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Parameter identifiability and input-output equations

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Document pages: 15 pages

Abstract: Structural parameter identifiability is a property of a differential modelwith parameters that allows for the parameters to be determined from the modelequations in the absence of noise. One of the standard approaches to assessingthis problem is via input-output equations and, in particular, characteristicsets of differential ideals. The precise relation between identifiability andinput-output identifiability is subtle. The goal of this note is to clarifythis relation. The main results are:1) identifiability implies input-output identifiability;2) these notions coincide if the model does not have rational firstintegrals;3) the field of input-output identifiable functions is generated by thecoefficients of a "minimal " characteristic set of the correspondingdifferential ideal.We expect that some of these facts may be known to the experts in the area,but we are not aware of any articles in which these facts are stated preciselyand rigorously proved.

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