Parameter nonidentifiable

For the identifiable parameters, we should obtain for solutions, = 0. For the nonidentifiable parameters there should not be such unique solutions. To check that, use row reduction to row echelon form, with pivoting on maximum elements. When completed, the equations should have the following form. 

The final step is to find the pairwise correlations for the identifiable parameters. Even if identifiable it may be difficult to estimate two parameters separately in the presence of measurement error if they are highly correlated. To check that, we reduce the matrix gj gs by eliminating rows and columns corresponding to the nonidentifiable parameters to obtain gi gi- Since gi gi is the matrix corresponding to the identifiable parameters, it is nonsingular so we can invert it to obtain (gi gi)The correlation matrix is obtained by dividing the i,j element of (g/gi) by the square root of the product of the /th and yth diagonal elements. 

A priori identifiability thus examines whether, given the ideal noise-free data y. Equation 9.13, and the error-free compartmental model structure. Equation 9.5 or Equation 9.6, it is possible to make unique estimates of aU the unknown model parameters. A model can be uniquely (globally) identifiable — that is all its parameters have one solution — or nonuniquely (locally) identifiable — that is, one or more of its parameters has more than one but a finite number of possible values — or nonidentifiable — that is, one or more of its parameters has an infinite number of solutions. For instance, the model of Figure 9.1 is uniquely identifiable, while that of Figure 9.3 is nonidentifiable. 

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