Bayesian analysis of the polarization of distant radio sources: Limits on cosmological birefringence

Physical Review D - Particles, Fields, Gravitation and Cosmology

Volumn 56, Issue 12, 1997, Pages 7507-7512

  Loredo, Thomas J ^a   Flanagan, Eanna E ^a   Wasserman, Ira M ^a  

^a Department of Obstetrics Gynecology   (United States)

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Indexed keywords

EID: 0039584868     PISSN: 15507998     EISSN: 15502368     Source Type: Journal    
DOI: 10.1103/PhysRevD.56.7507     Document Type: Article

References (11)

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2. J. P. Leahy, astro-ph/9704285.
3. J. F. C. Wardle, R. A. Perley, and M. H. Cohen, Phys. Rev. Lett. 79, 1801 (1997).
4. D. J. Eisenstein and E. F. Bunn, Phys. Rev. Lett. 74, 1957 (1997).
5. S. M. Carroll and G. B. Field, astro-ph/9704263.
6. More precisely, Nodland and Ralston took (Formula presented) where (Formula presented) is an integer such that (Formula presented) and (Formula presented); for each galaxy they chose between (Formula presented) and (Formula presented) according to the sign of (Formula presented) for the candidate (Formula presented) under consideration.
7. K. V. Mardia, Statistics of Directional Data (Academic, New York, 1972);
8. N. I. Fisher, T. Lewis, and B. J. J. Embleton, Statistical Analysis of Spherical Data (Cambridge University Press, Cambridge, England, 1987).
9. A brief introduction to Bayesian terminology and notation as used here appears in Sec. 2 of P. C. Gregory and T. J. Loredo, Astrophys. J. 398, 146 (1992); see also D. S. Sivia, Data Analysis: A Bayesian Tutorial (Clarendon, Oxford, 1996).
10. H. Jeffreys, Theory of Probability (Oxford University Press, Oxford, 1961).
11. We calculated this integral and other similar integrals over more than two dimensions using the adaptive quadrature algorithm given by A. C. Genz and A. A. Malik, J. Comput. Appl. Math. 6, 295 (1980).