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Estimating parametric semi-Markov models from panel data using phase-type approximations

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Estimating parametric semi-Markov models from panel data using phase-type approximations. / Titman, Andrew.
In: Statistics and Computing, Vol. 24, No. 2, 03.2014, p. 155-164.

Research output: Contribution to Journal/Magazine › Journal article › peer-review

Harvard

Titman, A 2014, 'Estimating parametric semi-Markov models from panel data using phase-type approximations', Statistics and Computing, vol. 24, no. 2, pp. 155-164. https://doi.org/10.1007/s11222-012-9360-6

APA

Titman, A. (2014). Estimating parametric semi-Markov models from panel data using phase-type approximations. Statistics and Computing, 24(2), 155-164. https://doi.org/10.1007/s11222-012-9360-6

Vancouver

Titman A. Estimating parametric semi-Markov models from panel data using phase-type approximations. Statistics and Computing. 2014 Mar;24(2):155-164. Epub 2012 Oct 1. doi: 10.1007/s11222-012-9360-6

Author

Titman, Andrew. / Estimating parametric semi-Markov models from panel data using phase-type approximations. In: Statistics and Computing. 2014 ; Vol. 24, No. 2. pp. 155-164.

Bibtex

@article{e102f5ddb3b4470c99afbcc2759b52fe,
title = "Estimating parametric semi-Markov models from panel data using phase-type approximations",
abstract = "Inference for semi-Markov models under panel data presents considerable computational difficulties. In general the likelihood is intractable, but a tractable likelihood with the form of a hidden Markov model can be obtained if the sojourn times in each of the states are assumed to have phase-type distributions. However, using phase-type distributions directly may be undesirable as they require estimation of parameters which may be poorly identified. In this article, an approach to fitting semi-Markov models with standard parametric sojourn distributions is developed. The method involves establishing a family of Coxian phase-type distribution approximations to the parametric distribution and merging approximations for different states to obtain an approximate semi-Markov process with a tractable likelihood. Approximations are developed for Weibull and Gamma distributions and demonstrated on data relating to post-lung-transplantation patients.",
keywords = "B-splines , gamma distribution, Hidden Markov model, misclassification, Panel data, Phase-type distribution, Semi-Markov, Weibull",
author = "Andrew Titman",
year = "2014",
month = mar,
doi = "10.1007/s11222-012-9360-6",
language = "English",
volume = "24",
pages = "155--164",
journal = "Statistics and Computing",
issn = "0960-3174",
publisher = "Springer Netherlands",
number = "2",

}

RIS

TY - JOUR

T1 - Estimating parametric semi-Markov models from panel data using phase-type approximations

AU - Titman, Andrew

PY - 2014/3

Y1 - 2014/3

N2 - Inference for semi-Markov models under panel data presents considerable computational difficulties. In general the likelihood is intractable, but a tractable likelihood with the form of a hidden Markov model can be obtained if the sojourn times in each of the states are assumed to have phase-type distributions. However, using phase-type distributions directly may be undesirable as they require estimation of parameters which may be poorly identified. In this article, an approach to fitting semi-Markov models with standard parametric sojourn distributions is developed. The method involves establishing a family of Coxian phase-type distribution approximations to the parametric distribution and merging approximations for different states to obtain an approximate semi-Markov process with a tractable likelihood. Approximations are developed for Weibull and Gamma distributions and demonstrated on data relating to post-lung-transplantation patients.

AB - Inference for semi-Markov models under panel data presents considerable computational difficulties. In general the likelihood is intractable, but a tractable likelihood with the form of a hidden Markov model can be obtained if the sojourn times in each of the states are assumed to have phase-type distributions. However, using phase-type distributions directly may be undesirable as they require estimation of parameters which may be poorly identified. In this article, an approach to fitting semi-Markov models with standard parametric sojourn distributions is developed. The method involves establishing a family of Coxian phase-type distribution approximations to the parametric distribution and merging approximations for different states to obtain an approximate semi-Markov process with a tractable likelihood. Approximations are developed for Weibull and Gamma distributions and demonstrated on data relating to post-lung-transplantation patients.

KW - B-splines

KW - gamma distribution

KW - Hidden Markov model

KW - misclassification

KW - Panel data

KW - Phase-type distribution

KW - Semi-Markov

KW - Weibull

U2 - 10.1007/s11222-012-9360-6

DO - 10.1007/s11222-012-9360-6

M3 - Journal article

VL - 24

SP - 155

EP - 164

JO - Statistics and Computing

JF - Statistics and Computing

SN - 0960-3174

IS - 2

ER -