Maximum Likelihood Estimation for Scaled Inhomogeneous Phase-Type Distributions from Discrete Observations
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arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866917154763309056 |
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| author | Baltazar-Larios, Fernando Quintos, Alejandra |
| author_facet | Baltazar-Larios, Fernando Quintos, Alejandra |
| contents | Inhomogeneous phase-type (IPH) distributions extend classical phase-type models by allowing transition intensities to vary over time, offering greater flexibility for modeling heavy-tailed or time-dependent absorption phenomena. We focus on the subclass of IPH distributions with time-scaled sub-intensity matrices of the form $Λ(t) = h_β(t)Λ$, which admits a time transformation to a homogeneous Markov jump process. For this class, we develop a statistical inference framework for discretely observed trajectories that combines Markov-bridge reconstruction with a stochastic EM algorithm and a gradient-based update. The resulting method yields joint maximum-likelihood estimates of both the baseline sub-intensity matrix $Λ$ and the time-scaling parameter $β$. Through simulation studies for the matrix-Gompertz and matrix-Weibull families, and a real-data application to coronary allograft vasculopathy progression, we demonstrate that the proposed approach provides an accurate and computationally tractable tool for fitting time-scaled IPH models to irregular multi-state data. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_16061 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Maximum Likelihood Estimation for Scaled Inhomogeneous Phase-Type Distributions from Discrete Observations Baltazar-Larios, Fernando Quintos, Alejandra Methodology Applications Inhomogeneous phase-type (IPH) distributions extend classical phase-type models by allowing transition intensities to vary over time, offering greater flexibility for modeling heavy-tailed or time-dependent absorption phenomena. We focus on the subclass of IPH distributions with time-scaled sub-intensity matrices of the form $Λ(t) = h_β(t)Λ$, which admits a time transformation to a homogeneous Markov jump process. For this class, we develop a statistical inference framework for discretely observed trajectories that combines Markov-bridge reconstruction with a stochastic EM algorithm and a gradient-based update. The resulting method yields joint maximum-likelihood estimates of both the baseline sub-intensity matrix $Λ$ and the time-scaling parameter $β$. Through simulation studies for the matrix-Gompertz and matrix-Weibull families, and a real-data application to coronary allograft vasculopathy progression, we demonstrate that the proposed approach provides an accurate and computationally tractable tool for fitting time-scaled IPH models to irregular multi-state data. |
| title | Maximum Likelihood Estimation for Scaled Inhomogeneous Phase-Type Distributions from Discrete Observations |
| topic | Methodology Applications |
| url | https://arxiv.org/abs/2512.16061 |