Correlation modelling of complex data – physics, statistics and heuristics

In this paper, we cover some principles and guidelines that are useful for modelling and interpreting data associated with highly complex physical phenomena such as occur in multidisciplinary fields. We compare and contrast the theoretical and statistical-empirical modelling paradigms and discuss how they interact and are complementary. Using an example taken from the field of fire engineering, we review how the approach can influence the efficiency and effectiveness of experimental or numerical investigations. We show how integrating dimensional analysis with experimental design techniques and regression modelling can reduce experimentation schedules and costs and improve insight. We further illustrate several useful strategies and caveats for modelling highly complex data. We describe some common limitations and misconceptions of data analysis along with features of graphical representation that can facilitate interpretation.