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