Principled phase-order selection for MAPH models

Develop a principled method for selecting the number of transient phases in Multi-Absorbing Phase-Type (MAPH) models rather than relying solely on externally chosen model-size criteria.

Background

The MAPH model uses a phase order $m$ that is selected externally, while the paper's experiments show that fit quality, computational cost, and convergence behavior depend on this choice. The conclusion explicitly identifies principled phase-order selection as an unresolved issue.