On the existence of identifiable reparametrizations for linear compartment models
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 for subdividing or deleting edges to ensure that a model has an identifiable scaling reparametrization.
|Journal||SIAM Journal on Applied Mathematics|
|Grant||This work was funded by the The Netherlands Organisation for Scientific Research (NWO); grant id nwo/639.072.309 - Statistical Models for Structural Genetic Variants in the Genome of the Netherlands|
Baaijens, J.A, & Draisma, J. (2016). On the existence of identifiable reparametrizations for linear compartment models. SIAM Journal on Applied Mathematics, 76(4), 1577–1605. doi:10.1137/15M1038013