Highly structured models for spectral analysis in high-energy astrophysics

Statistical Science

Volumn 19, Issue 2, 2004, Pages 275-293

  Van Dyk, David A ^a   Kang, Hosung ^b  

^a UNIVERSITY OF CALIFORNIA   (United States)

^b HARVARD UNIVERSITY   (United States)

Author keywords

Astrostatistics; Bayesian methods; Data augmentation; EM algorithm; Markov chain; Missing data; Monte Carlo; Nonignorable missing data; Pileup; Poisson model; Posterior predictive checks; Spectral analysis; The Chandra X Ray Observatory

Indexed keywords

EID: 14544284975     PISSN: 08834237     EISSN: None     Source Type: Journal    
DOI: 10.1214/088342304000000314     Document Type: Review

References (38)

1. BALLET, J. (1999). Pile-up on X-ray CCD instruments. Astronomy and Astrophysics Suppl. Ser. 135 371-381.
2. BAYARRI, M. J. and BERGER, J. O. (1999). Quantifying surprise in the data, and model verification. In Bayesian Statistics 6 (J. M. Bernardo, J. O. Berger, A. P. Dawid and A. F. M. Smith, eds.) 53-82. Oxford Univ. Press, London.
3. CASH, W. (1979). Parameter estimation in astronomy through application of the likelihood ratio. Astrophysical J. 228 939-947.
4. DAVIS, J. E. (2001). Event pileup in charge-coupled devices. Astrophysical J. 562 575-582.
5. DEMPSTER, A. P., LAIRD, N. M. and RUBIN, D. B. (1977). Maximum likelihood from incomplete data via the EM algorithm (with discussion). J. Roy. Statist. Soc. Ser. B 39 1-38.
6. ESCH, D. N. (2003). Extensions and applications of three statistical models. Ph.D. dissertation, Dept. Statistics, Harvard Univ.
7. ESCH, D. N., CONNORS, A., KAROVSKA, M. and VAN DYK, D. A. (2004). An image restoration technique with error estimates. Astrophysical J. 610 1213-1227.
8. FEIGELSON, E. D. and BABU, G. J., eds. (2003). Statistical Challenges in Modern Astronomy III. Springer, New York.
9. FESSLER, J. A. and HERO, A. O. (1994). Space-alternating generalized expectation-maximization algorithm. IEEE Trans. Signal Process. 42 2664-2677.
10. FREEMAN, P., GRAZIANI, C., LAMB, D., LOREDO, T., FENIMORE, E., MURAKAMI, T. and YOSHIDA, A. (1999). Statistical analysis of spectral line candidates in gamma-ray burst ORB 870303. Astrophysical J. 524 753-771.
11. GELFAND, A. E. and SMITH, A. F. M. (1990). Sampling-based approaches to calculating marginal densities. J. Amer. Statist. Assoc. 85 398-409.
12. GELMAN, A., MENG, X.-L. and STERN, H. (1996). Posterior predictive assessment of model fitness via realized discrepancies (with discussion). Statist. Sinica 6 733-807.
13. GELMAN, A. and RUBIN, D. B. (1992). Inference from iterative simulation using multiple sequences (with discussion). Statist. Sci. 7 457-472.
14. HANS, C. M. and VAN DYK, D. A. (2003). Accounting for absorption lines in high energy spectra. In Statistical Challenges in Modern Astronomy III (E. Feigelson and G. Babu, eds.) 429-430. Springer, New York.
15. KANG, H., VAN DYK, D. A., YU, Y., SIEMIGINOWSKA, A., CONNORS, A. and KASHYAP, V. (2003). New MCMC methods to address pile-up in the Chandra X-ray observatory. In Statistical Challenges in Modern Astronomy III (E. Feigelson and G. Babu, eds.) 449-450. Springer, New York.
16. LAMPTON, M., MARGON, B. and BOWYER, S. (1976). Parameter estimation in X-ray astronomy. Astrophysical J. 208 177-190.
17. LANGE, K. and CARSON, R. (1984). EM reconstruction algorithms for emission and transmission tomography. J. Computer Assisted Tomography 8 306-316.
18. LUCY, L. B. (1974). An iterative technique for the rectification of observed distributions. Astronomical J. 79 745-754.
19. MENG, X.-L. (1994). Posterior predictive p-values. Ann. Statist. 22 1142-1160.
20. MENG, X.-L. and VAN DYK, D. A. (1997). The EM algorithm - An old folk song sung to a fast new tune (with discussion). J. Roy. Statist. Soc. Ser. B 59 511-567.
21. MORRISON, R. and MCCAMMON, D. (1983). Interstellar photoelectric absorption cross sections, 0.03-10 keV. Astrophysical J. 270 119-122.
22. PROTASSOV, R., VAN DYK, D. A., CONNORS, A., KASHYAP, V. and SIEMIGINOWSKA, A. (2002). Statistics: Handle with care - Detecting multiple model components with the likelihood ratio test. Astrophysical J. 571 545-559.
23. RICHARDS, W. H. (1972). Bayesian-based iterative method of image restoration. J. Opt. Soc. Amer. 62 55-59.
24. RUBIN, D. B. (1984). Bayesianly justifiable and relevant frequency calculations for the applied statistician. Ann. Statist. 12 1151-1172.
25. SHEPP, L. A. and VARDI, Y. (1982). Maximum likelihood reconstruction for emission tomography. IEEE Trans. on Medical Imaging 1 113-122.
26. SIEMIGINOWSKA, A., ELIVIS, M., ALANNA, C., FREEMAN, P., KASHYAP, V. and FEIGELSON, E. (1997). AXAF data analysis challanges. In Statistical Challenges in Modern Astronomy II (G. Babu and E. Feigelson, eds.) 241-258. Springer, New York.
27. SMITH, A. F. M. and ROBERTS, G. O. (1993). Bayesian computation via the Gibbs sampler and related Markov chain Monte Carlo methods. J. Roy. Statist. Soc. Ser. B 55 3-23.
28. SOURLAS, N., VAN DYK, D. A., KASHYAP, V., DRAKE, J. and PEASE, D. (2003). Bayesian spectral analysis of "MAD" stars. In Statistical Challenges in Modern Astronomy III (E. Feigelson and G. Babu, eds.) 489-490. Springer, New York.
29. TANNER, M. A. and WONG, W. H. (1987). The calculation of posterior distributions by data augmentation (with discussion). J. Amer. Statist. Assoc. 82 528-550.
30. TITTERINGTON, D. M., SMITH, A. F. M. and MAKOV, U. E. (1985). Statistical Analysis of Finite Mixture Distributions. Wiley, New York.
31. VAN DYK, D. A. (2000a). Fast new EM-type algorithms with applications in astrophysics. Technical report.
32. VAN DYK, D. A. (2000b). Nesting EM algorithms for computational efficiency. Statist. Sinica 10 203-225.
33. VAN DYK, D. A. (2003). Hierarchical models, data augmentation, and Markov chain Monte Carlo (with discussion). In Statistical Challenges in Modern Astronomy III (E. Feigelson and G. Babu, eds.) 41-56. Springer, New York.
34. VAN DYK, D. A. and HANS, C. M. (2002). Accounting for absorption lines in images obtained with the Chandra X-ray Observatory. In Spatial Cluster Modelling (A. Lawson and D. Denison, eds.) 175-198. CRC Press, London.
35. VAN DYK, D. A., CONNORS, A., KASHYAP, V. and SIEMIGINOWSKA, A. (2001). Analysis of energy spectra with low photon counts via Bayesian posterior simulation. Astrophysical J. 548 224-243.
36. VAN DYK, D. A., CONNORS, A., ESCH, D. N., FREEMAN, P., KANG, H., KAROVSKA, M., KASHYAP, V., SIEMIGINOWSKA, A. and ZEZAS, A. (2004). Deconvolution in high energy astrophysics: Science, instrumentation, and methods (with discussion). Bayesian Analysis. To appear.
37. VAN DYK, D. A. and MENG, X.-L. (2000). Algorithms based on data augmentation. In Computing Science and Statistics: Proc. 31st Symposium on the Interface (M. Pourahmadi and K. Berk, eds.) 230-239. Interface Foundation of North America, Fairfax Station, VA.
38. VAN DYK, D. A. and MENG, X.-L. (2001). The art of data augmentation (with discussion). J. Comput. Graph. Statist. 10 1-111.