Statistical challenges in the analysis of cosmic microwave background radiation

Annals of Applied Statistics

Volumn 3, Issue 1, 2009, Pages 61-95

  Cabella, Paolo ^a   Marinucci, Domenico ^a  

^a UNIVERSITY OF ROME TOR VERGATA   (Italy)

Author keywords

Angular power spectrum; Bispectrum; Cosmic microwave background radiation; Local curvature; Spherical random fields; Spherical wavelets

Indexed keywords

EID: 70350109950     PISSN: 19326157     EISSN: 19417330     Source Type: Journal    
DOI: 10.1214/08-AOAS190     Document Type: Review

References (52)

1. Adler, R. J. and Taylor, J. E. (2007). Random Fields and Geometry. Springer, New York.
2. Antoine, J.-P. and Vandergheynst, P. (1999). Wavelets on the sphere: A group-theoretic approach. Appl. Comput. Harmon. Anal. 7 262-291.
3. Antoine, J.-P. and Vandergheynst, P. (2007). Wavelets on the sphere and other conic sections. J. Fourier Anal. Appl. 13 369-386.
4. Babich, D., Creminelli, P. and Zaldarriaga, M. (2004). The shape of non-Gaussianities. J. Cosmology and Astroparticle Phys. 8 009.
5. Baldi, P. and Marinucci, D. (2007). Some characterizations of the spherical harmonics coefficients for isotropic random fields. Statist. Probab. Lett. 77490-496.
6. Baldi, P., Marinucci, D. and Varadarajan, V. S. V. (2007). On the characterization of isotropic Gaussian fields on homogeneous spaces of compact groups. Electron. Commun. Probab. 12 291-302.
7. Baldi, P., Kerkyacharian, G., Marinucci, D. and Picard, D. (2006). Asymptotics for spherical needlets. Ann. Statist. To appear. Available at arXiv:math/0606599.
8. Baldi, P., Kerkyacharian, G. Marinucci, D. and Picard, D. (2007). Subsampling needlet coefficients on the sphere. Bernoulli. To appear.
9. Bartolo, N., Komatsu, E., Matarrese, S. and Riotto, A. (2004). Non-Gaussianity from inflation: Theory and observations. Phys. Rept. 402 103-266.
10. Bennett, C. L., Halpern, M., Hinshaw, G., Jarosik, N., Kogut, A., Limon, M., Meyer, S. S., Page, L., Spergel, D. N., Tucker, G. S., Wollack, E., Wright, E. L., Barnes, C., Greason, M. R., Hill, R. S., Komatsu, E., Nolta, M. R., Odegard, N., Peiris, H. V., Verde, L. and Weiland, J. L. (2003). First-year Wilkinson Microwave Anisotropy Probe (WMAP) observations: Preliminary maps and basic results. Astrophys. J. Suppl. Ser. 148 1-27.
11. Bishop, R. L. and Goldberg, S. (1980). Tensor Analysis on Manifolds. Dover, New York.
12. NL from WMAP data. Mon. Not. Roy. Astron. Soc. 358 684-692.
13. NL with WMAP data. Mon. Not. Roy. Astron. Soc. 369 819-824.
14. Cruz, M., Cayon, L., Martinez-Gonzalez, E., Vielva, P. and Jin, J. (2007). The non-Gaussian cold spot in the 3-year WMAP data. Astrophys. J. 655 11-20.
15. Cruz, M., Cayon, L., Martinez-Gonzalez, E. and Vielva, P. (2006). The non-Gaussian cold spot in WMAP: Significance, morphology and foreground contribution. Mont. Not. Roy. Astron. Soc. 369 57-67.
16. de Gasperis, G., Balbi, A., Cabella, P., Natoli, P. and Vittorio, N. (2005). ROMA: A map-making algorithm for polarised CMB data sets. Astronomy and Astrophysics 436 1159-1165.
17. Dodelson, S. (2003). Modern Cosmology. Academic Press, Amsterdam.
18. Doré, O., Colombi, S. and Bouchet, F. R. (2003). Probing non-Gaussianity using local curvature. Mon. Not. Roy. Astron. Soc. 344 905-916. Available at arXiv:astro-ph/0202135.
19. Doroshkevich, A. G., Naselsky, P. D., Verkhodanov, O. V., Novikov, D. I., Turchaninov, V. I., Novikov, I. D., Christensen, P. R. and Chiang, L.-Y. (2005). Gauss-Legendre Sky Pixelization (GLESP) for CMB Maps. Int. J. Mod. Phys. D 14 275. Available at arXiv:astro-ph/0305537.
20. Guilloux, F., Fay, G. and Cardoso, J.-F. (2007). Practical wavelet design on the sphere. Appl. Comput. Harmon. Anal. To appear.
21. Gorski, K. M., Hivon, E., Banday, A. J., Wandelt, B. D., Hansen, F. K., Reinecke, M. and Bartelman, M. (2005). HEALPix-a framework for high resolution discretization, and fast analysis of data distributed on the sphere. Astrophys. J. 622 759-771. Available at arXiv:astro-ph/0409513.
22. Hamann, J. and Wong, Y. Y. Y. (2008). The effects of Cosmic Microwave Background (CMB) temperature uncertainties on cosmological parameter estimation. Journal of Cosmology and Astroparticle Physics Issue 03 025.
23. Hansen, F. K., Cabella, P., Marinucci, D. and Vittorio, N. (2004). Asymmetries in the local curvature of the WMAP data. Astrophys. J. Lett. L67-L70.
24. Hausman, J. A. (1978). Specification tests in econometrics. Econometrica 61251-1271.
25. Hikage, C., Matsubara, T., Coles, P., Liguori, M., Hansen, F. K. and Matarrese, S. (2008). Primordial Non-Gaussianity from Minkowski functionals of the WMAP temperature anisotropies. Preprint. Available at arXiv:0802.3677.
26. Hinshaw, G., Weiland, J. L., Hill, R. S., Odegard, N., Larson, D., Bennett, C. L., Dunkley, J., Gold, B., Greason, M. R., Jarosik, N., Komatsu, E., Nolta, M. R., Page, L., Spergel, D. N., Wollack, E., Halpern, M., Kogut, A., Limon, M., Meyer, S. S., Tucker, G. S. and Wright, E. L. (2008). Five-year Wilkinson Microwave Anisotropy Probe (WMAP) observations: Data processing, sky maps, and basic results. Eprint. Available at arXiv:0803.0732.
27. Hivon, E., Gorski, K. M., Netterfield, C. B., Crill, B. P., Prunet, S. and Hansen, F. K. (2002). MASTER of the cosmic microwave background anisotropy power spectrum: A fast method for statistical analysis of large and complex cosmic microwave background data sets. Astrophys. J. 567 2-17.
28. Hu, W. (2001). Angular trispectrum of the cosmic microwave background. Phys. Rev. D 64 id.083005.
29. Keihänen, E., Kurki-Suonio, H. and Poutanen, T. (2005). MADAM-a map-making method for CMB experiments. Mont. Not. Roy. Astron. Soc. 360390-400.
30. Kerkyacharian, G., Petrushev, P., Picard, D. and Willer, T. (2007). Needlet algorithms for estimation in inverse problems. Electron. J. Statist. 1 30-76.
31. Lan, X. and Marinucci, D. (2008). The needlets bispectrum. Electron. J. Statist. 2 332-367.
32. Marinucci, D. (2006). High-resolution asymptotics for the angular bispectrum of spherical random fields. Ann. Statist. 34 1-41. Available at arXiv:math/0502434.
33. Marinucci, D. (2008). A central limit theorem and higher order results for the angular bispectrum. Probab. Theory Related Fields 3-4 389-409. Available at arXiv:math/0509430.
34. Marinucci, D. and Peccati, G. (2007). Group representations and high-resolution central limit theorems for subordinated spherical random fields. Available at arXiv:0706.2851.
35. Marinucci, D. and Peccati, G. (2008). Representations of SO(3) and angular polyspectra. Submitted. Available at arXiv:0807.0687.
36. Marinucci, D., Pietrobon, D., Balbi, A., Baldi, P., Cabella, P., Kerkyacharian, G., Natoli, P., Picard, D. and Vittorio, N. (2008). Spherical needlets for CMB data analysis. Mont. Not. Roy. Astron. Soc. 383 539-545. Available at arXiv:0707/0844.
37. McEwen, J. D., Vielva, P., Wiaux, Y., Barreiro, R. B., Cayon, L., Hobson, M. P., Lasenby, A. N., Martinez-Gonzalez, E. and Sanz, J. (2007). Cosmological applications of a wavelet analysis on the sphere. J. Fourier Anal. Appl. 13495-510.
38. Narcowich, F. J., Petrushev, P. and Ward, J. D. (2006a). Localized tight frames on spheres. SIAM J. Math. Anal. 38 574-594.
39. Narcowich, F. J., Petrushev, P. and Ward, J. D. (2006b). Decomposition of Besov and Triebel-Lizorkin spaces on the sphere. J. Funct. Anal. 238530-564.
40. Natoli, P., Degasperis, G., Marinucci, D. and Vittorio, N. (2002). Non-iterative methods to estimate the in-flight noise properties of CMB detectors. Astronomy and Astrophysics 383 1100-1112.
41. Park, C.-G. (2004). Non-Gaussian signatures in the temperature fluctuation observed by the Wilkinson microwave anisotropy probe. Mont. Not. Roy. Astron. Soc. 349 313-320.
42. Patanchon, G., Delabrouille, J., Cardoso, J.-F. and Vielva, P. (2005). CMB and foreground in WMAP first-year data. Mont. Not. Roy. Astronom. Soc. 3641185-1194.
43. Pietrobon, D., Balbi, A. and Marinucci, D. (2006). Integrated Sachs-Wolfe effect from the cross correlation of WMAP3 year and the NRAO VLA sky survey data: New results and constraints on dark energy. Phys. Rev. D 74 043524.
44. Polenta, G., Marinucci, D., Balbi, A., De Bernardis, P., Hivon, E., Masi, S., Natoli, P. and Vittorio, N. (2005). Unbiased estimation of angular power spectra.J. Cosmology and Astroparticle Physics Issue 11 n. 1.
45. Seljak, U. and Zaldarriaga, M. (1996). Line-of-sight integration approach to cosmic microwave background anisotropies. Astrophys. J. 469 437.
46. Smoot, G. F., Bennett, C. L., Kogut, A., Wright, E. L., Aymon, J., Boggess, N. W., Cheng, E. S., de Amici, G., Gulkis, S., Hauser, M. G., Hinshaw, G., Jackson, P. D., Janssen, M., Kaita, E., Kelsall, T., Keegstra, P., Lineweaver, C., Loewenstein, K., Lubin, P., Mather, J., Meyer, S. S., Moseley, S. H., Murdock, T., Rokke, L., Silverberg, R. F., Tenorio, L., Weiss, R. and Wilkinson, D. T. (1992). Structure in the COBE differential microwave radiometer first-year maps. Astrophys. J. Part 2 Lett. 396 L1-L5.
47. Varshalovich, D. A., Moskalev, A. N. and Khersonskii, V. K. (1988). Quantum Theory of Angular Momentum. World Scientific, Singapore.
48. Vielva, P., Martínez-González, E., Gallegos, J. E., Toffolatti, L. and Sanz, J. L. (2003). Point source detection using the spherical Mexican Hat Wavelet on simulated all-sky planck maps. Mont. Not. Roy. Astron. Soc. 344 89-104.
49. Vilenkin, N. J. and Klymik, A. U. (1991). Representation of Lie Groups and Special Functions. 1. Simplest Lie Groups Special Functions and Integral Transforms. Mathematics and Its Applications (Soviet Series) 72. Kluwer Academic, Dordrecht.
50. NL) in the WMAP 3-year data at above 99.5% confidence. Available at arXiv:0712.1148.
51. Wiaux, Y., Jacques, L. and Vandergheynst, P. (2005). Correspondence principle between spherical and Euclidean wavelets. Astrophys. J. 63215-28.
52. Wiaux, Y., McEwen, J. D. and Vielva, P. (2007). Complex data processing: Fast wavelet analysis on the sphere. J. Fourier Anal. Appl. 13 477-494.