In this section, we will consider what is perhaps the most important practical point about models. How are models conceived and how do we know what is the right model to use in a given situation?
These are not simple questions, and the process of designing and choosing appropriate models is as much an art as a science. At the risk of oversimplifying, we could say that probabilistic models can come from two sources:
In priori models, the researcher considers the relevant factors, identifies important quantities and relationships, and creates a description that fits the problem being considered
In limit models, the researcher attempts to find an approximation to a model that is too complex, either conceptually or computationally
In both cases, the resulting model may take several different forms. It can be, for example, a mathematical formula, simulation, or algorithm. Always, the model must be validated against real data after the experiments or observations are carried...