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SISTA

Abstract:

Some insight is provided in the analysis of the basic modeling problem in the simplest case, i. e. , the identification of linear relations from noisy data. The central idea is the nonuniqueness principle, which states that the solution of a noisy identification problem is intrinsically nonunique. Any uncertainty in the data implies that no particular model can be identified with certainty. In a situation of uncertainty (noise), it is unnatural to have mathematical formulations that lead to unique results. It is demonstrated how classical treatments of the problem have led to a unique solution because additional unverifiable a priori assumptions were imposed that forced uniqueness.