The H-method is concerned how we should solve mathematical modeling of data, when data are uncertain. The basic idea is to define 'atomic parts' by the H-principle that the model should be built upon, and judge the performance of these parts. Modeling stops when we cannot find atomic parts that improves the performance of the model.

When models are derived for predictions the uncertainties of the predictions are basically depending on two parts. The first part is the fit obtained and the second is the associated precision. In the formulae these terms appear in a symmetric way. Furthermore, at normal situations these aspects are mutually (stochastically) independent in the sense that results on fit does not give any information on the precision. Therefore, using the H-method these aspects are given equal weight.

The H-method is especially important when analysing industrial data. This is due to the relatively low rank that we typically find in industrial data. E.g., optical instruments like NIR data may give 1056 data values for each samples, thus producing 1056 variables, but the rank (obtained by the H-principle) may be 10 or less. Better and more reliable significance testing is obtained, when it is based on solution found by the H-principle.

This approach has obtained commercial success in several countries. In Denmark Foss-Electric has yearly sales of more than 200 mio euros of measurement instruments, where regression methods use NIR-based optical measurements to estimate chemical concentrations.

Methods based on the H-method will be the ones that future statistical methods will be based upon. The reason is the advance of computers. Computers are so fast that an extensive study of the prediction ability of the model as suggested by the H-principle can be carried out in a very short time. Inference in mathematical models is more reliable, when the solution has been derived by this approach than by traditional ones.