mathematical model
Let an agent explain mathematical models by type and purpose, help build, fit and validate models, and communicate assumptions and uncertainty honestly.
Research draft, second pass
A second pass drafted this model: the structure a model of this thing needs, and what is known about it in the world. The line under this one says how the second half was obtained - researched against sources, or recalled without web access, in which case nothing here was read anywhere and every claim is a lead to verify. Unreviewed either way.
written by Claude from model knowledge without web access - no source was read, every claim is a lead to verify
Researched by: Claude
Purpose and description
Let an agent explain mathematical models by type and purpose, help build, fit and validate models, and communicate assumptions and uncertainty honestly.
A description of a system using mathematical concepts, equations, functions and relations, such as linear systems, the Ising model, energy system models and epidemic models, used to explain behaviour, make predictions and support decisions, and validated against data within stated assumptions and limits.
What it is for: Understanding, predicting and designing systems.
It can be choose a model type for a problem; fit and validate a model; explain assumptions and limits; communicate model results with uncertainty.
Distinguishing features
Mathematical formulation
Assumptions and parameters
Validated against data
Deterministic or stochastic
What it looks like
Not physical; equations, code and diagrams.
How it is recognised
Equations and parameters
Fitted curves and simulations
Statistical models emphasise data and error
Related models
is a kind of - category
uses - foundation
is related to - formal results
is applied in - application
In practice
Families and kinds
linear and nonlinear models
differential equation models
statistical and machine learning models
agent-based and simulation models
physics models such as the Ising model
Standards and regulation
Model validation guidance in regulated fields such as finance and pharmacology
Reproducibility norms
Failure modes and hazards
Overfitting and extrapolation
Hidden assumptions
Overconfident predictions
Also called
+214
Where this came from
wikidata · CC0 1.0
Drafted structure
Bundle to layer to finding to question, as the second pass will find it: 4 bundles · 8 layers · 8 findings · 16 questions.
Choose Selecting a model.
Purpose drives choice.
Purpose
What the model is for.
Purpose
Purpose.
- What question should the model answer, and what data exist? definition
- Is explanation or prediction the goal? boundary
Type
Model family.
Type
Model family.
- Which model family fits the system, such as linear, differential or stochastic? definition
- What are the trade-offs? boundary
Build Fitting and validation.
Validation is essential.
Fit
Estimating parameters.
Fit
Fitting.
- How are parameters estimated from data? action
- How is goodness of fit assessed? measurement
Validate
Testing.
Validate
Validation.
- Does the model predict held-out data? measurement
- How sensitive are results to assumptions? measurement
Communicate Results and limits.
Honesty about uncertainty.
Assumptions
Stating limits.
Assumptions
Assumptions.
- What assumptions and simplifications does the model make? definition
- Where does it stop applying? boundary
Uncertainty
Confidence.
Uncertainty
Uncertainty.
- How uncertain are the predictions? measurement
- How should results be presented to decision makers? action
Examples Classic models.
Examples teach.
Classic
Famous models.
Classic
Famous models.
- What does the Ising model or another classic model describe? definition
- What did it reveal? provenance
Learn
Learning modelling.
Learn
Learning.
- Which resources teach mathematical modelling? action
- Which software is used? provenance
What the second pass must settle
- Should model families be separate entries?
- How should software tools be linked?
- How should validation be recorded?