Inverse Problems and Parameter Estimation

A comparison of designs obtained by statistical and deterministic methods is being carried out. Points that are difficult to address in the statistical approaches are considered. A formulation of a regularized solution to experimental design is described in detail. The peculiarities of the optimal design for three types of regressions are revealed. The main factors that govern the estimation errors are determined. It is proved that the non-zero noise generates a particular case of non-identifiable observations, and in starting with a specific threshold noise, the design problem offers no solution.The case study demonstrates that the statistical paradigm cannot determine the optimal design features revealed by the deterministic approach. The investigates depicts the effectiveness of the alternative viewpoint toward traditional solutions to design problems.