Identifiability and numerical algebraic geometry

Dataset

Description

A common problem when analyzing models, such as a mathematical modeling of a biological process, is to determine if the unknown parameters of the model can be determined from given input-output data. Identifiable models are models such that the unknown parameters can be determined to have a finite number of values given input-output data. The total number of such values over the complex numbers is called the identifiability degree of the model. Unidentifiable models are models such that the unknown parameters can have an infinite number of values given input-output data. For unidentifiable models, a set of identifiable functions of the parameters are sought so that the model can be reparametrized in terms of these functions yielding an identifiable model. In this work, we use numerical algebraic geometry to determine if a model is identifiable or unidentifiable. For identifiable models, we present a novel approach to compute the identifiability degree. For unidentifiable models, we present a novel numerical differential algebra technique aimed at computing a set of algebraically independent identifiable functions. Several examples are used to demonstrate the new techniques.

Attributes

Attribute NameValues
Creator
  • Jonathan Hauenstein

Contributor
  • Daniel Bates

  • Nicolette Meshkat

Publisher
  • Jonathan Hauenstein

Departments and Units
Record Visibility and Access Public
Content License
  • All rights reserved

Digital Object Identifier

doi:10.7274/R03T9F91

This DOI is the best way to cite this dataset.


Files

Please Note: You may encounter a delay before a download begins. Large or infrequently accessed files can take several minutes to retrieve from our archival storage system.