§ Overview

Unit 1.1 asks two questions before any computation begins: what kind of model are you building, and how will you build it responsibly? The first question is about classification — observational or explanatory, deterministic or stochastic, static or dynamic — and the answer determines what claims the model can support. The second is about process: the computational modelling lifecycle that every later module returns to.

Neither question is optional. A model that is never classified cannot be defended, and a model built without a defined process cannot be reproduced or audited. Both skills are assessed directly in Assignment 1.

§ Learning outcomes

§ Lessons

Work through the three lessons in order. Each lesson follows the standard MATH 4810 lesson structure: modelling context, mathematical formulation, a worked implementation, a verification check, and an independent modelling task.

§ Model taxonomy

The classification below is the one used throughout the course. The top-level split is between models that describe and models that explain. Static versus dynamic is an orthogonal axis: either branch can be static or dynamic, depending on whether time appears as a variable.

§ The computational modelling lifecycle

Lesson 3 develops the full cycle. It is repeated in every module of the course, and it is the structure you are expected to follow in Assignment 1 and the capstone.

1. Define the question and model purpose State what decision or understanding the model must support.
2. Establish the system boundary Decide what is inside the model and what is treated as external.
3. Define variables, parameters, units, and assumptions Make every quantity explicit and dimensionally consistent.
4. Select the modelling approach Deterministic or stochastic, static or dynamic, analytical or numerical.
5. Choose a numerical or simulation method Match the method to the structure, scale, and required accuracy.
6. Implement the model Build a transparent spreadsheet or code architecture.
7. Verify formulas, code, and model logic Confirm the implementation matches the intended specification.
8. Test numerical stability and convergence Vary step size, grid, and replication count deliberately.
9. Validate the model against evidence or known behaviour Compare with data, analytical solutions, or limiting cases.
10. Conduct uncertainty and sensitivity analysis Identify which inputs actually drive the outputs.
11. Compare scenarios Run designed experiments rather than one-off trials.
12. Interpret limitations State what the model cannot tell you.
13. Communicate findings Write for both technical and non-technical readers.
14. Archive reproducible model files Leave a trail another analyst could rerun.

§ Key terms

These definitions are used consistently throughout the course. If you use a term differently in your own writing, say so explicitly.

Observational model

A model that describes patterns in data without proposing a mechanism that generates them. Useful for prediction within the observed range; weak support for intervention.

Explanatory model

A model that proposes a mechanism connecting inputs to outputs. Can support counterfactual reasoning, but only to the extent that the mechanism is correct.

Deterministic model

A model in which identical inputs and parameters always produce identical outputs.

Stochastic model

A model containing random elements. Its output is a distribution, not a single number, and must be reported with an indication of sampling variability.

Static model

A model with no explicit time dependence — an equilibrium, a snapshot, or a steady-state relationship.

Dynamic model

A model in which the state evolves in time, typically expressed as a differential equation, a difference equation, or a state-transition rule.

System boundary

The line between what the model represents internally and what it treats as given from outside. Choosing the boundary is a modelling decision, not a technical one.

State variable

A quantity that describes the condition of the system at a point in time. The set of state variables defines the model's state space.

Parameter

A quantity held fixed within a single model run, estimated from data or assumed from domain knowledge. Parameters carry uncertainty, even when the model treats them as constants.

Exogenous vs. endogenous

Exogenous quantities are determined outside the model and supplied as inputs. Endogenous quantities are determined by the model itself.

Model purpose

The decision or understanding the model is meant to support. A model without a stated purpose cannot be validated, because there is no standard against which to judge it.

§ Self-check