Deterministic Analysis of Observations

Abstract

A usual modeling problem is given by the case that there are some relevant observations which may be obtained by measurements, and we would like to have a relatively simple mathematical function that provides a model for the observations. The purpose of finding such a function is to obtain a qualitative and quantitative understanding of observations, which is helpful for reacting to the observations in an appropriate way. The process of developing a mathematical model involves several basic steps. The first step is to present the problem as simple as possible, for example by transformations of data. The second step is to use modeling concepts to derive various reasonable models. The third step is to evaluate the models obtained in order to identify the optimal model. A model that is developed on the basis of observations represents the same information as given by the observations. However, a model should also provide an additional benefit. Thus, the fourth step is to demonstrate the advantage of the model development by deriving valuable conclusions that are not directly given by the observations.