Model building refers to the process of putting together symbols according to certain rules to form a structure which corresponds to a real-world system under study. A real-world system is too complex to be modelled in exact detail, so many factors are ignored and relevant factors are abstracted to make up an idealized version of the system. Another way to put it is that a model is an ordered set of assumptions about a complex system. It is an attempt to understand some aspect of the infinitely varied world by selecting from perceptions and past experiences a set of general observations, applicable to the problem at hand.
The construction of a model, as a scientific procedure, is founded on the belief that there can be order and reason in the mind, if not in the real world. The process of abstraction is usually an integrative one requiring experience, intuition, and judgement about the system being analysed, as well as skill in model construction. Modelling has the inherent capability of cutting across or integrating the inductive and deductive processes with the reality being confronted.
In the broadest sense, a model is simply a figurative or symbolic representation of something else. What is being modelled may be real or abstract, capable of precise definition or not, quantitative or qualitative. A mathematical model works with numerical data whereas a sociological model (e.g. in economics, politics, or psychology) may provide a theoretical projection in detail of a possible system of human relationships, only some variables of which are numeric.
In order to produce information, a symbolic model is usually a verbal or mathematical expression describing a set of relationships in a precise manner. It can be useful simply to explain or describe something, or it can be used to predict actions and events. Models can be distinguished and classified in many ways, including: by function, descriptive, predictive, and normative models; by time reference, static, and dynamic models; by uncertainty reference, deterministic, probabilistic, and game models; by generality, general, and specialized models.
Mathematical models provide the understanding that allows society to make sensible decisions over huge spatial and temporal scales. They also permit the inclusion of chance events—modelling frameworks for making decisions under uncertain circumstances.