Models
A model is a mathematical representation of the world. Models are most often used to make predictions about the world. These predictions can guide our decisions and make better outcomes more probable.
We will learn how to create simple models that enable us to gain insight into the problem we are investigating.
Review
How are models distinct from estimations and relationships?
- Estimations are an educated guess about the state of reality.
- Relationships are a feature of a natural system that we can observe.
Models are artificially constructed using estimations and relationships to gain insight and to improve decision making.
Estimations and Models
The estimations we created in the previous section were based on simple models.
To predict the catering order precisely, we’d need to know the schedules, appetite, and dietary preferences of every Sonoma State community member, an impractical problem.
Our models contained vast simplifications, but are still likely to provide decent predictions.
There is a statistical saying, “All models are wrong, some are useful.” that captures this idea.
Models
Here are a few ideas about models:
- A model is a simplified representation of a problem we’d like to solve
- A model is an approximation that allows us to think about the world
- Models:
- rectangle for the area of a plot of land
- linear functions
- exponential function for population growth
- a roll of a die or several dice for random events
- a bathtub with a faucet and a drain for atmospheric carbon
- a set of equations to predict motor behavior
Usefulness
These models can give us a way to conduct thought experiments and understand how a system might respond.
Types of models
- Top-down or empirical models
- Use collected data to infer a relationship between two quantities
- Bottom-up or mechanistic models
- Use a detailed model of underlying behavior to deduce a relationship between two quantities
Downsides of Models
Some models can be used to harm people or communities. These harms are often unintentional, but still significant.
- Opacity
- Scale
- Damage
Examples of Models
- General Circulation Model
- Predator–Prey Model
- Odom Silver Springs Model for Ecosystem Energy Flow
- Camera Trap Population Models
- Toxin Exposure–Risk Models
- Occupancy Sensor Models
- Climate Change Temperature Models
- Climate Change Economic Models
Journal Article
Pick a topic of interest for you and search the scientific literature for models related to your topic. Read the abstract and paper to find a description of a model. Post a brief description of your topic and model in the cloud worksheet and include a link to the paper.