD samples all uncertain parameters simultaneously from their joint distribution and propagates the full uncertainty through every time step of the simulation, producing a distribution of trajectories rather than a set of single-parameter perturbations. SSD therefore captures interaction effects between parameters and gives statistically valid confidence bands; sensitivity analysis gives directional insight into which parameters matter most.

For median and interquartile range stability, 500 replications are usually sufficient. For 95th-percentile tails, 2,000–5,000 runs are typically recommended. For rare-event probabilities near the 99th percentile, 10,000 or more runs may be needed. Latin hypercube sampling can reduce the required replications by two- to fivefold compared with simple Monte Carlo by ensuring better coverage of the input space.

Choose SSD when the system is appropriately described at an aggregate, continuous-flow level — populations, inventories, energy stocks — and individual heterogeneity is not the key research question. Agent-based modelling is preferred when individual-level differences, social networks, or spatially explicit interactions drive the phenomena of interest. For homogeneous populations at moderate to large sizes, SSD is computationally cheaper and produces equivalent probabilistic output.

Yes, but indirectly. Policy parameters (e.g., vaccination rates, inventory reorder points) can be varied systematically across replications to identify settings that minimise expected cost or maximise robustness across the distribution of outcomes. For formal optimisation, Stochastic System Dynamics is often combined with simulation-optimisation algorithms such as stochastic search or response-surface methods.

Validation proceeds on two levels: structural tests confirm that the stock-and-flow equations and feedback loops are mechanistically correct under extreme conditions; behaviour tests confirm that the distribution of simulated trajectories is statistically consistent with observed historical data — check that observed values fall within the simulated confidence bands at an appropriate frequency. Parameter distributions should also be independently justified from empirical data or published literature rather than calibrated purely to match output.