Assessment of the adequacy of mathematical models

Models are mathematical representations of mechanisms that govern natural phenomena that are not fully recognized, controlled, or understood. They have become indispensable tools via decision support systems for policy makers and researchers to provide ways to express the scientific knowledge. Model usefulness has to be assessed through its sustainability for a particular purpose. Adequate statistical analysis is an indispensable step during development, evaluation, and revision phases of a model. Therefore, in this paper we discussed and compared several techniques to evaluate mathematical models designed for predictive purposes. The identification and acceptance of wrongness of a model is an important step towards the development of more reliable and accurate models. The assessment of the adequacy of models is only possible through the combination of several statistical analyses and proper investigation regarding the purposes for which the mathematical model was initially conceptualized and developed for. The use of only a few techniques may be misleading in selecting the appropriate model in a given scenario.