2412.01135
GRAPH-BASED PROOFS OF INDISTINGUISHABILITY OF LINEAR COMPARTMENTAL MODELS
Cashous Bortner, John Gilliana, Dev Patel, Zaia Tamras
correcthigh confidence
- Category
- Not specified
- Journal tier
- Specialist/Solid
- Processed
- Sep 28, 2025, 12:56 AM
- arXiv Links
- Abstract ↗PDF ↗
Audit review
The paper proves the indistinguishability claims for skeletal path models via graph-theoretic generation of input–output coefficients (Propositions 3.1 and 3.3) and explicit parameter bijections (Theorems 3.4 and 3.5). The model’s solution arrives at the same conclusions using a transfer-function/linear-algebra route, computing H(s) = e_n^T(sI − A)^{-1}e_1 and identifying the same denominator factorizations and constant numerator. The two arguments are consistent and yield identical input–output equations under appropriate parameter relabelings.
Referee report (LaTeX)
\textbf{Recommendation:} minor revisions
\textbf{Journal Tier:} specialist/solid
\textbf{Justification:}
The manuscript correctly re-establishes known indistinguishability results for skeletal path linear compartmental models using a graph-theoretic method. This alternative vantage point is pedagogically valuable and may facilitate generalizations where graph structure is more transparent than matrix algebra. The exposition is clear, with rigorous coefficient derivations and explicit parameter bijections. Minor improvements to index notation, explicit mapping summaries, and a short comparison to the transfer-function approach would further aid readers.