A Critical Appraisal of Analytical Methods

Abstract

The urge to construct models¹ of the world we live in has been with us since prehistoric days. It has been the driving force in the evolution of a wide range of disciplines: mathematics, physics, engineering, biology, economics, and more recently the social and environmental sciences. The main goals of model building are the interpretation and understanding of the fundamental structure of a complex system, and the prediction of future events that may occur in the system or further properties of the system. The model is derived from the original system by a process of simplification, idealization, and approximation. The purpose of the model is to test some hypotheses on the functional relationships between the quantifiable attributes of the system. The use of simplification and approximation in setting-up the model leaves open the question of the value of the model as a functional description of the process. Thus model validation is an essential step in the modelling procedure. Model validation is a closed loop process of hypothesis and testing. Models can only be rejected — their acceptance is only based on their lack of rejection at a given level of confidence as depicted in the flow diagram of Figure 1. There are material models, analogue models and symbolic models.

‘If you ask the wrong question of a scientific problem and you ask it correctly — you will obtain the correct answer to a wrong question. If in addition you use proper statistical analysis — you will obtain a statistically valid, correct answer to a wrong question.’

B.K. Selinger, Nyholm Memorial Lecture, Sydney, 1978