A Panorama of Statistics

13 Models in statistics

‘Yes, the world is a complicated place.’ You have probably heard this in social conversation, and the speaker generally lets it go at that. But consider what it means for someone who is trying to understand how things actually work in this complicated world – how the brain detects patterns, how consumers respond to rises in credit card interest rates, how aeroplane wings deflect during supersonic flight, and so on. Understanding will not get very far without some initially simplified representation of whatever situation is being examined.

Such a simplified representation of reality is called a model. A neat definition of a model is ‘a concise abstraction of reality’. It is an abstraction in the sense that it does not include every detail of reality, but only those details that are centrally relevant to the matter under investigation. It is concise in the sense that it is relatively easy to comprehend and to work with.

A simple example of a model is a street map. It shows the layout and names of streets in a certain locality and represents, by a colour coding, the relative importance of the streets as traffic arteries. It is an abstraction of reality, in that it supplies the main information that a motorist needs, but little else. For example, it is two‐dimensional, and so does not show the steepness of hills, nor all the buildings that line the streets. The map is also concise in that it reduces the scale of reality to something much smaller (typically, ...