Descriptive Modeling

Modeling is the construction of a less-complex representation of something that exists in the real world. A good model describes something from the real world while leaving out most of the real world information. In that way, a map of the United States is a model of some of the geographic and political features of that country. Models don’t have to be visual. When an actor’s motion is captured for use in a CGI (computer graphic imagery) film sequence, the system uses a ">mathematical model that represents the real motion of the actor, but is actually much less complex.

Overview

Simplified models of real-world events are used to perform many common tasks, even though the mathematics behind them can be very complex. Descriptive models are used to forecast the weather , predict the outcomes of elections, determine if a car is safe to drive or a road is safe to drive on, and calculate the odds on sporting or gaming competitions.

In each of these cases, a model is created by selecting some of the features of a complex system. One of the challenges of building a good model is finding a selection of features that is as small as possible and yet still representative of the real-world event being described. This problem is generally solved by following an iterative process, that is, by trying over and over again, while learning from each attempt.

To begin the process of building a descriptive model, describe any features or patterns of features based on observation. This is our first descriptive model. This model is then used in an attempt to predict possible outcomes. The differences between what was predicted and what happened to to make a more accurate descriptive model. That model is then tested again, and so on.

Eventually either a descriptive model will be developed that can be used to predict events in the real world, or the modeling attempt will be abandoned and the event described as "unpredictable." This iterative cycle is how babies learn to recognize familiar sights and sounds and flavors, and it is also how people learn to walk and coordinate their movements, use and understand speech, write, and use mathematics.

Bibliography

Banerjee, Sandip. Mathematical Modeling: Models, Analysis, and Applications. London: Chapman, 2014.

DiStefano, Joseph, III. Dynamic Systems Biology Modeling and Simulation. Waltham, MA: Academic P, 2013.

Giordano, Frank R, William P. Fox, and Steven B. Horton. A First Course in Mathematical Modeling. 5th ed. Boston: Cengage, 2013.

Meerschaert, Mark. Mathematical Modeling. 4th ed. Waltham, MA: Academic P, 2013.