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RE: Questions about identifiability

From: Pereira, Luis <Luis.Pereira>
Date: Thu, 19 Apr 2007 15:47:56 -0400

Dear Silke
Usually the parameter structural identifiability problem is dealt with
in terms of local identifiability (see Grewal MS, IEEE
Trans.Autom.Control, 21:833-837, 1976) and less often in terms of global
identifiability (by Laplace transformation, Taylor series expansion or
similarity transformation/reparametrization). Different issues pertain
to structural admissibility, reachability and observability. Keith
Godfrey has researched extensively on these topics (start maybe with
Godfrey KR and DiStefano JJ, 'Identifiability of model parameters' in
'Identifiability of parametric models', Walter E, Ed. 1987, Pergamon
IMHO, dealing with biological data, the identifiability problem becomes
essentially local and is always pragmatic in nature. Hat matrix entries,
information matrices and sensitivity to different initial estimates are
usually valuable, but no warranty for structural identifiability
(particularly global). Simulation exercises are always prone to what I
use to call the 'mirror syndrome' and you may just get what you put in,
ending up biased.
Realization theory based on Markov parameters provides usually good
insights for time-invariant finite-dimensional linear systems. My
preferred approach is Information theory based on the concept that each
observation has an intrinsic amount of information (Shannon Information)
which is the upper bound for every inference exercise. But again, with
routinely encountered problems we usually get away with small enough
confidence intervals for our adjustable parameters.
Luis M. Pereira, Ph.D.
Assistant Professor, Biopharmaceutics and Pharmacokinetics
Massachusetts College of Pharmacy and Health Sciences
179 Longwood Ave, Boston, MA 02115
Phone: (617) 732-2905
Fax: (617) 732-2228

Received on Thu Apr 19 2007 - 15:47:56 EDT

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