Gravitational-wave data analysis. Formalism and sample applications: The Gaussian case

Living Reviews in Relativity

Volumn 8, Issue , 2005, Pages

  Jaranowski, Piotr ^a   Królak, Andrzej ^b,c  

^a UNIVERSITY OF BIALYSTOK   (Poland)

^b ALBERT EINSTEIN INSTITUT   (Germany)

^c INSTITUTE OF MATHEMATICS   (Poland)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 17544371187     PISSN: 14338351     EISSN: 14338351     Source Type: Journal    
DOI: 10.12942/lrr-2005-3     Document Type: Review

References (89)

1. Abbott, B. et al. (LIGO Scientific Collaboration), "Analysis of LIGO data for gravitational waves from binary neutron stars", Phys. Rev. D, 69, 122001-1-16, (2004). Related online version (cited on 08 January 2005): http://arXiv.org/abs/gr-qc/0308069. 1, 4.9
2. Abbott, B. et al. (LIGO Scientific Collaboration), "First upper limits from LIGO on gravitational wave bursts", Phys. Rev. D, 89, 102001-1-21, (2004). Related online version (cited on 08 January 2005): http://arXiv.org/abs/gr-qc/0312056. 1
3. Abbott, B. et al. (LIGO Scientific Collaboration), "Setting upper limits on the strength of periodic gravitational waves from PSR J1939+2134 using the first science data from the GEO 600 and LIGO detectors", Phys. Rev. D, 69, 082004-1-16, (2004). Related online version (cited on 08 January 2005): http://arXiv.org/abs/gr-qc/0308050. 1, 4.9
4. Adler, R.J., The Geometry of Random Fields, (Wiley, Chichester, U.K.; New York, U.S.A., 1981). 4.5.2
5. Allen, B., "The stochastic gravity-wave background: Sources and detection", in Marck, J.A., and Lasota, J.-P., eds., Relativistic gravitation and gravitational radiation, Proceedings of the Les Houches School of Physics, held in Les Houches, Haute Savoie, 26 September 6 October, 1995, Cambridge Contemporary Astrophysics, (Cambridge University Press, Cambridge, U.K., 1997). Related online version (cited on 08 January 2005): http://arXiv.org/abs/astro-ph/9604033. 1
6. Allen, B., Blackburn, J.K., Brady, P.R., Creighton, J.D., Creighton, T., Droz, S., Gillespie, A.D., Hughes, S.A., Kawamura, S., Lyons, T.T., Mason, J.E., Owen, B.J., Raab, F.J., Regehr, M.W., Sathyaprakash, B.S., Savage Jr, R.L., Whitcomb, S., and Wiseman, A.G., "Observational Limit on Gravitational Waves from Binary Neutron Stars in the Galaxy", Phys. Rev. Lett., 83, 1498-1501, (1999). Related online version (cited on 08 January 2005): http://arXiv.org/abs/gr-qc/9903108. 1
7. Apostolatos, T.A., "Search templates for gravitational waves from precessing, inspiraling binaries", Phys. Rev. D, 52, 605-620, (1995). 1, 4.7
8. Armstrong, J.W., Estabrook, F.B., and Tinto, M., "Time-delay interferometry for space-based gravitational wave searches", Astrophys. J., 527, 814-826, (1999). 2
9. Arnaud, N., Barsuglia, M., Bizouard, M., Brisson, V., Cavalier, F., Davier, M., Hello, P., Kreckelbergh, S., and Porter, E.K., "Coincidence and coherent data analysis methods for gravitational wave bursts in a network of interferometric detectors", Phys. Rev. D, 68, 102001-1-18, (2003). Related online version (cited on 08 January 2005): http://arXiv.org/abs/gr-qc/0307100. 4.6
10. Astone, P., "Long-term operation of the Rome "Explorer" cryogenic gravitational wave detector", Phys. Rev. D, 47, 362-375, (1993). 2, 4.11
11. Astone, P., Babusci, D., Baggio, L., Bassan, M., Blair, D.G., Bonaldi, M., Bonifazi, P., Busby, D., Carelli, P., Cerdonio, M., Coccia, E., Conti, L., Cosmelli, C., D'Antonio, S., Fafone, V., Falferi, P., Fortini, P., Frasca, S., Giordano, G., Hamilton, W.O., Heng, I.S., Ivanov, E.N., Johnson, W.W., Marini, A., Mauceli, E., McHugh, M.P., Mezzena, R., Minenkov, Y., Modena, I., Modestino, G., Moleti, A., Ortolan, A., Pallottino, G.V., Pizzella, G., Prodi, G.A., Quintieri, L., Rocchi, A., Rocco, E., Ronga, F., Salemi, F., Santostasi, G., Taffarello, L., Terenzi, R., Tobar, M.E., Torrioli, G., Vedovato, G., Vinante, A., Visco, M., Vitale, S., and Zendri, J.P., "Methods and results of the IGEC search for burst gravitational waves in the years 1997-2000", Phys. Rev. D, 68, 022001-1-33, (2003). 4.10
12. Astone, P., Babusci, D., Bassan, M., Borkowski, K.M., Coccia, E., D'Antonio, S., Fafone, V., Giordano, G., Jaranowski, P., Królak, A., Marini, A., Minenkov, Y., Modena, I., Modestino, G., Moleti, A., Pallottino, G.V., Pietka, M., Pizzella, G., Quintieri, L., Rocchi, A., Ronga, F., Terenzi, R., and Visco, M., "All-sky upper limit for gravitational radiation from spinning neutron stars", Class. Quantum Grav., 20, S665-S676, (2003). Paper from the 7th Gravitational Wave Data Analysis Workshop, Kyoto, Japan, 17-19 December 2002. 1, 4.9
13. Astone, P., Babusci, D., Bassan, M., Borkowski, K.M., Coccia, E., D'Antonio, S., Fafone, V., Giordano, G., Jaranowski, P., Królak, A., Marini, A., Minenkov, Y., Modena, I., Modestino, G., Moleti, A., Pallottino, G.V., Pietka, M., Pizzella, G., Quintieri, L., Rocchi, A., Ronga, F., Terenzi, R., and Visco, M., "All-sky upper limit for gravitational radiation from spinning neutron stars", Class. Quantum Grav., 20, S665-S676, (2003). Paper from the 7th Gravitational Wave Data Analysis Workshop, Kyoto, Japan, 17-19 December 2002. 1, 4.9
14. Astone, P., Borkowski, K.M., Jaranowski, P., and Królak, A., "Data Analysis of gravitational-wave signals from spinning neutron stars. IV. An all-sky search", Phys. Rev. D, 65, 042003-1-18, (2002). 4.6, 4.7
15. Astone, P., Lobo, J.A., and Schutz, B.F., "Coincidence experiments between interferometric and resonant bar detectors of gravitational waves", Class. Quantum Grav., 11, 2093-2112, (1994). 4.10
16. Balasubramanian, R., and Dhurandhar, S.V., "Estimation of parameters of gravitational waves from coalescing binaries", Phys. Rev. D, 57, 3408-3422, (1998). 1
17. Balasubramanian, R., Sathyaprakash, B.S., and Dhurandhar, S.V., "Gravitational waves from coalescing binaries: detection strategies and Monte Carlo estimation of parameters", Phys. Rev. D, 53, 3033-3055, (1996). Related online version (cited on 08 January 2005): http://arXiv.org/abs/gr-qc/ 9508011. Erratum: Phys. Rev. D 54 (1996) 1860. 4.6, 4.8.3
18. Bayes, T., "An essay towards solving a problem in doctrine of chances", Philos. Trans. R. Soc. London, 53, 293-315, (1763). 4.2
19. Blanchet, L., "Gravitational Radiation from Post-Newtonian Sources and Inspiralling Compact Binaries", Living Rev. Relativity, 5, (2002). URL (cited on 08 January 2005): http://relativity.livingreviews.org/lrr-2002-3. 2
20. Bonazzola, S., and Gourgoulhon, E., "Gravitational waves from pulsars: Emission by the magnetic field induced distortion", Astron. Astrophys., 312, 675, (1996). Related online version (cited on 08 January 2005): http://arXiv.org/abs/astro-ph/9602107. 2
21. Brady, P.R., Creighton, T., Cutler, C., and Schutz, B.F., "Searching for periodic sources with LIGO", Phys. Rev. D, 57, 2101-2116, (1998). Related online version (cited on 08 January 2005): http://arXiv.org/abs/gr-qc/ 9702050. 1, 4,6
22. Brooks, C., Introductory econometrics for finance, (Cambridge University Press, Cambridge, U.K.; New York, U.S.A., 2002). 4.11
23. Buonanno, A., Chen, Y., and Vallisneri, M., "Detection template families for gravitational waves from the final stages of binary-black-hole inspirals: Nonspinning case", Phys. Rev. D, 67, 024016-1-50, (2003). Related online version (cited on 08 January 2005): http://arXiv.org/abs/gr-qc/ 0205122. 4.7
24. Conover, W.J., Practical Nonparametric Statistic, (Wiley, New York, U.S.A., 1980), 2nd edition. 4.11
25. Conway, J.H., and Sloane, N.J.A., Sphere Packings, Lattices and Groups, vol. 290 of Grundlehren der mathematischen Wissenschaften, (Springer, New York, U.S.A., 1999), 3rd edition. 4.6
26. Croce, R.P., Demma, Th., Longo, M., Marano, S., Matta, V., Pierro, V., and Pinto, I.M., "Correlator bank detection of gravitational wave chirps - False-alarm probability, template density, and thresholds: Behind and beyond the minimal-match issue", Phys. Rev. D, 70, 122001-1-19, (2004). Related online version (cited on 08 January 2005): http : X/arXiv.org/abs/gr-qc/0405023. 4.5.2
27. Cutler, C., Apostolatos, T.A., Bildsten, L., Finn, L.S., Flanagan, É.É., Kennefick, D., Markovic, D.M., Ori, A., Poisson, E., Sussman, G.J., and Thorne, K.S., "The Last Three Minutes: Issues in Gravitational Wave Measurements of Coalescing Compact Binaries", Phys. Rev. Lett., 70, 2984-2987, (1993). Related online version (cited on 08 January 2005): http://arXiv.org/abs/astro-ph/9208005. 1
28. Cutler, C., and Flanagan, É.É., "Gravitational Waves from Merging Compact Binaries: How Accurately Can One Extract the Binary's Parameters from the Inspiral Waveform?", Phys. Rev. D, 49, 2658-2697, (1994). Related online version (cited on 08 January 2005): http://arXiv.org/abs/ gr-qc/9402014. 1, 4.10
29. Davis, M.H.A., "A Review of Statistical Theory of Signal Detection", in Schutz, B.F., ed., Gravitational Wave Data Analysis, Proceedings of the NATO Advanced Research Workshop, held at Dyffryn House, St. Nichols, Cardiff, Wales, 6-9 July 1987, vol. 253 of NATO ASI Series C, 73-94, (Kluwer, Dordrecht, Netherlands; Boston, U.S.A., 1989). 3.4, 3.4.1
30. Dhurandhar, S.V., and Sathyaprakash, B.S., "Choice of filters for the detection of gravitational waves from coalescing binaries. II. Detection in colored noise", Phys. Rev. D, 49, 1707-1722, (1994). 4.6
31. Dhurandhar, S.V., and Schutz, B.F., "Filtering coalescing binary signals: Issues concerning narrow banding, thresholds, and optimal sampling", Phys. Rev. D, 50, 2390-2405, (1994). 4.5.2
32. Estabrook, F.B., and Wahlquist, H.D., "Response of Doppler spacecraft tracking to gravitational radiation", Gen. Relativ. Gravit., 439, 439-447, (1975). 2
33. Finn, L.S., "Observing binary inspiral in gravitational radiation: One interferometer", Phys. Rev. D, 47, 2198-2219, (1993). Related online version (cited on 08 January 2005): http://arXiv.org/abs/gr-qc/9301003. 1
34. Finn, L.S., "Aperture synthesis for gravitational-wave data analysis: Deterministic Sources", Phys. Rev. D, 63, 102001-1-18, (2001). Related online version (cited on 08 January 2005): http://arXiv.org/abs/gr-qc/ 0010033. 4.10, 4.1.1
35. Fisz, M., Probability Theory and Mathematical Statistics, (Wiley, New York, U.S.A., 1963). 3
36. Giampieri, G., "On the antenna pattern of an orbiting interferometer", Mon. Not. R. Astron. Soc., 289, 185-195, (1997). 2
37. Gürsel, Y., and Tinto, M., "Nearly optimal solution to the inverse problem for gravitationalwave bursts", Phys. Rev. D, 40, 3884-3938, (1989). 4.10
38. Helström, C.W., Statistical Theory of Signal Detection, vol. 9 of International Series of Monographs in Electronics and Instrumentation, (Pergamon Press, Oxford, U.K., New York, U.S.A., 1968), 2nd edition. 3, 4.5.1
39. Hinich, M.J., "Testing for Gaussianity and linearity of a stationary time series", J. Time Series Analysis, 3, 169-176, (1982). 4.11
40. Jaranowski, P., and Królak, A., "Optimal solution to the inverse problem for the gravitational wave signal of a coalescing binary", Phys. Rev. D, 49, 1723-1739, (1994). 4.10
41. Jaranowski, P., and Królak, A., "Data Analysis of gravitational-wave signals from spinning neutron stars. III. Detection statistics and computational requirements", Phys. Rev. D, 61, 062001-1-32, (2000). 4.5.1, 4.5.2, 4.7, 4.8.1, 4.8.2, 4.8.3, 4.8.3, 4.8.3
42. Jaranowski, P., Królak, A., and Schutz, B.F., "Data Analysis of gravitational-wave signals from spinning neutron stars: The signal and its detection", Phys. Rev. D, 58, 063001-1-24, (1998). 1, 2, 2, 4.5.2, 4.5.2
43. Judge, G.G., Hill, R.C., Griffiths, W.E., Lutkepohl, H., and Lee, T.-C., The Theory and Practice of Econometrics, (Wiley, New York, U.S.A., 1980). 4.11
44. Kafka, P., "Optimal Detection of Signals through Linear Devices with Thermal Noise Sources and Application to the Munich-Prascati Weber-Type Gravitational Wave Detectors", in De Sabbata, V., and Weber, J., eds., Topics in Theoretical and Experimental Gravitation Physics, Proceedings of the International School of Cosmology and Gravitation held in Erice, Trapani, Sicily, March 13-25, 1975, vol. 27 of NATO ASI Series B, 161, (Plenum Press, New York, U.S.A., 1977). 1
45. Kendall, M., and Stuart, A., The Advanced Theory of Statistics. Vol. 2: Inference and Relationship, number 2, (C. Griffin, London, 1979). 3
46. Kokkotas, K.D., Królak, A., and Tsegas, G., "Statistical analysis of the estimators of the parameters of the gravitational-wave signal from a coalescing binary", Class. Quantum Grav., 11, 1901-1918, (1994). 4.8.3
47. Kotelnikov, V.A., The theory of optimum noise immunity, (McGraw-Hill, New York, U.S.A., 1959). 3
48. Królak, A., Kokkotas, D., and Schäfer, G., "On estimation of the post-Newtonian parameters in the gravitational-wave emission of a coalescing binary", Phys. Rev. D, 52, 2089-2111, (1995). Related online version (cited on 08 January 2005): http://arXiv.org/abs/gr-qc/9503013. 1
49. Królak, A., Lobo, J.A., and Meers, B.J., "Estimation of the parameters of the gravitationalwave signal of a coalescing binary system", Phys. Rev. D, 48, 3451-3462, (1993). 1
50. Królak, A., and Schutz, B.F., "Coalescing binaries - probe to the Universe", Gen. Relativ. Gravit., 19, 1163-1171, (1987). 1
51. Królak, A., Tinto, M., and Vallisneri, M., "Optimal filtering of the LISA data", Phys. Rev. D, 70, 022003-1-24, (2004). Related online version (cited on 08 January 2005): http://arXiv.org/abs/gr-qc/0401108. 1, 2, 2, 4.5.2, 4.8.1, 4.8.2, 4.8.2, 4.10
52. Lagarias, J.C., Reeds, J.A., Wright, M.H., and Wright, P.E., "Convergence properties of the Nelder-Mead simplex method in low dimensions", SIAM J. Optimization, 9, 112-147, (1998). 4.8.1
53. Lehmann, E.L., Testing Statistical Hypothesis, (Wiley, New York, U.S.A., 1959). 3
54. Lehmann, E.L., Theory of Point Estimation, (Wiley, New York, U.S.A., 1983). 4
55. Liptser, R.S., and Shiryaev, A.N., Statistics of Random Processes, 2 Volumes, vol. 5-6 of Applications of Mathematics, (Springer, New York, U.S.A., 1977). 3
56. LISA: Pre-phase A report, December 1998, MPQ 223, (Max-Planck-Institut für Quantenoptik, Garching, Germany, 1998). 2
57. McDonough, R.N., and Whalen, A.D., Detection of signals in noise, (Academic Press, San Diego, U.S.A., 1995), 2nd edition. 3
58. Meyer, C., Matrix Analysis and Applied Linear Algebra, (SIAM, Philadelphia, U.S.A., 2000). 4.4.1, 4.4.1, 4.6
59. Mohanty, S., and Dhurandhar, S.V., "Hierarchical search strategy for the detection of gravitational waves from coalescing binaries", Phys. Rev. D, 54, 7108-7128, (1996). 4.8.1
60. Mohanty, S.D., "Hierarchical search strategy for the detection of gravitational waves from coalescing binaries: Extension to post-Newtonian waveforms", Phys. Rev. D, 57, 630-658, (1998). Related online version (cited on 08 January 2005): http://arXiv.org/abs/gr-qc/9703081. 4.5.2, 4.8.1
61. Mohanty, S.D., "A robust test for detecting non-stationarity in data from gravitational wave detectors", Phys. Rev. D, 61, 122002-1-12, (2000). Related online version (cited on 08 January 2005): http://arXiv.org/abs/gr-qc/ 9910027. 4.11
62. Nayak, K.R., Pai, A., Dhurandhar, S.V., and Vinet, J.-Y., "Improving the sensitivity of LISA", Class. Quantum Grav., 20, 1217-1232, (2003). 4.10
63. Nicholson, D., Dickson, C.A., Watkins, W.J., Schutz, B.F., Shuttleworth, J., Jones, G.S., Robertson, D.I., MacKenzie, N.L., Strain, K.A., Meers, B.J., Newton, G.P., Ward, H., Cantley, C.A., Robertson, N.A., Hough, J., Danzmann, K., Niebauer, T.M., Rüdiger, A., Schilling, R., Schnupp, L., and Winkler, W., "Results of the first coincident observations by two laserinterferometric gravitational wave detectors", Phys. Lett. A, 218, 175-180, (1996). 1
64. Nicholson, D., and Vecchio, A., "Bayesian bounds on parameter estimation accuracy for compact coalescing binary gravitational wave signals", Phys. Rev. D, 57, 4588-4599, (1998). Related online version (cited on 08 January 2005): http : //arXiv.org/abs/gr-qc/9705064. 4.8.3, 4.8.3
65. Niebauer, T.M., Rüdiger, A., Schilling, R., Schnupp, L., Winkler, W., and Danzmann, K., "Pulsar search using data compression with the Garching gravitational wave detector", Phys. Rev. D, 47, 3106-3123, (1993). 1
66. Owen, B.J., "Search templates for gravitational waves from inspiraling binaries: Choice of template spacing", Phys. Rev. D, 53, 6749-6761, (1996). Related online version (cited on 08 January 2005): http://arXiv.org/abs/gr-qc/9511032. 1, 4.4.1, 4.5.2, 4.6
67. Pai, A., Dhurandhar, S.V., and Bose, S., "Data-analysis strategy for detecting gravitationalwave signals from inspiraling compact binaries with a network of laser-interferometric detectors", Phys. Rev. D, 64, 042004-1-30, (2001). Related online version (cited on 08 January 2005): http://arXiv.org/ abs/gr-qc/0009078. 4.10
68. Poor, H.V., An Introduction to Signal Detection and Estimation, (Springer, New York, U.S.A., 1994), 2nd edition. 3
69. Prince, T.A., Tinto, M., Larson, S.L., and Armstrong, J.W., "The LISA optimal sensitivity", Phys. Rev. D, 66, 122002-1-7, (2002). 4.10
70. Rife, D.C., and Boorstyn, R.R., "Single tone parameter estimation from discrete-time observations", IEEE Transactions on Information Theory, 20, 591-598, (1974). 4.8.3
71. Rowan, S., and Hough, J., "Gravitational Wave Detection by Interferometry (Ground and Space)", Living Rev. Relativity, 3, (2000). URL (cited on 08 January 2005): http://relativity.livingreviews.org/lrr-2000-3. 2
72. Rubbo, L.J., Cornish, N.J., and Poujade, O., "Forward modeling of space-borne gravitational wave detectors", Phys. Rev. D, 69, 082003-1-14, (2003). Related online version (cited on 08 January 2005): http://arXiv.org/abs/ gr-qc/0311069. 2
73. Sathyaprakash, B.S., and Dhurandhar, S.V., "Choice of filters for the detection of gravitational waves from coalescing binaries", Phys. Rev. D, 44, 3819-3834, (1991). 4.6
74. Schutz, B.F., "Determining the nature of the Hubble constant", Nature, 323, 310, (1986). 1
75. Schutz, B.F., ed., Gravitational Wave Data Analysis, Proceedings of the NATO Advanced Research Workshop held at Dyffryn House, St. Nichols, Cardiff, Wales, 6-9 July 1987, vol. 253 of NATO ASI Series C, (Kluwer, Dordrecht, Netherlands; Boston, U.S.A., 1989). 1
76. Schutz, B.F., "Data processing, analysis and storage for interferometric antennas", in Blair, D.G., ed., The Detection of Gravitational Waves, 406-452, (Cambridge University Press, Cambridge, U.K.; New York, U.S.A., 1991). 1, 4.8.2
77. Sengupta, S.A., Dhurandhar, S.V., and Lazzarini, A., "Faster implementation of the hierarchical search algorithm for detection of gravitational waves from inspiraling compact binaries", Phys. Rev. D, 67, 082004-1-14, (2003). 4.8.1
78. Tagoshi, H. at al. (The TAMA Collaboration), "First search for gravitational waves from inspiraling compact binaries using TAMA300 data", Phys. Rev. D, 63, 062001-1-5, (2001). Related online version (cited on 08 January 2005): http://arXiv.org/abs/gr-qc/0012010. 1
79. Tanaka, T., and Tagoshi, H., "Use of new coordinates for the template space in hierarchical search for gravitational waves from inspiraling binaries", Phys. Rev. D, 62, 082001-1-8, (2000). Related online version (cited on 08 January 2005): http://arXiv.org/abs/gr-qc/0001090. 4.7, 4.8.1
80. Thorne, K.S., "Gravitational radiation", in Hawking, S.W., and Israel, W., eds., Three Hundred Years of Gravitation, 386-391, (Cambridge University Press, Cambridge, U.K.; New York, U.S.A., 1987). 1, 2
81. Tinto, M., and Armstrong, J.W., "Cancellation of laser noise in an unequal-arm interferometer detector of gravitational radiation", Phys. Rev. D, 59, 102003-1-11, (1999). 2
82. Table of Q Functions, RAND Research Memorandum, M-339, (U.S. Air Force, Rand Corporation, Santa Monica, U.S.A., 1950). 4.5.1
83. Van Trees, H.L., Detection, Estimation and Modulation Theory. Part 1: Detection, Estimation, and Linear Modulation Theory, number 1, (Wiley, New York, U.S.A., 1968). 3, 4.8.3
84. Wainstein, L.A., and Zubakov, V.D., Extraction of signals from noise, (Prentice-Hall, Englewood Cliffs, U.S.A., 1962). 3
85. Weber, J., "Evidence for discovery of gravitational radiation", Phys. Rev. Lett., 22, 1320-1324, (1969). 1
86. Wong, E., Introduction to Random Processes, (Springer, New York, U.S.A., 1983). 3
87. Wong, E., and Hajek, B., Stochastic Processes in Engineering Systems, (Springer, New York, U.S.A., 1985). 3
88. Woodward, P.M., Probability and information theory with applications to radar, (Pergamon Press, London, U.K., 1953). 3
89. Zieliński, R., "Theory of parameter estimation", in Królak, A., ed., Mathematics of Gravitation. Part II: Gravitational Wave Detection, Proceedings of the Workshop on Mathematical Aspects of Theories of Gravitation, held in Warsaw, February 29-March 30, 1996, vol. 41(II) of Banach Center Publications, 209-220, (Institute of Mathematics, Polish Academy of Sciences, Warsaw, Poland, 1997). 4