Models And Simulation Outtakes
1. Three takes on "model"
1. representation: as in "scale model" or "diagram"
2. abstract (usually mathematical) description of a system
1. more

These are questions that will get revisited at least implicitly all semester, but it is useful to take a crack at them at the start. You will come to appreciate that there's not one simple, definitive answer.

For now, a model is an abstract representation of a thing or process that helps us understand how it works. A simulation is a model that "runs" — allowing us to see the thing or process in action. In this lecture we'll survey the range of definitions and try our hands at a few.

We are all, already, modelers and simulators. All science, all human activity, is based on models. We observe the world around us, abstract and infer a model of it, and act in a manner that is consistent with our model's predictions ("teachers like it when you ask questions, so ask whether modeling always has to be conscious or not"). We look at the status quo and conjure up processes that lay behind it ("he looks grumpy this morning; probably didn't get much sleep last night…") to either explain and describe or to predict and prescribe.

This course is an attempt to push this natural, everyday process in three directions: make it more systematic (vs. ad hoc, haphazard, etc.); use proven techniques (vs. improvisation and intuition); focus on problems in social and policy sciences. We start by defining "model," describing the range of models and purposes for which they can be used, and then talking about the mechanics of the course.

Definitions

For the purposes of this book, a model is a physical, mathematical, or verbal representation, often abstracted and simplified, of a real world phenomenon or process usually constructed with an aim to understanding how it works, came to be, or will behave in the future. Under "model" one will find dozens of Wikipedia entries (see below). Most relevant to our purposes

Example

What is an eclipse?

How does a thermostat work?

Why are some maps different from others?

How should we decide who the number one student is?

"Wikipedia cannot work in theory, it can only work in practice."

How often should an insurance company pay for its insureds to get mammograms? PSA tests?

The importance of systems

Models are what we use to understand how systems work and to try to predict how they will behave.

Models and Simulation

Sometimes we can use a model to come up with an analytical solution to a problem, that is, an expression which evaluates to particular outcome values for a given set of inputs. Other times the model will produce the behavior of a system but not in a way that can be reduced to an fixed expression. To make predictions about how the system will behave we "run" the model repeatedly for different values of its inputs and build up an empirical picture of the system's behavior. This use of models is called simulation.