In

scientific research, there are two kinds of modeling:

statistical and

simulation. Both modeling efforts intend to uncover the mechanisms governing a particular natural system, be it

meteorological,

biological,

physical, etc.

Statistical modeling is the application of a statistical test to a series of data in the hopes of producing either the most predictive or most parsimonious relationship. Most statistical models rely either on regression techniques or their multivariate equivalents (see: redundancy analysis, canonical correspondance analysis, PCA). In more recent years, sophisticated numerical techniques, such as artifical neural networks, have also been used in place of the more traditional ones. The end result is the creation of one or more equations that explain some of the variability of one or more variables using the explanatory variables.(see dependant and independant variable, respectively). These equations are then later used to predict the behaviour of other systems or to generate new hypotheses.

Simulation modeling is done without a novel data set, but instead relies upon existing relationships (probably the result of statistical modeling) or educated guesses to create a simulation of the system of interest. Many simulation models are constructed with a computer, but pure mathematical modeling also falls into this category. In general, the researcher attempts to recreate known dynamics in a simplified version of the system of interest in the hopes that this will indicate which factors are most important in controlling the system.

In modern science, there is a give and take between the two modeling efforts. Scientists will examine a natural system, rely on statistical models to identify the strongest relationships within the system and subsequently will simulate a simplified version of the system in order to determine whether they have completely understood the system and to generate new hypotheses. An example (semi-hypothetical) of such an effort can be found in the management of cod stocks. Scientists have been following the dynamics of cod for years. They have also collected numerous data concerning the cod's habitat, prey, population densities etc. Statistical models lead them to the hypothesis that factors A, B and C are the most important for the maintenance of strong cod stocks. Simulation modeling is used to determine whether or not A, B and C together can produce the same kinds of dynamics observed in nature. The differences between the results of the simulation and the statistics lead to further hypotheses, study, and subsequently modeling.