Uncertainty & Sensitivity

John M. Drake

Key questions about uncertainty

  1. Which facators are most important to determining model behavior?
  2. How will the model outcome (trajectories, equilibria, etc.) change if the conditions (parameters, initial state) change?
  3. What range of outcomes are consistent with my knowledge of the observables? With my knowledge of the parameters?
  4. What processes do I need more information about and how much information do I need?
  5. If something changes (i.e. intervention), how will the model outputs change?

Discussion: What is the difference between uncertainty and sensitivity? When does it matter?

Different kinds of uncertainty/error

Models are idealizations and subject to approximation

  • Model mis-specification (structural epistemic uncertainty)
  • Inaccurate parameterization (parameter epistemic uncertainty)
  • The propagation of intrinsic noise/stochasticity (aleatory uncertainty)

\[ \begin{aligned} \frac{dX}{dt} &= - \beta XY \\ \frac{dY}{dt} &= \beta XY - \gamma Y \\ \frac{dZ}{dt} &= \gamma Y \end{aligned} \]

Discussion: Explain how these kinds of approximation are reflected in this model.

Note: The difference between epistemic and aleatory uncertainty is somewhat semantic

Simple models

In simple deterministic models with few state variables and few parameters we can often produce model visualizations to answer such questions