Populations, crime statistics, and budgets often have ample historical data for forecasting. The mathematical models used in forecasting may take into account the forces that influence trends to adjust the predictions. This includes a wide variety of techniques to represent a process or problem in some way that leads to predicting behavior or finding solutions. Quantitative models represent the problem in some mathematical form that allows calculating interactions or outputs. Qualitative models require clear identification of concepts, relationships, and interactions.
Quantitative models require all that plus measurements of some kind as the basis for calculations.
Models that take into account the feedback of effects from one part of a system to another are called system dynamics models. While usually quite complicated, these models provide a way to explore the dynamic interactions that are not represented in other techniques. Simplified reality for testing. These kinds of models provide a simplified version of reality against which to test ideas and explore consequences. They are most useful in the kind of complex situations characteristic of justice systems and their information flows.