This chapter has reviewed the fundamentals of probabilistic modeling, with emphasis on modeling physical situations in an urban setting. In practice there is no magic procedure for developing such models. In fact, it is the reduction of a situation to a sample space with its probability assignment and random variables that is usually the most difficult step. The formal manipulation that follows from that point is (relatively) straightforward but still quite interesting. By having described physical situations in terms of word statements, we hope to have given the reader some feeling for the problem definition process. However, our problems in this book are preselected to illustrate concepts relevant to that portion of the text. They are also usually selected to yield a tractable analysis. No such guarantee is available in an actual city, and one is hard-pressed to find problems tightly worded with no ambiguity. But these complexities contribute to the challenge of urban analysis, which in many ways is as much an art form as a formalism.

Armed with the prerequisite background of Chapters 1 and 2, we now proceed to methods, procedures, and points of view in modeling analysis that are especially important in an urban setting.