A Method for Fitting Empirical Surfaces To Physical or Chemical Data

The central problem of data analysis is the achievement of just the right balance between prior assumptions on the one hand and the findings based on observation of the data on the other hand. This paper is concerned with a special case of this problem. To analyze a set a data without any prior assumptions about an underlying model is impossible. To adopt too rigid a set of assumptions, on the other hand, results in forcing the data into a mold in which they may not fit at all well. There exist cases in which this problem is of secondary importance: those are the relatively rare instances in which a completely specified mathematical model is available prior to analysis. In contrast, the problem is most pertinent when all the information available to the data analyst is that contained in the data themselves. Between those extremes, which we may refer to respectively as the purely theoretical case and the purely empirical case, lie a multitude of situations in which prior information is available to some extent, subject however to confirmation by the experiment, which also serves to supply the missing parts of the assumed model.