Baaijens, Jasmijn A.; Draisma, Jan
(2016).
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On the existence of identifiable reparametrizations for linear compartment models.
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SIAM journal on applied mathematics, 76(4), pp. 1577-1605.
Society for Industrial and Applied Mathematics
10.1137/15M1038013

Text
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The parameters of a linear compartment model are usually estimated from experimental input-output data. A problem arises when infinitely many parameter values can yield the same result; such a model is called unidentifiable. In this case, one can search for an identifiable reparametrization of the model: a map which reduces the number of parameters, such that the reduced model is identifiable. We study a specific class of models which are known to be unidentifiable. Using algebraic geometry and graph theory, we translate a criterion given by Meshkat and Sullivant for the existence of an identifiable scaling reparametrization to a new criterion based on the rank of a weighted adjacency matrix of a certain bipartite graph. This allows us to derive several new constructions to obtain graphs with an identifiable scaling reparametrization. Using these constructions, a large subclass of such graphs is obtained. Finally, we present a procedure of subdividing or deleting edges to ensure that a model has an identifiable scaling reparametrization.

## Item Type: |
Journal Article (Original Article) |
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## Division/Institute: |
08 Faculty of Science > Department of Mathematics and Statistics > Institute of Mathematics |

## UniBE Contributor: |
Draisma, Jan |

## Subjects: |
500 Science > 510 Mathematics |

## ISSN: |
0036-1399 |

## Publisher: |
Society for Industrial and Applied Mathematics |

## Language: |
English |

## Submitter: |
Olivier Bernard Mila |

## Date Deposited: |
07 Aug 2017 16:54 |

## Last Modified: |
07 Aug 2017 16:54 |

## Publisher DOI: |
10.1137/15M1038013 |

## ArXiv ID: |
1509.02551v2 |

## BORIS DOI: |
10.7892/boris.99757 |

## URI: |
https://boris.unibe.ch/id/eprint/99757 |