  We advocate a numerically reliable and accurate approach for practical
parameter identifiability analysis: Applying column subset selection (CSS) to
the sensitivity matrix, instead of computing an eigenvalue decomposition of the
Fischer information matrix. Identifiability analysis via CSS has three
advantages: (i) It quantifies reliability of the subsets of parameters selected
as identifiable and unidentifiable. (ii) It establishes criteria for comparing
the accuracy of different algorithms. (iii) The implementations are numerically
more accurate and reliable than eigenvalue methods applied to the Fischer
matrix, yet without an increase in computational cost. The effectiveness of the
CSS methods is illustrated with extensive numerical experiments on sensitivity
matrices from six physical models, as well as on adversarial synthetic
matrices. Among the CSS methods, we recommend an implementation based on the
strong rank-revealing QR algorithm because of its rigorous accuracy guarantees
for both identifiable and non-identifiable parameters.
