Inference with minimal Gibbs free energy in information field theory

Physical Review E - Statistical, Nonlinear, and Soft Matter Physics

Volumn 82, Issue 5, 2010, Pages

  Enßlin, Torsten A ^a   Weig, Cornelius ^a  

^a MAX PLANCK INSTITUT FÜR ASTROPHYSIK   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

FIELD THEORY; GAMMA-RAY ASTRONOMY; GAUSSIAN APPROXIMATIONS; GAUSSIAN SIGNALS; GAUSSIANS; INFERENCE PROBLEM; KNOWLEDGE STATE; LOG-NORMAL; NON-GAUSSIAN; NON-LINEAR; NONGAUSSIAN SIGNALS; POINT-SPREAD FUNCTION; POISSONIAN; POSTERIOR PROBABILITY; RED SHIFT; RENORMALIZATION;

FREE ENERGY; GAMMA RAYS; GAUSSIAN NOISE (ELECTRONIC); GIBBS FREE ENERGY; MEASUREMENT THEORY; OPTICAL TRANSFER FUNCTION;

GAUSSIAN DISTRIBUTION;

EID: 78651370395     PISSN: 15393755     EISSN: 15502376     Source Type: Journal    
DOI: 10.1103/PhysRevE.82.051112     Document Type: Article

References (54)

1. E. T. Jaynes, Phys. Rev. 106, 620 (1957). 10.1103/PhysRev.106.620
2. E. T. Jaynes, Phys. Rev. 108, 171 (1957). 10.1103/PhysRev.108.171
3. J. N. Fry, Astrophys. J. 289, 10 (1985). 10.1086/162859
4. E. Bertschinger, Astrophys. J. 323, L103 (1987). 10.1086/185066
5. W. Bialek and A. Zee, Phys. Rev. Lett. 58, 741 (1987). 10.1103/PhysRevLett.58.741
6. W. Bialek and A. Zee, Phys. Rev. Lett. 61, 1512 (1988). 10.1103/PhysRevLett.61.1512
7. W. Bialek, C. G. Callan, and S. P. Strong, Phys. Rev. Lett. 77, 4693 (1996). 10.1103/PhysRevLett.77.4693
8. J. C. Lemm, e-print arXiv:physics/9912005.
9. T. A. Enßlin, M. Frommert, and F. S. Kitaura, Phys. Rev. D 80, 105005 (2009). 10.1103/PhysRevD.80.105005
10. J. C. Lemm, Bayesian Field Theory (Johns Hopkins University Press, Baltimore, Maryland, 2003).
11. T. A. Enßlin and M. Frommert, e-print arXiv:1002.2928.
12. R. T. Cox, Am. J. Phys. 14, 1 (1946). 10.1119/1.1990764
13. R. T. Cox, Am. J. Phys. 31, 66 (1963). 10.1119/1.1969248
14. S. F. Gull and G. J. Daniell, Nature (London) 272, 686 (1978). 10.1038/272686a0
15. J. Skilling, A. W. Strong, and K. Bennett, Mon. Not. R. Astron. Soc. 187, 145 (1979).
16. R. K. Bryan and J. Skilling, Mon. Not. R. Astron. Soc. 191, 69 (1980).
17. S. F. Burch, S. F. Gull, and J. Skilling, Comput. Vis. Graph. Image Process. 23, 113 (1983). 10.1016/0734-189X(83)90108-1
18. S. F. Gull and J. Skilling, Indirect Imaging. Measurement and Processing for Indirect Imaging (Cambridge University Press, Cambridge, England, 1983), p. 267.
19. S. Sibisi, J. Skilling, R. G. Brereton, E. D. Laue, and J. Staunton, Nature (London) 311, 446 (1984). 10.1038/311446a0
20. D. M. Titterington and J. Skilling, Nature (London) 312, 381 (1984). 10.1038/312381b0
21. J. Skilling and R. K. Bryan, Mon. Not. R. Astron. Soc. 211, 111 (1984).
22. R. K. Bryan and J. Skilling, J. Mod. Opt. 33, 287 (1986). 10.1080/713821934
23. S. F. Gull, in Maximum Entropy and Bayesian Methods, edited by, J. Skilling, (Kluwer Academic Publishers, Dordtrecht, 1989), pp. 53-71.
24. S. F. Gull and J. Skilling, The MEMSYS5 User's Manual (Maximum Entropy Data Consultants Ltd., Royston, 1990).
25. J. Skilling, in Maximum Entropy and Bayesian Methods, edited by, G. J. Erickson,,, J. T. Rychert,, and, C. R. Smith,, 1998), p. 1.
26. S. Kullback and R. Leibler, Ann. Math. Stat. 22, 79 (1951). 10.1214/aoms/1177729694
27. E. Hubble, Astrophys. J. 79, 8 (1934). 10.1086/143517
28. F. S. Kitaura, J. Jasche, C. Li, T. A. Enßlin, R. B. Metcalf, B. D. Wandelt, G. Lemson, and S. D. M. White, Mon. Not. R. Astron. Soc. 400, 183 (2009). 10.1111/j.1365-2966.2009.15470.x
29. D. Layzer, Astron. J. 61, 383 (1956). 10.1086/107366
30. P. Coles and B. Jones, Mon. Not. R. Astron. Soc. 248, 1 (1991).
31. R. K. Sheth, Mon. Not. R. Astron. Soc. 277, 933 (1995).
32. I. Kayo, A. Taruya, and Y. Suto, Astrophys. J. 561, 22 (2001). 10.1086/323227
33. R. Vio, P. Andreani, and W. Wamsteker, PASP 113, 1009 (2001). 10.1086/322919 (Pubitemid 33405875)
34. M. C. Neyrinck, I. Szapudi, and A. S. Szalay, Astrophys. J. 698, L90 (2009). 10.1088/0004-637X/698/2/L90
35. J. Jasche and F. S. Kitaura, Mon. Not. R. Astron. Soc. 407, 29 (2010). 10.1111/j.1365-2966.2010.16897.x
36. J. Jasche, F. S. Kitaura, C. Li, and T. A. Enßlin, e-print arXiv:0911.2498.
37. F. Kitaura, J. Jasche, and R. B. Metcalf, Mon. Not. R. Astron. Soc. 403, 589 (2010). 10.1111/j.1365-2966.2009.16163.x
38. C. Weig and T. A. Enßlin, e-print arXiv:1003.1311.
39. T. J. Hebert and R. Leahy, IEEE Trans. Signal Process. 40, 2290 (1992). 10.1109/78.157228 (Pubitemid 23562491)
40. T. J. Cornwell and K. F. Evans, Astron. Astrophys. 143, 77 (1985).
41. G. Wang, L. Fu, and J. Qi, Phys. Med. Biol. 53, 593 (2008). 10.1088/0031-9155/53/3/006 (Pubitemid 351496207)
42. C. Oh and B. Roy Frieden, Opt. Commun. 282, 2489 (2009). 10.1016/j.optcom.2009.03.043
43. D. H. Roberts, J. Lehar, and J. W. Dreher, Astron. J. 93, 968 (1987). 10.1086/114383
44. G. B. Rybicki and W. H. Press, Astrophys. J. 398, 169 (1992). 10.1086/171845
45. J. Li and P. Stoica, IEEE Trans. Signal Process. 44, 1469 (1996). 10.1109/78.506612
46. P. Stoica, H. Li, and J. Li, IEEE Signal Process. Lett. 6, 205 (1999). 10.1109/97.774866
47. P. Stoica, E. G. Larsson, and J. Li, Astron. J. 120, 2163 (2000). 10.1086/301572
48. P. K. Kitanidis, Water Resour. Res. 22, 499 (1986). 10.1029/ WR022i004p00499
49. G. Rydbeck, Astrophys. J. 675, 1304 (2008). 10.1086/527270
50. U. Seljak, Astrophys. J. 503, 492 (1998). 10.1086/306019 (Pubitemid 128120332)
51. B. D. Wandelt, D. L. Larson, and A. Lakshminarayanan, Phys. Rev. D 70, 083511 (2004). 10.1103/PhysRevD.70.083511 (Pubitemid 44947544)
52. H. K. Eriksen, I. J. O'Dwyer, J. B. Jewell, B. D. Wandelt, D. L. Larson, K. M. Górski, S. Levin, A. J. Banday, and P. B. Lilje, Astrophys. J. 155, 227 (2004). 10.1086/425219 (Pubitemid 40131821)
53. J. Jewell, S. Levin, and C. H. Anderson, Astrophys. J. 609, 1 (2004). 10.1086/383515 (Pubitemid 39046726)
54. J. Jasche, F. S. Kitaura, B. D. Wandelt, and T. A. Enßlin, Mon. Not. R. Astron. Soc. 406, 60 (2010).