On the Non-uniqueness of Representations of Coxian Phase-Type Distributions

TL;DR

This paper addresses the non-uniqueness in Coxian phase-type distribution representations, proposing a method to identify all equivalent models efficiently, which enhances understanding of the data-generating mechanisms.

Contribution

The authors develop a novel approach that guarantees finding all equivalent Coxian phase-type representations from a single model fit, improving over standard multiple refits.

Findings

The method reliably finds all model representations.

It reduces computational effort compared to traditional approaches.

Supports better understanding of model non-uniqueness.

Abstract

Parameter estimation in Coxian phase-type models can be challenging due to their non-unique representation leading to a multi-modal likelihood. Since each representation corresponds to a different underlying data-generating mechanism, it is of interest to identify those supported by given data (i.e., find all likelihood modes). The standard approach is to simply refit using various initial values, but this has no guarantee of working. Thus, we develop new properties specific to this class of models, and employ these to determine all the equivalent model representations. The proposed approach only requires fitting the model once, and is guaranteed to find all representations.