Abstract
This chapter and its companion form an extended version of notes provided to participants in the Valencia September 2004 summer school on Data Analysis in Cosmology. The lectures offer a pedagogical introduction to the problem of estimating the power spectrum from galaxy surveys. The intention is to focus on concepts rather than on technical detail, but enough mathematics is provided to point the student in the right direction.
This first lecture presents background material. It collects some essential definitions, discusses traditional methods for measuring power, notably the Feldman–Kaiser–Peacock [2] method, and introduces Bayesian analysis, Fisher matrices, and maximum likelihood. For pedagogy and brevity, several derivations are set as exercises for the reader. At the summer school, multiple choice questions, included herein, were used to convey some didactic ideas, and provoked a little lively debate.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
Baumgart, D.J., Fry, J.N.: Fourier spectra of three-dimensional data. ApJ 375, 25 (1991)
Feldman, H.A., Kaiser, N., Peacock, J.A.: Power spectrum analysis of three-dimensional redshift surveys. ApJ 426, 23–37 (1994)
Fisher, R.A.: The logic of inductive inference. J. Roy. Stat. Soc. 98, 39–54 (1935)
Fisher, K.B., Scharf, C.A., Lahav, O.: A spherical harmonic approach to redshift distortion and a measurement of Ω0 from the 1.2 Jy IRAS redshift survey. MNRAS, 266, 219 (1994)
Hamilton, A.J.S.: Towards optimal measurement of power spectra - I. Minimum variance pair weighting and the Fisher matrix. MNRAS 289, 285 (1997)
Heavens, A.F., Taylor, A.N.: A spherical harmonic analysis of redshift space. MNRAS 275, 483–497 (1995)
Kendall, M.G., Stuart, A.: The Advanced Theory of Statistics. Hafner Publishing, New York (1967)
Komatsu, E., et al. (15 authors; WMAP collaboration): First-Year Wilkinson Microwave Anisotropy Probe (WMAP) observations: tests of Gaussianity, ApJS 148, 119 (2003)
Peebles, P.J.E.: Statistical analysis of catalogues of extragalactic objects. I. Theory, ApJ 185, 413–440 (1973)
Tegmark, M.: How to measure CMB power spectra without losing information. Phys. Rev. D 55, 5895 (1997)
Tegmark, M., Taylor, A., Heavens, A.: Karhunen-Loeve eigenvalue problems in cosmology: how should we tackle large data sets?. ApJ 480, 22 (1997)
Yu, J.T., Peebles, P.J.E.: Superclusters of galaxies?. ApJ 158, 103–113 (1969)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2008 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Hamilton, A. (2008). Power Spectrum Estimation. I. Basics. In: Martinez, V., Saar, E., Gonzales, E., Pons-Borderia, M. (eds) Data Analysis in Cosmology. Lecture Notes in Physics, vol 665. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-44767-2_12
Download citation
DOI: https://doi.org/10.1007/978-3-540-44767-2_12
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-23972-7
Online ISBN: 978-3-540-44767-2
eBook Packages: Physics and AstronomyPhysics and Astronomy (R0)