Markov chain Monte Carlo methods for Bayesian gravitational radiation data analysis

Physical Review D - Particles, Fields, Gravitation and Cosmology

Volumn 58, Issue 8, 1998, Pages

  Christensen, Nelson ^a   Meyer, Renate ^a  

^a UNIVERSITY OF AUCKLAND   (New Zealand)

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Indexed keywords

EID: 0542418289     PISSN: 15507998     EISSN: 15502368     Source Type: Journal    
DOI: 10.1103/PhysRevD.58.082001     Document Type: Article

References (31)

1. A. Abramovici, W. E. Althouse, R. W. P. Drever, Y. Gürsel, S. Kawamura, F. J. Raab, D. Shoemaker, L. Sievers, R. E. Spero, K. S. Thorne, R. E. Vogt, R. Weiss, S. E. Whitcomb, and M. E. Zucker, Science 256, 325 (1992).
2. C. Bradaschia, Nucl. Instrum. Methods Phys. Res. A 289, 518 (1990).
3. K. S. Thorne, in 300 Years of Gravitation, edited by S. W. Hawking and W. Israel (Cambridge University Press, Cambridge, England, 1987), pp. 330–458.
4. L. S. Finn and D. F. Chernoff, Phys. Rev. D 47, 2198 (1993).
5. B. F. Schutz, Nature (London) 323, 310 (1986).
6. C. Cutler and E. F. Flanagan, Phys. Rev. D 49, 2658 (1994).
7. L. S. Finn, Phys. Rev. D 53, 2878 (1996).
8. C. Cutler, T. A. Apostolatos, L. Bildsten, L. S. Finn, E. E. Flanagan, D. Kennefick, D. M. Marković, A. Ori, E. Poisson, G. J. Sussman, and K. S. Thorne, Phys. Rev. Lett. 70, 2984 (1993).
9. E. E. Flanagan and S. A. Hughes, Phys. Rev. D 57, 4535 (1998).
10. P. C. Gregory and T. J. Loredo, Astrophys. J. 398, 146 (1992).
11. L. S. Finn, gr-qc/9709077.
12. L. S. Finn, Phys. Rev. D 46, 5236 (1992).
13. D. Nicholson and A. Vecchio, Phys. Rev. D 57, 4588 (1998).
14. W. R. Gilks, S. Richardson, and D. J. Spiegelhalter, Markov Chain Monte Carlo in Practice (Chapman and Hall, London, 1996).
15. S. Geman and D. Geman, IEEE Trans. Pattern. Anal. Mach. Intell. 6, 721 (1984).
16. D. Marković, Phys. Rev. D 48, 4738 (1993).
17. C. P. Robert, The Bayesian Choice (Springer, New York, 1996).
18. M. K. Cowles, B. P. Carlin, J. Am. Stat. Assoc. 91, 883 (1996).
19. N. G. Best, M. K. Cowles, and S. K. Vines, CODA manual version 0.30 (MRC Biostatistics Unit, Cambridge, England, 1995).
20. L. Devroye, Non-Uniform Random Variate Generation (Springer, New York, 1986).
21. W. R. Gilks and P. Wild, Appl. Stat. 41, 337 (1992).
22. B. D. Ripley, Stochastic Simulation (Wiley, New York, 1987).
23. W. R. Gilks, in Bayesian Statistics 4, edited by J. M. Bernardo, J. O. Berger, A. P. Dawid, A. F. M. Smith (Oxford University Press, Oxford, 1992), pp. 89–114.
24. W. R. Gilks, N. G. Best, and K. K. C. Chan, Appl. Stat.44, 455–472 (1995).
25. L. Tierney, Ann. Stat. 22, 1701 (1994).
26. S. Chib and E. Greenberg, Am. Stat.49, 327 (1995).
27. A. E. Gelfand and T. M. Lee, J. R. Stat. Soc. B 55, 72 (1993).
28. W. R. Gilks and R. M. Neal, Appl. Stat. 46, 541 (1997).
29. E. E. Flanagan (private communication).
30. B. W. Silverman, Density Estimation for Statistics and Data Analysis (Chapman and Hall, London, 1986).
31. The method for determining the “best-fit” or “maximum-likelihood” parameters is not addressed here. Our purpose in this present paper is only to display the MCMC methods for Bayesian computation in systems that may seem prohibitive due to the complexity of the multidimensional integrals. We feel that a proper Bayesian approach to parameter estimation in the coalescing compact binary systems has not been adequately described; this is a topic of current research by us and will be discussed in a forthcoming publication.