2.1 Modeling and simulation
There is mounting evidence that the “model-building era”” that dominated the theoretical activities of the sciences for a long time is about to be succeeded or at least lastingly supplemented by the “simulation era”.6
Modeling is one of the most important topics you may ever learn. It is used in microbiology, macroeconomics, urban studies, sociology, psychology, public health, computer science, and of course, statistics. In fact, modeling is a method that is used in almost every discipline. Many think that it is an important skill to learn because it is so pervasive. While this is true, even more important is how closely the skills of modeling tie to the more general skills of problem solving. Starfield, Smith, and Bleloch (1994) summed this sentiment up nicely when they wrote, “learning to model is bound up with learning to solve problems and to think imaginatively and purposefully” (p. x).7
A model is a simplified representation of a system that can be used to promote an understanding of a more complex system. For example, meteorologists use computers to build models of the climate to understand and predict the weather. The computer model includes behaviors or properties which correspond, in some way, to the particular real-world system of climate. The computer models, however, do not include every possible detail about climate. All models leave things out and get some things—many things—wrong. This is because all models are simplifications of reality. Since all models are simplifications of reality there is always a trade-off as to what level of detail is included in the model. If too little detail is included in the model one runs the risk of missing relevant interactions and the resultant model does not promote understanding. If too much detail is included in the model, the model may become overly complicated and actually preclude the development of understanding.
Models have many purposes, but are primarily used to better understand phenomena in the real-world. Common uses of models are for description, exploration, prediction, and classification. For example, Google builds models to understand and predict peoples’ internet searching tendencies. These models are then used to help Google carry out more efficient and better searches of information. As another example, Netflix builds models to understand the characteristics of movies that their customers have rated highly so that they can then recommend other movies that the person may enjoy. Amazon and Apple iTunes both use models in similar manners.
2.1.1 Generating Data from Models
One core skill of a practicing statistician is to be able to generate random data from a model. Most of the models you will encounter in this course are referred to as probability models. That is just a fancy way of associating probabilities with different events, or outcomes, in a model.
For example, the model of flipping a “fair” coin is a probability model. There are two events/outcomes in the model: heads and tails. Each of these outcomes has a probability of 0.5 associated with it. (Note that although we could say 50%, that probabilities are on the scale from 0 to 1, so are defined using decimal values.)
- A model is a simplified representation of a system
- A probability model is a model where the different outcomes are associated with probabilities.