University of Birmingham > Talks@bham > Artificial Intelligence and Natural Computation seminars > Structural Identifiability and Indistinguishability Analyses: Tools for Systems Modelling

Structural Identifiability and Indistinguishability Analyses: Tools for Systems Modelling

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If you have a question about this talk, please contact Hector Basevi.

Host: Dr Iain Styles

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Abstract: For many systems (certainly those in biology and medicine) the mathematical models that are generated invariably include state variables that cannot be directly measured and associated model parameters, many of which may be unknown and which also cannot be measured. For such systems there is also often limited access for inputs or perturbations. These limitations cause immense problems when investigating the existence of hidden pathways or attempting to estimate unknown parameters and this can severely hinder model validation. It is therefore highly desirable to have a formal approach to determine what additional inputs and/or measurements are necessary in order to reduce, or remove these limitations and permit the derivation of models that can be used for practical purposes with greater confidence.

Structural identifiability arises in the inverse problem of inferring from the known, or assumed, properties of a biomedical or biological system a suitable model structure and estimates for the corresponding rate constants and other parameters. Structural identifiability analysis considers the uniqueness of the unknown model parameters from the input-output structure corresponding to proposed experiments to collect data for parameter estimation (under an assumption of the availability of perfect, noise-free observations). This is an important, but often overlooked, theoretical prerequisite to experiment design, system identification and parameter estimation, since estimates for unidentifiable parameters are effectively meaningless. If parameter estimates are to be used to inform about intervention or inhibition strategies, or other critical decisions, then it is essential that the parameters be uniquely identifiable.

Numerous techniques for performing a structural identifiability analysis on linear parametric models exist and this is a well-understood topic. In comparison, there are relatively few techniques available for nonlinear systems (the Taylor series approach, similarity transformation based approaches, differential algebra techniques and the more recent observable normal form approach) and significant (symbolic) computational problems can arise, even for relatively simple models.

Structural indistinguishability for systems models is concerned with determining the uniqueness between possible candidates for the model (or mechanism) structure. The analysis is concerned with whether the underlying possibilities for the parameterised mathematical model can be distinguished using the inputs (perturbations or interventions) and observations (or measurements) available for the system under investigation.

For linear systems the analysis is generally exhaustive with all competing mechanisms generated from a given one , but for nonlinear systems the approach is generally only for pairs of candidate models, though in some cases a parameterised family of such candidates can be generated.

In this talk an introduction to structural identifiability and indistinguishability analyses will be provided demonstrating the application of the techniques available to both linear and nonlinear systems to examples of various degrees of complexity.

This talk is part of the Artificial Intelligence and Natural Computation seminars series.

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