The estimation of phase-type related functionals using Markov chain Monte Carlo methods

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Standard

The estimation of phase-type related functionals using Markov chain Monte Carlo methods. / Bladt, Mogens; Gonzalez, Antonio; Lauritzen, Steffen L.

In: Scandinavian Actuarial Journal, Vol. 2003, No. 4, 2003, p. 280-300.

Research output: Contribution to journal › Journal article › Research › peer-review

Harvard

Bladt, M, Gonzalez, A & Lauritzen, SL 2003, 'The estimation of phase-type related functionals using Markov chain Monte Carlo methods', Scandinavian Actuarial Journal, vol. 2003, no. 4, pp. 280-300. https://doi.org/10.1080/03461230110106435

APA

Bladt, M., Gonzalez, A., & Lauritzen, S. L. (2003). The estimation of phase-type related functionals using Markov chain Monte Carlo methods. Scandinavian Actuarial Journal, 2003(4), 280-300. https://doi.org/10.1080/03461230110106435

Vancouver

Bladt M, Gonzalez A, Lauritzen SL. The estimation of phase-type related functionals using Markov chain Monte Carlo methods. Scandinavian Actuarial Journal. 2003;2003(4):280-300. https://doi.org/10.1080/03461230110106435

Author

Bladt, Mogens ; Gonzalez, Antonio ; Lauritzen, Steffen L. / The estimation of phase-type related functionals using Markov chain Monte Carlo methods. In: Scandinavian Actuarial Journal. 2003 ; Vol. 2003, No. 4. pp. 280-300.

Bibtex

@article{338bdee081e84724a3be153e2bdd62cc,
title = "The estimation of phase-type related functionals using Markov chain Monte Carlo methods",
abstract = "In this paper we present a method for estimation of functionals depending on one or several phase-type distributions. This could for example be the ruin probability in a risk reserve process where claims are assumed to be of phase-type. The proposed method uses a Markov chain Monte Carlo simulation to reconstruct the Markov jump processes underlying the phase-type variables in combination with Gibbs sampling to obtain a stationary sequence of phase-type probability measures from the posterior distribution of these given the observations. This enables us to find quantiles of posterior distributions of functionals of interest, thereby representing estimation uncertainty in a flexible way. We compare our estimates to those obtained by the method of maximum likelihood and find a good agreement. We illustrate the statistical potential of the method by estimating ruin probabilities in simulated examples.",
author = "Mogens Bladt and Antonio Gonzalez and Lauritzen, {Steffen L.}",
year = "2003",
doi = "10.1080/03461230110106435",
language = "English",
volume = "2003",
pages = "280--300",
journal = "Scandinavian Actuarial Journal",
issn = "0346-1238",
publisher = "Taylor & Francis Scandinavia",
number = "4",

}

RIS

TY - JOUR

T1 - The estimation of phase-type related functionals using Markov chain Monte Carlo methods

AU - Bladt, Mogens

AU - Gonzalez, Antonio

AU - Lauritzen, Steffen L.

PY - 2003

Y1 - 2003

N2 - In this paper we present a method for estimation of functionals depending on one or several phase-type distributions. This could for example be the ruin probability in a risk reserve process where claims are assumed to be of phase-type. The proposed method uses a Markov chain Monte Carlo simulation to reconstruct the Markov jump processes underlying the phase-type variables in combination with Gibbs sampling to obtain a stationary sequence of phase-type probability measures from the posterior distribution of these given the observations. This enables us to find quantiles of posterior distributions of functionals of interest, thereby representing estimation uncertainty in a flexible way. We compare our estimates to those obtained by the method of maximum likelihood and find a good agreement. We illustrate the statistical potential of the method by estimating ruin probabilities in simulated examples.

AB - In this paper we present a method for estimation of functionals depending on one or several phase-type distributions. This could for example be the ruin probability in a risk reserve process where claims are assumed to be of phase-type. The proposed method uses a Markov chain Monte Carlo simulation to reconstruct the Markov jump processes underlying the phase-type variables in combination with Gibbs sampling to obtain a stationary sequence of phase-type probability measures from the posterior distribution of these given the observations. This enables us to find quantiles of posterior distributions of functionals of interest, thereby representing estimation uncertainty in a flexible way. We compare our estimates to those obtained by the method of maximum likelihood and find a good agreement. We illustrate the statistical potential of the method by estimating ruin probabilities in simulated examples.

U2 - 10.1080/03461230110106435

DO - 10.1080/03461230110106435

M3 - Journal article

VL - 2003

SP - 280

EP - 300

JO - Scandinavian Actuarial Journal

JF - Scandinavian Actuarial Journal

SN - 0346-1238

IS - 4

ER -

ID: 128112932