Identifiable paths and cycles in linear compartmental models

TL;DR

This paper introduces identifiable path/cycle models in linear compartmental systems, providing conditions for their identifiability based on graph structure, and offers methods to derive locally identifiable models by removing leaks.

Contribution

It defines a new class of models with identifiable parameters linked to graph cycles and paths, and establishes necessary and sufficient conditions for their identifiability.

Findings

Identifiable path/cycle models have identifiable monomial functions of parameters.

Provided graph-based tests to determine if a model is an identifiable path/cycle model.

Established conditions under which models become locally identifiable after removing leaks.

Abstract

We introduce a class of linear compartmental models called identifiable path/cycle models which have the property that all of the monomial functions of parameters associated to the directed cycles and paths from input compartments to output compartments are identifiable and give sufficient conditions to obtain one. Removing leaks, we then show how one can obtain a locally identifiable model from an identifiable path/cycle model. These identifiable path/cycle models yield the only identifiable models with certain conditions on their graph structure and thus we provide necessary and sufficient conditions for identifiable models with certain graph properties. A sufficient condition based on the graph structure of the model is also provided so that one can test if a model is an identifiable path/cycle model by examining the graph itself. We also provide some necessary conditions for identifiability based on graph structure. Our proofs use algebraic and combinatorial techniques.