1000 — Uncertainty quantification¶
This chapter introduces uncertainty quantification (UQ) through a concrete sustainability problem: calibrating a simplified climate model to historical observations.
In sustainable aviation studies, uncertainty is unavoidable:
- uncertain technology trajectories,
- uncertain policy and demand scenarios,
- uncertain non-CO₂ effects,
- uncertain model parameters and structural assumptions.
UQ is not an “add-on”; it is how we avoid false certainty and misleading point estimates.
Exercises in this chapter¶
1000.UQ.1 — Bayesian inference for a simple climate model¶
A full Bayesian calibration workflow:
- define a forward model (ODE-based climate model),
- identify uncertain parameters,
- specify their prior distributions,
- define a likelihood against historical observations,
- infer posterior distributions using MCMC (emcee),
- perform posterior predictive evaluations,
- explore sensitivity (time-dependent Sobol-style variance contributions).
Learning outcomes¶
After completing this chapter, you should be able to:
-
Explain the difference between:
- parameter uncertainty,
- data uncertainty,
- model discrepancy (structural uncertainty)
-
Build a Bayesian workflow: prior → likelihood → posterior
- Interpret MCMC results (convergence, autocorrelation, degeneracy)
- Produce posterior predictive checks and assess goodness-of-fit honestly
- Understand why uncertainty can matter more than mean predictions in decision contexts