**About this document**

This text corresponds to the slides of the Module 1 of the Simulation-based inference workshop held in 2021. Head on to the workshop page for the rest of the content.

🄯 Álvaro Tejero-Cantero for all the text, licensed under a CC-BY-SA license.

ℹ️ Practical parts are indicated in red background. Speaker's notes are under ▸ §.

**Module's****learning goals****Table of contents**

- making models is part of the scientific method
- models capture only some aspects of reality
- when formalized, they enable quantitative, testable hypotheses

- model functionalities
- prediction — to support decisions
- understanding — to select interventions

- the structure that doesn't change
*is*the model- the malleable part are parameters
- parameters are 'tuned' based on observations

- multiple
**input parameter set**s can lead to the same**output prediction***equifinality*,*degeneracy*are key to resilience, homeostasis of complex systems

$$\frac{{\rm d}^2 \theta}{{\rm d} t^2} + \frac{g}{\ell}\, \sin\theta = 0$$

- Can
*predict*angles $\theta(t)$ given $g/\ell$ and $\theta(0)$. - Can
*infer*$g/\ell$ from measured $\theta(t)$.- for small amplitudes $\sin\theta\simeq\theta$ and timing one oscillation $T=2\pi \sqrt{\ell/g}$ approximately suffices to infer $g/\ell$ → $T$
*summarises*$\theta(t)$ for inference.

- for small amplitudes $\sin\theta\simeq\theta$ and timing one oscillation $T=2\pi \sqrt{\ell/g}$ approximately suffices to infer $g/\ell$ → $T$
- And extract understading wrt. interventions and counterfactuals.
- §