The estimation of phase-type related functionals using markov chain monte carlo methods

Scandinavian Actuarial Journal

Volumn 2003, Issue 4, 2003, Pages 280-300

  Bladt, Mogens ^a   Gonzalez, Antonio ^b   Lauritzen, Steffen L ^c  

^a UNIVERSIDAD NACIONAL AUTÓNOMA DE MÉXICO   (Mexico)

^b BENEMÉRITA UNIVERSIDAD AUTÓNOMA DE PUEBLA   (Mexico)

^c AALBORG UNIVERSITY   (Denmark)

Author keywords

Bayesian analysis; Markov chain monte carlo; Phase type distribution; Ruin probabilities

Indexed keywords

EID: 85011479509     PISSN: 03461238     EISSN: 16512030     Source Type: Journal    
DOI: 10.1080/03461230110106435     Document Type: Article

References (31)

1. Asmussen S. (1987). Applied probability and queues. John Wiley & Sons. Chichester and New York
2. Asmussen, S. (2000a). Ruin probabilities. Advanced Series on Statistical Science & Applied Probability (Vol. 2). World Scientific, Singapore.
3. Asmussen, S. (2000b). Matrix-analytic models and their analysis. Scand. J. Statist. 27, 193-226.
4. Asmussen, S. & Bladt, M. (1994). Poisson's equation for queues driven by a Markovian marked point process. Queueing Systems 17, 235-274.
5. Asmussen, S. & Bladt, M. (1996). Phase-type distributions and risk processes with state-dependent premiums. Scand. Actuar. J. 96, 19-36.
6. Asmussen, S. & Bladt, M. (1997). Renewal theory and queueing algorithms for matrix-exponential distributions. In: Alfa, A. S. & Chakravarty, S. (eds.). Matrix-analytic methods in stochastic models. pp. 313-341.
7. Asmussen, S., Nerman, O. & Olsson, M. (1996). Fitting phase-type distributions via the EM-algorithm. Scand. J. Statist. 23, 419-441.
8. Asmussen, S. & Olsson, O. (1998). Phase-type distributions. Encyclopedia of statistical sciences, update volume 2. (Kotz, Read, Banks eds.), John Wiley and Sons, Chichester and New York.
9. Asmussen, S. & Rolski, T. (1991). Computational methods in risk theory: A matrix-algorithmic approach. Insurance: Mathematics and Economics 10, 259-274.
10. Benckert, L.-G. (1962). The lognormal model for the distribution of one claim. Austin Bulletin 2, 9-23.
11. Benckert, L.-G. & Jung, J. (1974). Statistical models of claims distributions in fire insurance. Austin Bulletin 8, 1-25.
12. Bernardo, J. M. & Smith, A. F. M. (1994). Bayesian Theory. John Wiley & Sons, Chichester and New York.
13. Bladt, M. (1996). The variance constant for the PH/PH/1 actual waiting time. Ann. Appl. Probab. 6, 766-777.
14. Diaconis, P. & Ylvisaker, D. (1979). Conjugate priors for exponential families, Ann. Statist., 7, 269-281.
15. Gelfand, A. E. & Smith, A. F. M. (1990). Sampling-based approaches to calculating marginal densities. J. Amer. Statist. Assoc. 85, 398-409.
16. Geman, S. & Geman, D. (1984). Stochastic relaxation, Gibbs distributions, and the Bayesian restoration of images. IEEE Transactions on Pattern Analysis and Machine Intelligence 6, 721-741.
17. Geyer, C. J. (1992). Practical Markov chain Monte Carlo. Statist. Sci. 7, 457- 511.
18. Geyer, C. J. & Thompson, E. A. (1992). Constrained Monte Carlo maximum likelihood for dependent data (with discussion). J. Roy. Statist. Soc. Ser. B 54, 657-699.
19. Gilks, W. R., Richardson, S. & Spiegelhalter, D. J. (1996). Markov chain Monte Carlo in practice. Chapman & Hall, London.
20. Green, P. (1995). Reversible jump Markov chain Monte Carlo computation and Bayesian model determination. Biometrika 82, 711-732.
21. Green, P. (2001). A primer on Markov chain Monte Carlo. In Complex Stochastic Systems. (Barndorff-Nielsen et al. (eds)), pp. 1-62. Chapman and Hall/CRC, London/Boca Raton.
22. Giuterrez-Pena, E. & Smith, A. F. M. (1995). Conjugate parametrizations for natural exponential families. J. Amer. Statist. Assoc. 90, 1347-1356.
23. Hald, A. (1952). Statistical Theory with Engineering Applications. John Wiley and Sons, New York.
24. HAustings, W. K. (1970). Monte Carlo sampling methods using Markov chains and their applications. Biometrika 57, 97-109.
25. Hipp, C. (1989a). Efficient estimates for ruin probabilities. Proc. fourth Prague symp on asymptotic statistics (P. Mandel & M. Huskova, eds.), 259-268.
26. Hipp, C. (1989b). Estimates and bootstrap confidence intervals for ruin probabilities. Austin Bulletin 19, 57-70.
27. Metropolis, N., Rosenbluth, A. W., Rosenbluth, M. N., Teller, A. H. & Teller, E. (1953). Equations of state calculations by fast computing machines. Journal of Chemical Physics 21, 1087-1092.
28. Neuts, M. F. (1981). Matrix-geometric solutions in stochastic models. Johns Hopkins University Press, Baltimore and London.
29. Rolski, T., Schmidli, H., Schmidt, V. & Teugels, J. (1999). Stochastic processes for insurance and finance. John Wiley & Sons, Chichester and New York.
30. Stanford, D. A. & Stroinski, K. J. (1994). Recursive methods for computing finite-time ruin probabilities for phase-type claim sizes. Austin Bulletin 24, 235-254.
31. Wei, G. C. G. & Tanner, M. A. (1990). A Monte Carlo implementation of the EM-algorithm and the poor man's augmentation algorithms. J. Amer. Statist. Assoc. 85, 699-704.