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Bayesian inference in physics

Udo von Toussaint*

Udo von Toussaint*

  • Max-Planck-Institute for Plasmaphysics, Boltzmannstrasse 2, 85748 Garching, Germany

  • *udo.v.toussaint@ipp.mpg.de
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Rev. Mod. Phys. 83, 943 – Published 19 September, 2011

DOI: https://doi.org/10.1103/RevModPhys.83.943

Abstract

Bayesian inference provides a consistent method for the extraction of information from physics experiments even in ill-conditioned circumstances. The approach provides a unified rationale for data analysis, which both justifies many of the commonly used analysis procedures and reveals some of the implicit underlying assumptions. This review summarizes the general ideas of the Bayesian probability theory with emphasis on the application to the evaluation of experimental data. As case studies for Bayesian parameter estimation techniques examples ranging from extra-solar planet detection to the deconvolution of the apparatus functions for improving the energy resolution and change point estimation in time series are discussed. Special attention is paid to the numerical techniques suited for Bayesian analysis, with a focus on recent developments of Markov chain Monte Carlo algorithms for high-dimensional integration problems. Bayesian model comparison, the quantitative ranking of models for the explanation of a given data set, is illustrated with examples collected from cosmology, mass spectroscopy, and surface physics, covering problems such as background subtraction and automated outlier detection. Additionally the Bayesian inference techniques for the design and optimization of future experiments are introduced. Experiments, instead of being merely passive recording devices, can now be designed to adapt to measured data and to change the measurement strategy on the fly to maximize the information of an experiment. The applied key concepts and necessary numerical tools which provide the means of designing such inference chains and the crucial aspects of data fusion are summarized and some of the expected implications are highlighted.

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References (469)

  1. Abramowitz, M., and I. Stegun, 1965, NBS Handbook of Mathematical Functions (U.S. GPO, Washington, DC).
  2. Adams, R. P., and D. J. MacKay, 2007, Bayesian Online Changepoint Detection, Technical Report arXiv:0710.3742v1 [stat.ML], University of Cambridge.
  3. Agarwal, D. K., and A. E. Gelfand, 2005, Stat. Comput. 15, 61.
  4. Ahlers, H., and A. Engel, 2008, Eur. Phys. J. B 62, 357.
  5. Aji, S. M., and R. J. McEliece, 2000, IEEE Trans. Inf. Theory 46, 325.
  6. Akaike, H., 1974, IEEE Trans. Autom. Control 19, 716.
  7. Albert, J., 2009, Bayesian Computation with R (Springer, New York).
  8. Alimov, V. K., M. Mayer, and J. Roth, 2005, Nucl. Instrum. Methods Phys. Res., Sect. B 234, 169.
  9. Amsel, G., and W. A. Lanford, 1984, Annu. Rev. Nucl. Part. Sci. 34, 435.
  10. Andrieu, C., and A. Doucet, 1999, IEEE Trans. Signal Process. 47, 2667.
  11. Andrieu, C., and J. Thoms, 2008, Stat. Comput. 18, 343.
  12. Arshad, S., J. Cordey, D. McDonald, A. Dinklage, J. Farthing, R. Fischer, E. Joffrin, M. von Hellermann, C. Roach, and JET EFDA contributors, 2007, EFDA-JET-Report EFDA-JET-PR(06)26.
  13. Atkinson, A. C., A. Donev, and R. Tobias, 2007, Optimum Experimental Designs, with SAS (Oxford University Press, Oxford, UK).
  14. Bagchi, P., and J. Kadane, 1991, Can. J. Stat. 19, 67.
  15. Bailey, T., and H. Durrant-Whyte, 2006, Robotics and Automation Magazine 13, 108.
  16. Balden, M., and J. Roth, 2000, J. Nucl. Mater. 280, 39.
  17. Baraffe, I., G. Chabrier, and T. Barman, 2010, Rep. Prog. Phys. 73, 016901.
  18. Bartelmann, M., 2010, Rev. Mod. Phys. 82, 331.
  19. Bassett, B. A., S. Tsujikawa, and D. Wands, 2006, Rev. Mod. Phys. 78, 537.
  20. Basseville, M., and I. Nikiforov, 1993, Detection of Abrupt Changes: Theory and Application (Prentice-Hall, Englewood Cliffs, NJ).
  21. Belisle, C., 1998, Can. J. Stat. 26, 629.
  22. Bellman, R. E., 1957, Dynamic Programming (Princeton University Press, Princeton, NJ).
  23. Bennett, C. L., et al., 2003, Astr. Phys. J. 583, 1.
  24. Berger, J. O., 1985, Statistical Decision Theory and Bayesian Analysis (Springer, New York).
  25. Berger, J. O., and J. M. Bernardo, 1992, in Bayesian Statistics, edited by J. Bernardo, J. Berger, A. Dawid, and A. Smith (Oxford University Press, Oxford), Vol. 4, p. 35.
  26. Berger, J. O., and D. A. Berry, 1988, Am. Sci. 76, 159 [http://www.jstor.org/stable/27855070].
  27. Berger, J. O., B. Boukai, and Y. Wang, 1997, Stat. Sci. 12, 133.
  28. Berger, J. O., L. D. Brown, and R. L. Wolpert, 1994, Ann. Stat. 22, 1787.
  29. Berger, J. O., J. K. Gosh, and N. Mukhopadhyay, 2003, J. Stat. Plann. Infer. 112, 241.
  30. Berger, J. O., and L. R. Pericchi, 1988, in Model Selection, edited by P. Lahiri, IMS Lecture Notes—Monograph Series Vol. 38 (IMS, Beachwood, OH), p. 135.
  31. Berger, J. O., and T. Sellke, 1987, J. Am. Stat. Assoc. 82, 112.
  32. Berger, J. O., and R. L. Wolpert, 1988, The Likelihood Principle (IMS, Hayward, CA), 2nd ed.
  33. Bernardo, J. M., 1979a, Ann. Stat. 7, 686.
  34. Bernardo, J. M., 1979b, J. R. Stat. Soc. Ser. B 41, 113 [http://www.jstor.org/stable/2985028].
  35. Bernardo, J. M., 2005, Reference Analysis (Elsevier, Amsterdam).
  36. Bernardo, J. M., and A. F. M. Smith, 2000, Bayesian Theory (Wiley, Chichester, UK).
  37. Bickel, P., 1981, Ann. Stat. 9, 1301.
  38. Birnbaum, A., 1962, J. Am. Stat. Assoc. 57, 269.
  39. Bishop, C., 2006, Pattern Recognition and Machine Learning (Springer, New York).
  40. Bishop, C., D. Spiegelhalter, and J. Winn, 2003, in Advances in Neural Information Processing Systems, edited by S. Becker, S. Thrun, and K. Obermeyer (MIT Press, Cambridge, MA), Vol. 15, p. 793.
  41. Bittner, E., A. Nussbaumer, and W. Janke, 2008, Phys. Rev. Lett. 101, 130603.
  42. Borenstein, J., B. Everett, and L. Feng, 1996, Navigating Mobile Robots: Systems and Techniques (A.K. Peters, Ltd, Wellesley, MA).
  43. Borth, D. M., 1975, J. R. Stat. Soc. Ser. B 37, 77 [http://www.jstor.org/stable/2984993].
  44. Box, G. E. P., and G. C. Tiao, 1992, Bayesian Inference in Statistical Analysis (John Wiley, New York) (reprint from 1973).
  45. Bradley, N. L., A. C. Leopold, J. Ross, and W. Huffaker, 1999, Proc. Natl. Acad. Sci. U.S.A. 96, 9701.
  46. Bretthorst, G. L., 1988, Bayesian Spectrum Analysis and Parameter Estimation (Springer, New York).
  47. Bretthorst, G. L., 1990a, J. Magn. Reson. 88, 533.
  48. Bretthorst, G. L., 1990b, J. Magn. Reson. 88, 552.
  49. Bretthorst, G. L., 1990c, J. Magn. Reson. 88, 571.
  50. Bretthorst, G. L., 1991, J. Magn. Reson. 93, 369.
  51. Bretthorst, G. L., 1996, in Bayesian Inference and Maximum Entropy Methods in Science and Engineering, edited by G. R. Heidbreder (Kluwer Academic Publishers, Dordrecht), p. 1.
  52. Bretthorst, G. L., 2001, in Bayesian Inference and Maximum Entropy Methods in Science and Engineering, edited by A. Mohammad-Djafari, AIP Conf. Proc. 568 (AIP, New York), p. 241.
  53. Bridges, M., F. Feroz, M. P. Hobson, and A. N. Lasenby, 2009, Mon. Not. R. Astron. Soc. 400, 1075.
  54. Brockwell, A. E., and J. B. Kadane, 2003, J. Comput. Graph. Stat. 12, 566.
  55. Brooks, A., and T. Bailey, 2008, Workshop on the Algorithmic Fundamentals of Robotics 30.11.2008.
  56. Brooks, J., D. Alman, G. Federici, D. Ruzic, and D. White, 1999, J. Nucl. Mater. 266–269, 58.
  57. Brooks, S., P. Giudici, and G. Roberts, 2003, J. R. Stat. Soc. Ser. B 65, 3.
  58. Brooks, S., and G. Roberts, 1999, Biometrika 86, 710.
  59. Cappé, O., R. Douc, A. Guillin, J. M. Marin, and C. P. Robert, 2008, Stat. Comput. 18, 447.
  60. Cappé, O., S. Godsill, and E. Moulines, 2007, Proc. IEEE 95, 899.
  61. Cappé, O., A. Guillin, J. Marin, and C. Robert, 2004, J. Comput. Graph. Stat. 13, 907.
  62. Carlin, B. P., A. E. Gelfand, and A. F. M. Smith, 1992, J. Roy. Stat. Soc. C 41, 389, http://www.jstor.org/stable/2347570.
  63. Carlin, B. P., and T. A. Louis, 1998, Bayes and Empirical bayes Methods for Data Analysis (Chapman & Hall/CRC, Boca Raton).
  64. Caticha, A., 2008, Lectures on probability, entropy and statistical physics, http://arxiv.org/pdf/0808.0012.
  65. Celeux, G., M. Hurn, and C. Robert, 2000, J. Am. Stat. Assoc. 95, 957.
  66. Chaloner, K., and I. Verdinelli, 1995, Stat. Sci. 10, 273.
  67. Chambers, J., 2010, Nature (London) 467, 405.
  68. Charvin, K., K. Gallagher, G. Hampson, and R. Labourdette, 2009, Basin Research 21, 5.
  69. Chen, J., and A. K. Gupta, 2000, Parametric Statistical Change Point Analysis (Birkhäuser Verlag, Boston).
  70. Chen, M. H., Q. M. Shao, and J. G. Ibrahim, 2001, Monte Carlo Methods for Bayesian Computation (Springer, New York).
  71. Cheng, J., and M. J. Druzdzel, 2000, J. Artif. Intell. Res. 13, 155.
  72. Chernoff, H., 1972, Sequential Analysis and Optimal Design (SIAM, Philadelphia).
  73. Chick, S. E., and S. H. Ng, 2002, in Proceedings of the 2002 Winter Simulation Conference, edited by E. Yücesan, C.-H. Chen, J. L. Snowdon, and J. M. Charnes (IEEE, San Diego, CA), p. 400.
  74. Chopin, N., and C. Robert, 2007, in Bayesian Statistics, edited by J. Bernardo, M. J. Bayarri, J. Berger, A. Dawid, D. Heckermann, A. Smith, and M. West (Oxford University Press, Oxford), Vol. 8, p. 491.
  75. Chopin, N., and C. Robert, 2008, arXiv:0801.3887.
  76. Chopin, N., and C. Robert, 2010, Biometrika 97, 741.
  77. Clyde, M., and E. I. George, 2004, Stat. Sci. 19, 81.
  78. Clyde, M., P. Müller, and G. Parmigiani, 1993, in Case Studies in Bayesian Statistics, II (Springer-Verlag, Berlin), p. 278.
  79. Clyde, M. A., J. O. Berger, F. Bullard, E. B. Ford, W. H. Jefferys, R. Luo, R. Paulo, and T. Loredo, 2007, in Statistical Challenges in Modern Astronomy IV, edited by G. J. Babu and E. D. Feigelson (ASP), Vol. 371, p. 224.
  80. Clyde, M. A., and R. L. Wolpert, 2007, in Bayesian Statistics, edited by J. Bernardo, M. J. Bayarri, J. Berger, A. Dawid, D. Heckermann, A. Smith, and M. West (Oxford University Press, Oxford), Vol. 8, p. 1.
  81. Coluzza, I., and D. Frenkel, 2005, Chem. Phys. Chem. 6, 1779.
  82. Cooper, G., 1990, Artif. Intell. 42, 393.
  83. Cornebise, J., E. Moulines, and J. Olsson, 2008, Stat. Comput. 18, 461.
  84. Cornfield, J., 1969, Biometrics 25, 617.
  85. Cornu, A., and R. Massot, 1979, Compilation of Mass Spectral Data (Heyden, London).
  86. Cowell, R. G., A. P. Dawid, S. L. Lauritzen, and D. J. Spiegelhalter, 1999, Probabilistic Networks and Expert Systems (Springer, New York).
  87. Cowles, M., and B. Carlin, 1996, J. Am. Stat. Assoc. 91, 883.
  88. Cox, D. R., 2006, Principles of Statistical Inference (Cambridge University Press, Cambridge).
  89. Cox, R. T., 1946, Am. J. Phys. 14, 1.
  90. Cox, R. T., 1961, The Algebra of Probable Inference (John Hopkins Press, Baltimore, MD).
  91. Currin, C., T. Mitchell, M. Moris, and D. Ylvisaker, 1991, J. Am. Stat. Assoc. 86, 953.
  92. Daghofer, M., and W. von der Linden, R. Preuss2004, in Bayesian Inference and Maximum Entropy Methods in Science and Engineering, edited by R. Fischer, , and U. von Toussaint, AIP Conf. Proc. No.  735 (AIP, Melville, NY), p. 355.
  93. D’Agostini, G., 1999, in Bayesian Reasoning in High-Energy Physics: Principles and Applications, CERN 99-03 (CERN, Geneva).
  94. D’Agostini, G., 2003, Rep. Prog. Phys. 66, 1383.
  95. Dagum, P., and M. Luby, 1993, Artif. Intell. 60, 141.
  96. Darwiche, A., 2009, Modeling and Reasoning with Bayesian Networks (Cambridge University Press, Cambridge, UK).
  97. DasGupta, A., 1996, in Handbook of Statistics 13: Design and Analysis of Experiments, edited by S. Gosh and C. R. Rao (Elsevier, Amsterdam).
  98. Davidoff, F., 1999, Ann. Intern. Med. 130, 1019.
  99. Davis, P., and P. Rabinowitz, 1984, Methods of Numerical Integration (Academic Press, Orlando, FL).
  100. Dawid, A., 1979, J. R. Stat. Soc. Ser. B 41, 1 [http://www.jstor.org/stable/2984718].
  101. DeGroot, M. H., 1962, Ann. Math. Stat. 33, 404.
  102. DeGroot, M. H., 1986, in Recent Developments in the Foundations of Utility and Risk Theory, edited by L. Daboni, A. Montesano, and M. Lines (Reidel, Dordrecht), p. 265.
  103. de Laplace, P. S., 1812, Theorie Analytique des Probabilites (Courcier Imprimeur, Paris).
  104. Denison, D. G. T., B. K. Mallick, and A. F. M. Smith, 1998, J. R. Stat. Soc. Ser. B 60, 333.
  105. Devroye, L., 1986, Non-uniform Random Variate Generation (Springer, New York).
  106. DiCiccio, T., R. Kass, A. Raftery, and L. Wassermann, 1997, J. Am. Stat. Assoc. 92, 903.
  107. Dickinson, C., H. K. Eriksen, A. J. Banday, J. B. Jewell, K. M. Gorski, G. Huey, C. R. Lawrence, I. J. O’Dwyer, and B. D. Wandelt, 2009, Astrophys. J. 705, 1607.
  108. Dieboldt, J., and C. Robert, 1994, J. R. Stat. Soc. Ser. B 56, 363 [http://www.jstor.org/stable/2345907].
  109. DiMatteo, I., C. R. Genovese, and R. E. Kass, 2001, Biometrika 88, 1055.
  110. Dinklage, A., R. Fischer, J. Geiger, G. Kühner, H. Maassberg, J. Svensson, and U. von Toussaint, 2003, in 30th EPS Conference on Controlled Fusion and Plasma Physics, edited by R. Koch and S. Lebedev (Europ. Phys. Soc., Geneva), Vol. ECA 27A, p. P-4.80.
  111. Dinklage, A., R. Fischer, and J. Svensson, 2003, in Proceedings of PLASMA 2003 ‘Research and Applications of Plasmas, p. I-1.1.
  112. Dinklage, A., R. Fischer, and J. Svensson, 2004, Fusion Sci. Technol. 46, 355.
  113. Dissanayake, G., P. Newman, S. Clark, H. Durrant-Whyte, and M. Csorba, 2001, IEEE Transactions on Robotics and Automation 17, 229.
  114. Dobrozemsky, R., and G. Schwarzinger, 1992, J. Vac. Sci. Technol. A 10, 2661.
  115. Dose, V., 2002, Bayes in five days.
  116. Dose, V., 2003a, Rep. Prog. Phys. 66, 1421 [stacks.iop.org/RoPP/66/1421].
  117. Dose, V., 2003b, in Bayesian Inference and Maximum Entropy Methods in Science and Engineering, edited by C. J. Williams, AIP Conf. Proc. No. 659 (AIP, Melville, NY), p. 350.
  118. Dose, V., R. Fischer, and W. von der Linden, 1998, in Maximum Entropy and Bayesian Methods, edited by G. Erickson (Kluwer Academic, Dordrecht), p. 147.
  119. Dose, V., and A. Menzel, 2004, Global Change Biology 10, 259.
  120. Dose, V., and A. Menzel, 2006, Global Change Biology 12, 1451.
  121. Dose, V., R. Preuss, and J. Roth, 2001, J. Nucl. Mater. 288, 153.
  122. Dose, V., and W. von der Linden, 1999, in Maximum Entropy and Bayesian Methods, edited by W. von der Linden, V. Dose, R. Fischer, and R. Preuss (Kluwer Academic Publishers, Dordrecht).
  123. Doucet, A., N. de Freitas, and N. Gordon, 2001, Eds., Sequential Monte Carlo in Practice (Springer, New York).
  124. Doucet, A., and A. Johansen, 2008, in Oxford Handbook of Nonlinear Filtering, edited by D. Crisan and B. Rozovsky (Oxford University Press) [www.cs.ubc.ca/~arnaud/doucet_johansen_tutorialPF.pdf].
  125. Draper, D., 1995, J. R. Stat. Soc. Ser. B 57, 45 [http://www.jstor.org/stable/2346087].
  126. Dreier, H., A. Dinklage, R. Fischer, M. Hirsch, and P. Kornejew, 2006a, Rev. Sci. Instrum. 77, 10F323.
  127. Dreier, H., A. Dinklage, R. Fischer, M. Hirsch, and P. Kornejew, 2008a, Rev. Sci. Instrum. 79, 10E712.
  128. Dreier, H., A. Dinklage, R. Fischer, M. Hirsch, and P. Kornejew, 2008b, in PLASMA 2007, edited by H. J. Hartfuss, M. Dudeck, J. Musielok, and M. J. Sadowski, AIP Conf. Proc. No. 993 (AIP, Melville, NY), p. 183.
  129. Dreier, H., A. Dinklage, R. Fischer, M. Hirsch, P. Kornejew, and E. Pasch, 2006b, Fusion Sci. Technol. 50, 262.
  130. Duane, S., A. Kennedy, B. Pendleton, and D. Roweth, 1987, Phys. Lett. B 195, 216.
  131. Dunkley, J., et al., 2009, Astrophys. J. 701, 1804.
  132. Durrant-Whyte, H., and T. Bailey, 2006, IEEE Robotics & Automation Magazine 13, 99.
  133. Durrer, R., 2008, The Cosmic Microwave Background (Cambridge University Press, Cambridge, UK).
  134. Earl, D., and M. Deem, 2005, Phys. Chem. Chem. Phys. 7, 3910.
  135. Evans, M., 2007, in Bayesian Statistics, edited by J. Bernardo, M. J. Bayarri, J. Berger, A. Dawid, D. Heckermann, A. Smith, and M. West (Oxford University Press, Oxford), Vol. 8, p. 491.
  136. Fearnhead, P., 2006, Stat. Comput. 16, 203.
  137. Fedorov, V. V., 1972, Theory of Optimal Experiments (Academic, New York).
  138. Feller, W., 1991, An Introduction to Probability Theory and Its Applications (Wiley, Chichester), Vol. 2.
  139. Feroz, F., M. P. Hobson, and M. Bridges, 2009, Mon. Not. R. Astron. Soc. 398, 1601.
  140. Fiore, C. E., and M. G. E. da Luz, 2010, Phys. Rev. E 82, 031104.
  141. Fischer, R., 2004, in Bayesian Inference and Maximum Entropy Methods in Science and Engineering, edited by R. Fischer, R. Preuss, and U. von Toussaint, AIP Conf. Proc. No. 735 (AIP, Melville, NY), p. 76.
  142. Fischer, R., and A. Dinklage, 2004, Rev. Sci. Instrum. 75, 4237.
  143. Fischer, R., A. Dinklage, and E. Pasch, 2003, Plasma Phys. Controlled Fusion 45, 1095.
  144. Fischer, R., H. Dreier, A. Dinklage, B. Kurzan, and E. Pasch, 2005, in Bayesian Inference and Maximum Entropy Methods in Science and Engineering, edited by K. Knuth, A. Abbas, R. Morris, and J. Castle, AIP Conf. Proc. No. 803 (AIP, Melville, NY), p. 440.
  145. Fischer, R., K. M. Hanson, V. Dose, and W. von der Linden, 2000, Phys. Rev. E 61, 1152.
  146. Fischer, R., M. Mayer, W. von der Linden, and V. Dose, 1997, Phys. Rev. E 55, 6667.
  147. Fischer, R., M. Mayer, W. von der Linden, and V. Dose, 1998, Nucl. Instrum. Methods Phys. Res., Sect. B 136–138, 1140.
  148. Fischer, R., C. Wendland, A. Dinklage, S. Gori, V. Dose, and The W7-AS team, 2002, Plasma Phys. Controlled Fusion 44, 1501.
  149. Fischer, R., E. Wolfrum, J. Schweinzer, and The ASDEX Upgrade Team, 2008, Plasma Phys. Controlled Fusion 50, 085009.
  150. Flynn, A. M., 1988, Int. J. Robotics Research 7, 5.
  151. Fox, D., W. Burgard, and S. Thrun, 1999, J. Artif. Intell. Res. 11, 391.
  152. Frenkel, D., 1986, in Molecular Dynamics Simulation of Statistical-Mechanical Systems, edited by G. Ciccotti and W. Hoover (North-Holland, Amsterdam), p. 151.
  153. Frese, U., 2006, Autonomous Robots 20, 25.
  154. Friedman, N., and D. Koller, 2003, Mach. Learn. 50, 95.
  155. Fröhner, F., 2000, Evaluation and Analysis of Nuclear Resonance Data, JEFF Report 18 (OECD Nuclear Energy Agency, Paris).
  156. Gallagher, K., K. Charvin, S. Nielsen, M. Sambridge, and J. Stephenson, 2009, Marine and Petroleum Geology 26, 525.
  157. Gamerman, D., 1997, Markov Chain Monte Carlo (Chapman & Hall, London).
  158. Gamerman, D., and H. F. Lopes, 2006, Markov Chain Monte Carlo: Stochastic Simulation for Bayesian Inference (Chapman & Hall, London).
  159. Garnett, R., M. A. Osborne, and S. J. Roberts, 2009, in ICML ’09: Proceedings of the 26th Annual International Conference on Machine Learning (ACM, New York), p. 345, ISBN [Amazon][WorldCat].
  160. Gautier, R., and L. Pronzato, 1998, in New Developments and Applications in Experimental Design (Institute of Mathematical Statistics, Hayward, CA), Vol. 34, pp. 138–151 [http://www.jstor.org/stable/4356069].
  161. Gelfand, A. E., S. E. Hills, A. Racine-Poon, and A. F. M. Smith, 1990, J. Am. Stat. Assoc. 85, 972.
  162. Gelfand, A. E., and S. K. Sahu, 1994, J. Comp. Graph. Statist. 3, 261 [http://www.jstor.org/stable/1390911].
  163. Gelfand, A. E., and A. F. M. Smith, 1990, J. Am. Stat. Assoc. 85, 398.
  164. Gelman, A., J. B. Carlin, H. S. Stern, and D. B. Rubin, 2004, Bayesian Data Analysis (Chapman and Hall/CRC, Boca Raton).
  165. Gelman, A., and X. Meng, 1998, Stat. Sci. 13, 163.
  166. Gelman, A., and D. Rubin, 1992, Stat. Sci. 7, 457.
  167. Geman, S., and D. Geman, 1984, IEEE Trans. Pattern Anal. Mach. Intell. PAMI-6, 721.
  168. George, E. I., 2000, J. Am. Stat. Assoc. 95, 1304.
  169. Geyer, C., 1991, in Computing Science and Statistics: Proceedings of the 23rd Symposium on the Interface (American Statistical Association, New York), p. 156.
  170. Geyer, C., 1992, Stat. Sci. 7, 473.
  171. Geyer, C., and E. Thompson, 1995, J. Am. Stat. Assoc. 90, 909.
  172. Gilks, W. R., 1992, in Bayesian Statistics, edited by J. Bernardo, J. Berger, A. Dawid, and A. Smith (Oxford University Press, Oxford), Vol. 4, p. 641.
  173. Gilks, W. R., N. Best, and K. Tan, 1995, Appl. Statist. 44, 455 [http://www.jstor.org/stable/2986138].
  174. Gilks, W. R., S. Richardson, and D. Spiegelhalter, 1996, Markov Chain Monte Carlo in Practice (Chapman & Hall, London).
  175. Gilks, W. R., G. Roberts, and S. Sahu, 1998, J. Am. Stat. Assoc. 93, 1045.
  176. Gilks, W. R., and P. Wild, 1992, Appl. Statist. 41, 337 [http://www.jstor.org/stable/2347565].
  177. Gilks, W. R., A. Thomas, and D. J. Spiegelhalter, 1994, The Statistician 43, 169 [http://www.jstor.org/stable/2348941].
  178. Girolami, M., and B. Calderhead, 2011, J. R. Stat. Soc. Ser. B 73, 1.
  179. Goggans, P. M., and Y. Chi, 2007, in Bayesian Inference and Maximum Entropy Methods in Science and Engineering, edited by A. M. Djafari, AIP Conf. Proc. No. 872 (AIP, Melville, NY), p. 533.
  180. Goldstein, M., 1992, in Bayesian Statistics, edited by J. M. Bernardo, J. O. Berger, A. P. Dawid, and A. F. M. Smith (Oxford University Press, Oxford), Vol. 4, p. 477.
  181. Golfarelli, M., D. Maio, and S. Rizzi, 1998, in Proceedings of the IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS) (IEEE, New York), p. 905.
  182. Goodman, S. N., 1999a, Ann. Intern. Med. 130, 995 [http://www.annals.org/content/130/12/995.abstract].
  183. Goodman, S. N., 1999b, Ann. Intern. Med. 130, 1005 [http://www.annals.org/content/130/12/1005.abstract].
  184. Gordon, N., D. Salmond, and A. Smith, 1993, Radar and Signal Processing, IEE Proceedings F Vol. 140, p. 107 [ieeexplore.ieee.org/xpls/abs_all.jsp?arnumber=210672].
  185. Green, P. J., 1995, Biometrika 82, 711.
  186. Green, P. J., 2003, in Highly Structured Stochastic Systems, edited by P. J. Green, N. L. Hjort, and S. Richardson (Oxford University Press, Oxford), p. 179.
  187. Gregory, P. C., 1999, Astrophys. J. 520, 361.
  188. Gregory, P. C., 2005, Bayesian Logical Data Analysis for the Physical Sciences (Cambridge University Press, Cambridge).
  189. Gregory, P. C., and T. Loredo, 1992, Astrophys. J. 398, 146.
  190. Gregory, P. C., 2002, Astrophys. J. 575, 427.
  191. Gregory, P. C., 2005, Astrophys. J. 631, 1198.
  192. Gregory, P. C., and D. A. Fischer, 2010, Mon. Not. R. Astron. Soc. 403, 731.
  193. Gregory, P. C., and T. J. Loredo, 1993, in Maximum Entropy Method and Bayesian Methods, edited by A. Mohammad-Djafari, and G. Demoment (Kluwer Academic Press, Dordrecht), p. 225.
  194. Gregory, P. C., and T. J. Loredo, 1996, Astrophys. J. 473, 1059.
  195. Grote, H., et al., 1999, J. Nucl. Mater. 266–269, 1059.
  196. GSL, 2008, GNU Scientific Library [http://www.gnu.org/software/gsl/].
  197. Guglielmetti, F., R. Fischer, and V. Dose, 2009, Mon. Not. R. Astron. Soc. 396, 165.
  198. Guglielmetti, F., R. Fischer, V. Dose, W. Voges, and G. Boese, 2004, in ASP Conference Series Volumes, Astronomical Data Analysis Software and Systems (ADASS) XIII, edited by M. G. A. Francois Ochsenbein and D. Egret (Astronomical Society of the Pacific, San Francisco), Vol. CS 314, p. O03.3.
  199. Haario, H., M. Laine, A. Mira, and E. Saksman, 2006, Stat. Comput. 16, 339.
  200. Habeck, M., M. Nilges, and W. Rieping, 2005, Phys. Rev. Lett. 94, 018105.
  201. Habeck, M., W. Rieping, and M. Nilges, 2004, in Bayesian Inference and Maximum Entropy Methods in Science and Engineering, edited by G. Erickson and Y. Zhai, AIP Conf. Proc. No. 707 (AIP, Melville, NY), p. 157.
  202. Hagan, A. O., and H. Le, 1994, in Aspects of Uncertainty: A Tribute to D. V. Lindley, edited by P. R. Freeman, and A. F. M. Smith (Wiley, Chichester), p. 311.
  203. Hall, D. L., 2004, Mathematical Techniques in Multisensor Data Fusion (Artech House, Norwood).
  204. Han, C., and B. P. Carlin, 2001, J. Am. Stat. Assoc. 96, 1122.
  205. Hansmann, U. H. E., Y. Okamoto, and F. Eisenmenger, 1996, Chem. Phys. Lett. 259, 321.
  206. Harney, H. L., 2003, Bayesian Inference: Parameter Estimation and Decisions (Springer, Berlin).
  207. Hastings, W., 1970, Biometrika 57, 97.
  208. Higdon, D., 1998, J. Am. Stat. Assoc. 93, 585.
  209. Hinshaw, G., et al., 2009, Astrophys. J. Suppl. Ser. 180, 225.
  210. Hitchcock, D. B., 2003, The American Statistician 57, 254.
  211. Hjalmarsson, H., 2005, Automatica 41, 393.
  212. Hoeting, J. A., D. Madigan, A. E. Raftery, and C. T. Volinsky, 1999, Stat. Sci. 14, 382.
  213. Hole, M., G. von Nessi, J. Bertram, J. Svensson, L. C. Appel, B. D. Blackwell, R. L. Dewar, and J. Howard, 2009, J. Plasma Fusion Res. Series 9, 479.
  214. Horowitz, A., 1991, Phys. Lett. B 268, 247.
  215. Hsu, D. A., 1982, J. Am. Stat. Assoc. 77, 29.
  216. Huang, C., and A. Darwiche, 1996, Intl. J. Approx. Reasoning 15, 225.
  217. Huelsenbeck, J. P., F. Ronquist, R. Nielsen, and J. P. Bollback, 2001, Science 294, 2310.
  218. Hukushima, K., H. Takayama, and K. Nemoto, 1996, Int. J. Mod. Phys. C 7, 337.
  219. Huzurbazar, V. S., 1976, Sufficient Statistics (Marcel Dekker, New York).
  220. Jaakkola, T., 2001, in Advances in Mean Field Methods, edited by M. Opper and D. Saad (MIT Press, Cambridge, MA), p. 129.
  221. Jaakkola, T., and M. Jordan, 2000, Stat. Comput. 10, 25.
  222. Jarosik, N., et al., 2011, Astrophys. J. Suppl. Ser. 192, 14.
  223. Jarzynski, C., 1997, Phys. Rev. Lett. 78, 2690.
  224. Jarzynski, C., 2006, Phys. Rev. E 73, 046105.
  225. Jasra, A., C. Holmes, and D. Stephens, 2005, Stat. Sci. 20, 50.
  226. Jasra, A., D. Stephens, K. Gallagher, and C. Holmes, 2006, Math. Geol. 38, 269.
  227. Jaynes, E. T., 1957a, Phys. Rev. 106, 620.
  228. Jaynes, E. T., 1957b, Phys. Rev. 108, 171.
  229. Jaynes, E. T., 1968, IEEE Trans. Syst. Sci. Cybern. 4, 227.
  230. Jaynes, E. T., 1983, in Papers on Probability, Statistics and Statistical Physics, edited by W. L. Harper and C. A. Hooker (Reidel, Dordrecht).
  231. Jaynes, E. T., 1976, in Foundations of Probability Theory, Statistical Inference, and Statistical Theories of Science, edited by W. L. harper and C. A. Hooker (Reidel, Dordrecht), p. 252.
  232. Jaynes, E. T., 1979, J. Am. Stat. Assoc. 74, pp. 740.
  233. Jaynes, E. T., and L. Bretthorst, 2003, Probability Theory, The Logic of Science (Oxford University Press, Oxford).
  234. Jeffreys, H., 1939, Theory of Probability (Oxford University Press, Oxford), 3rd ed., revised edition 1961.
  235. Jeffreys, H., 1961, Theory of Probability (Oxford University Press, Oxford).
  236. Jensen, C., A. Kong, and U. Kjaerulff, 1995, Int. J. Human-Comput. Stud., Special Issue on Real-World Applications of Uncertain Reasoning, 42, 647.
  237. Jensen, F. V., 2001, Bayesian Networks and Decision Graphs (Springer, New York).
  238. Ji, X., et al., et al.2009, in RoboCup, edited by L. Iocchi , Lecture Notes in Computer Science Vol. 5399 (Springer, Berlin), p. 507.
  239. Jordan, M. I., 1999, Learning in Graphical Models (MIT Press, Cambridge, MA).
  240. Jordan, M. I., 2004, Stat. Sci. 19, 140.
  241. Jordan, M. I., Z. Ghahramani, T. S. Jaakkola, and L. K. Saul, 1999, in Learning in Graphical Models, edited by M. I. Jordan (MIT Press, Cambridge, MA), p. 105.
  242. Kaelbling, L. P., M. L. Littman, and A. R. Cassandra, 1998, Artif. Intell. 101, 99.
  243. Kaelbling, L. P., M. L. Littman, and A. W. Moore, 1996, J. Artif. Intell. Res. 4, 237.
  244. Kang, H., and V. Dose, 2003, J. Vac. Sci. Technol. A 21, 1978.
  245. Kapur, J., and H. Kesavan, 1992, Entropy Optimization Principles with Applications (Academic, Boston).
  246. Kass, R. E., et al., 1988, in Bayesian Statistics, edited by J. Bernardo (Oxford University Press, New York), Vol. 3, p. 261.
  247. Kass, R. E., and A. E. Raftery, 1995, J. Am. Stat. Assoc. 90, 773.
  248. Katz, M., 1961, Ann. Math. Stat. 32, 136.
  249. Katzgraber, H., S. Trebst, D. Huse, and M. Troyer, 2006, J. Stat. Mech., P03018.
  250. Kendall, M., and P. Moran, 1963, Geometrical Probability (Griffin, London).
  251. Kennedy, A., et al., 1990, in Probabilistic Methods in Quantum Field Theory and Quantum Gravity, edited by P. D. Damgaard, H. Hüffel, and A. Rosenblum (Springer, New York).
  252. Kennedy, M. C., and A. O’Hagan, 2001, J. R. Stat. Soc. Ser. B 63, 425.
  253. Kerler, W., and P. Rehberg, 1994, Phys. Rev. E 50, 4220.
  254. Kinney, W. H., 2001, Phys. Rev. D 63, 043001.
  255. Knuth, K. H., 2004, in Bayesian Inference and Maximum Entropy Methods in Science and Engineering, edited by G. Erickson and Y. Zhai, AIP Conf. Proc. No. 707 (AIP, Melville, NY), p. 204.
  256. Knuth, K. H., P. M. Erner, and S. Frasso, 2007, in Bayesian Inference and Maximum Entropy Methods in Science and Engineering, edited by K. Knuth, A. Caticha, J. Center, A. Giffin, and C. Rodrigues, AIP Conf. Proc. No. 954 (AIP, Melville, NY), p. 203.
  257. Koch, D. G., et al., 2010, Astrophys. J. Lett. 713, L79.
  258. Kolb, E. W., and M. S. Turner, 1990, The Early Universe (Addison-Wesley, Redwood City).
  259. Komatsu, E., et al., 2009, Astrophys. J. Suppl. Ser. 180, 330.
  260. Kone, A., and D. Kofke, 2005, J. Chem. Phys. 122, 206101.
  261. Kornejew, P., M. Hirsch, T. Bindemann, A. Dinklage, H. Dreier, and H. J. Hartfuss, 2006, Rev. Sci. Instrum. 77, 10F128.
  262. Kosowsky, A., and M. S. Turner, 1995, Phys. Rev. D 52, R1739.
  263. Krieger, K., U. von Toussaint, and The ASDEX-Upgrade team, 1999, in Proceedings of the 26th EPS Conference on Controlled Fusion and Plasma Physics (European Physical Society, Maastricht), Vol. ECA 23J, pp. 1529.
  264. Kschischang, F. R., B. J. Frey, and H. A. Loeliger, 2001, IEEE Trans. Inf. Theory 47, 498.
  265. Kulcsar, C., L. Pronzato, and E. Walter, 1994, Int. J. Bio-Medical Computing 36, 95.
  266. Lauritzen, S. L., 1996, Graphical Models (Oxford University Press, Oxford, UK).
  267. Lauritzen, S. L., and D. J. Spiegelhalter, 1988, J. R. Stat. Soc. Ser. B 50, 157 [http://www.jstor.org/stable/2345762].
  268. Leach, S. M., A. R. Liddle, J. Martin, and D. J. Schwarz, 2002, Phys. Rev. D 66, 023515.
  269. Leamer, E. E., 1978, Specification Searches: Ad Hoc Inference With Nonexperimental Data (John Wiley, New York).
  270. Leonard, J. J., and H. Durrant-Whyte, 1992, Directed Sonar Sensing for Mobile Robot Navigation (Kluwer, Dordrecht).
  271. Leonard, T., and J. Hsu, 1999, Bayesian Methods: An Analysis for Statisticians and Interdisciplinary Researchers (Cambridge University Press, Cambridge).
  272. Lepage, G., 1980, VEGAS: An Adaptive Multidimensional Integration Program, Technical Report No. CLNS-80/447, Department of Engineering, Cornell University.
  273. Lewis, A., A. Challinor, and A. Lasenby, 2000, Astrophys. J. 538, 473.
  274. Liddle, A. R., 2004, Mon. Not. R. Astron. Soc. 351, L49.
  275. Liddle, A. R., 2007, Mon. Not. R. Astron. Soc. 377, L74.
  276. Lidsay, J. E., A. R. Liddle, E. W. Kolb, E. J. Copeland, and T. Barreiro, 1997, Rev. Mod. Phys. 69, 373.
  277. Linde, A. D., 1983, Phys. Lett. B 129, 177.
  278. Linde, A. D., 1994, Phys. Rev. D 49, 748.
  279. Lindley, D., et al., 1980, in Bayesian Statistics, edited by J. M. Bernardo, M. H. DeGroot, D. V. Lindley, and A. F. M. Smith (Valencia University Press, Valencia, Spain), p. 223.
  280. Lindley, D. V., 1956, Ann. Math. Stat. 27, 986.
  281. Lindley, D. V., 1972, Bayesian Statistics—A Review (SIAM, Philadelphia).
  282. Liu, J., 2001, Monte Carlo Strategies in Scientific Computing (Springer, New York).
  283. Loredo, T. J., 1990, in Maximum Entropy and Bayesian Methods, edited by P. Fougere (Kluwer Academic Publishers, Dordrecht), p. 81.
  284. Loredo, T. J., 1992, in Statistical Challenges in Modern Astronomy, edited by E. Feigelson and G. Babu (Springer, New York), p. 275.
  285. Loredo, T. J., and D. Chernoff, 2003a, in Statistical Challenges in Astronomy, edited by E. Feigelson and G. Babu (Springer, Berlin), p. 57.
  286. Loredo, T. J., and D. Chernoff, 2003b, in Bayesian Inference and Maximum Entropy Methods in Science and Engineering, edited by G. Erickson and Y. Zhai, AIP Conf. Proc. No. 707 (AIP, Melville, NY), p. 330.
  287. Loredo, T. J., 1994, The Return of the Prodigal: Bayesian Inference in Astrophysics, manuscript, 37 pages [http://www.astro.cornell.edu/staff/loredo/bayes/return.pdf].
  288. Loredo, T. J., 1999, in ASP Conference Series 172: Astronomical Data Analysis Software and Systems VIII, edited by D. M. Mehringer, R. L. Plante, and D. A. Roberts (ASP, San Francisco), Vol. 8, p. 297.
  289. Loredo, T. J., J. Rice, and M. L. Stein, 2009, Ann. Appl. Stat. 3, 1.
  290. Loschi, R. H., F. R. B. Cruz, R. H. C. Takahashi, P. L. Iglesias, R. B. Arellano-Valle, and J. MacGregor Smith, 2008, Comput. Oper. Res. 35, 156.
  291. Lunn, D. J., A. Thomas, N. Best, and D. Spiegelhalter, 2000, Stat. Comput. 10, 325.
  292. Luttrell, S. P., 1985, Inverse Probl. 1, 199.
  293. MacKay, D., 2003, Information Theory, Inference and Learning Algorithms (Cambridge University Press, Cambridge).
  294. MacKay, D. J. C., 1992a, Neural Comput. 4, 415.
  295. MacKay, D. J. C., 1992b, Neural Comput. 4, 590.
  296. Mackenzie, D., 2004, New Sci. 2453, 36 [http://www.newscientist.com/article/mg18224535.500-vital-statistics.html].
  297. Madigan, D., and A. E. Raftery, 1994, J. Am. Stat. Assoc. 89, 1535.
  298. Malinverno, A., and V. Briggs, 2004, Geophysics 69, 1005.
  299. Manyika, J., and H. Durrant-Whyte, 1995, Data Fusion and Sensor Management: A Decentralized Information-Theoretic Approach (Prentice Hall PTR, Upper Saddle River, NJ).
  300. Marchand, E., and W. Strawderman, 2004, in A Festschrift for Herman Rubin, edited by A. DasGupta, Monograph Series 45 (Institute of Mathematical Statistics Lecture Notes, Beachwood, OH), p. 21.
  301. Marin, J., K. Mengersen, and C. P. Robert, 2005, in Handbook of Statistics, edited by D. Dey and C. R. Rao (Elsevier, Amsterdam), Vol. 25.
  302. Marinari, E., and G. Parisi, 1992, Europhys. Lett. 19, 451.
  303. Mather, J. C., 2007, Rev. Mod. Phys. 79, 1331.
  304. Matoba, T., T. Itagaki, T. Yamauchi, and A. Funahashi, 1979, Jpn. J. Appl. Phys. 18, 1127.
  305. Matthews, P., 1993, Stat. Prob. Lett. 17, 231.
  306. Mayer, M., 1999, in Proceedings of the 15th International Conference on the Application of Accelerators in Research and Industry, edited by J. Duggan and I. Morgan, AIP Conf. Proc. No. 475 (AIP, Melville, NY), p. 541.
  307. Mayer, M., R. Fischer, S. Lindig, U. v. Toussaint, R. W. Stark, and V. Dose, 2005, Nucl. Instrum. Methods Phys. Res., Sect. B 228, 349.
  308. Mayor, M., and D. Queloz, 1995, Nature (London) 378, 355.
  309. McEliece, R. J., D. J. C. MacKay, and J. F. Cheng, 1998, IEEE J. Selected Areas Comm. 16, 140.
  310. Meier, M., R. Preuss, and V. Dose, 2003, New J. Phys. 5, 133.
  311. Mengersen, K., C. Robert, and C. Cuihenneuc-Jouyaux, 1999, in Bayesian Statistics, edited by J. Bernardo, J. Berger, A. Dawid, and A. Smith (Clarendon Press, Oxford), Vol. 6, p. 415.
  312. Mertens, S., 2002, Comput. Sci. Eng. 4, 31.
  313. Metropolis, N., A. Rosenbluth, M. Rosenbluth, A. Teller, and E. Teller, 1953, J. Chem. Phys. 21, 1087.
  314. Miller, A. J., 1984, J. R. Stat. Soc. Ser. A (General) 147, 389.
  315. Möller, W., and F. Besenbacher, 1980, Nucl. Instrum. Methods 168, 111.
  316. Montemerlo, M., S. Thrun, D. Koller, and B. Wegbreit, 2002, in Proceedings of the Eighteenth National Conference on Artificial Intelligence (AAAI-02) (AAAI Press, Edmonton, Alberta, Canada).
  317. Moral, P. D., A. Doucet, and A. Jasra, 2006, J. R. Stat. Soc. Ser. B 68, 411.
  318. Mukherjee, P., D. Parkinson, P. S. Corasaniti, A. R. Liddle, and M. Kunz, 2006, Mon. Not. R. Astron. Soc. 369, 1725.
  319. Mukherjee, P., D. Parkinson, and A. Liddle, 2006, Astrophys. J. 638, L51.
  320. Muller, H., 1992, Ann. Stat. 20, 737.
  321. Müller, P., 1999, in Bayesian Statistics, edited by J. M. Bernardo, J. O. Berger, A. P. Dawid, and A. F. M. Smith (Oxford University Press, Oxford), Vol. 6, p. 459.
  322. Müller, P., D. Berry, A. Grieve, M. Smith, and M. Krams, 2007, J. Stat. Plann. Infer. 137, 3140.
  323. Müller, P., and G. Parmigiani, 1995, in Bayesian Statistics and Econometrics: Essays in Honor of A. Zellner, edited by D. A. Berry, K. M. Chaloner, and J. F. Geweke (Wiley, New York), p. 397.
  324. Müller, P., B. Sansó, and M. Delorio, 2004, J. Am. Stat. Assoc. 99, 788.
  325. Murphy, K., 2001, Learning Bayes Net Structure from Sparse Data Sets, Technical Report, Comp. Sci. Division, UC Berkeley.
  326. Murphy, K., Y. Weiss, and M. I. Jordan, 1999, in Uncertainty in Artificial Intelligence: Proceedings of the Fifteenth Conference (Morgan and Kaufmann, Stockholm), p. 467.
  327. Murray, C. D., and S. F. Dermott, 1999, Solar System Dynamics (Cambridge University Press, Cambridge).
  328. Myers, R. H., A. I. Khuri, and W. H. Carter, 1989, Technometrics 31, 137.
  329. NAG, 2008, The Numerical Algorithms Group Ltd (Barnett House, 53 Fountain Street, Manchester).
  330. Neal, R., 1993, Probabilistic Inference Using Markov Chain Monte Carlo Methods, Technical Report No. CRG-TR-93-1, University of Toronto.
  331. Neal, R., 1996, Bayesian Learning for Neural Networks, Lecture Notes in Statistics Vol. 18 (Springer, New York).
  332. Neal, R., 1999a, in Bayesian Statistics, edited by J. M. Bernardo, J. O. Berger, A. P. Dawid, and A. F. M. Smith (Oxford University Press, Oxford), Vol. 6, p. 69.
  333. Neal, R., 1999b, in Learning in Graphical Models, edited by M. Jordan (MIT Press, MIT), p. 205.
  334. Neal, R., 2003, Ann. Stat. 31, 705.
  335. Neal, R., 2011, in Handbook of Markov Chain Monte Carlo, edited by S. Brooks, A. Gelman, G. Jones, and X. Meng (CRC Press, Boca Raton) [http://www.cs.utoronto.ca/~radford/ftp/ham-mcmc.ps].
  336. Ng, A. Y., and M. I. Jordan, 2000, in Uncertainty in Artificial Intelligence: Proceedings of the Sixteenth Conference (Morgan Kaufmann, Stanford, CA), p. 406.
  337. Oakley, J. E., and A. O’Hagan, 2004, J. R. Stat. Soc. Ser. B 66, 751.
  338. Oakley, J. E., and A. O’Hagan, 2007, Biometrika 94, 427.
  339. Obric, M., et al., 2006, Mon. Not. R. Astron. Soc. 370, 1677.
  340. Ogata, Y., 1989, Numer. Math. 55, 137.
  341. O’Hagan, A., 1994, Advanced Theory of Statistics, Bayesian Inference (Arnold, London), Vol. 2B.
  342. O’Hagan, A., 2006, Bayesian Analysis 1, 445.
  343. O’Hagan, A., and J. O. Berger, 1988, J. Am. Stat. Assoc. 83, 503.
  344. O’Hagan, T., and M. West, 2010, The Oxford Handbook of Applied Bayesian Analysis (Oxford University Press, Oxford, UK).
  345. Padayachee, J., V. M. Prozesky, W. von der Linden, M. S. Nkwinika, and V. Dose, 1999, Nucl. Instrum. Methods Phys. Res., Sect. B 150, 129.
  346. Pahud, C., A. R. Liddle, P. Mukherjee, and D. Parkinson, 2007, Mon. Not. R. Astron. Soc. 381, 489.
  347. Pearl, J., 1987, Artif. Intell. 32, 245.
  348. Pearl, J., 1988, Probabilistic Reasoning in Intelligent Systems (Morgan and Kaufmann, San Mateo, CA).
  349. Pearl, J., 2000, Causality (Cambridge University Press, Cambridge, UK).
  350. Peebles, P. J. E., 1982, Astrophys. J. 263, L1.
  351. Peot, M., and R. Shachter, 1991, Artif. Intell. 48, 299.
  352. Perreault, L., J. Bernier, B. Bobee, and E. Parent, 2000, J. Hydrology 235, 221.
  353. Peskun, P., 1973, Biometrika 60, 607.
  354. Pohl, C., and J. Van Genderen, 1998, Int. J. Remote Sensing 19, 823.
  355. Polsen, N., 1996, in Bayesian Statistics, edited by J. Bernardo, J. Berger, A. Dawid, and A. Smith (Oxford University Press, Oxford), Vol. 5, p. 297.
  356. Press, W., S. Teukolsky, W. Vetterlin, and B. Flannery, 1996, Numerical Recipes in Fortran 90 (Cambridge University Press, Cambridge, England).
  357. Preuss, R., H. Dreier, A. Dinklage, and V. Dose, 2008, Europhys. Lett. 81, 55 001.
  358. Preuss, R., H. Kang, T. Schwarz-Selinger, and V. Dose, 2002, in Bayesian Inference and Maximum Entropy Methods in Science and Engineering, edited by R. L. Fry, AIP Conf. Proc. No. 617 (AIP, Melville, NY), p. 155.
  359. Preuss, R., M. Maraschek, H. Zohm, and V. Dose, 2003, in Bayesian Inference and Maximum Entropy Methods in Science and Engineering, edited by C. Williams, AIP Conf. Proc. No. 659 (AIP, Melville, NY), p. 124.
  360. Preuss, R., P. Pecher, and V. Dose, 2001, in Bayesian Inference and Maximum Entropy Methods in Science and Engineering, edited by C. R. S. J. Rychert and G. Erickson, AIP Conf. Proc. No. 567 (AIP, Melville, NY), p. 213.
  361. Preuss, R., and U. von Toussaint, 2007, in Bayesian Inference and Maximum Entropy Methods in Science and Engineering, edited by K. Knuth, A. Caticha, J. Center, A. Giffin, and C. Rodriguez, AIP Conf. Proc. No. 954 (AIP, Melville, NY), p. 221.
  362. Pronzato, L., 2008, Automatica 44, 303.
  363. Prosper, H. B., 1984, J. Phys. Colloques 45, C3-185.
  364. Prosper, H. B., 1985, Nucl. Instrum. Methods Phys. Res., Sect. A 241, 236.
  365. Prosper, H. B., 1988, Phys. Rev. D 37, 1153.
  366. Prosper, H. B., 2007, in Statistical Challenges in Modern Astronomy IV, edited by G. J. Babu and E. D. Feigelson (ASP, Orem, UT), Vol. 371, p. 87.
  367. Pukelsheim, F., 1993, Optimal Design of Experiments (Wiley, New York).
  368. Punska, O., 1999, Bayesian Approaches to Multi-Sensor Data Fusion, Ph.D. thesis, University of Cambridge, Cambridge, UK.
  369. Quartulli, M., and M. Datcu, 2003, IEEE Transactions on Geoscience and Remote Sensing 41, 1976.
  370. Raftery, A. E., D. Madigan, and J. A. Hoeting, 1997, J. Am. Stat. Assoc. 92, 179.
  371. Rathore, N., M. Chopra, and J. de Pablo, 2005, J. Chem. Phys. 122, 024111.
  372. Redner, R., and H. Walker, 1984, SIAM Rev. 26, 195.
  373. Reichardt, C. L., P. A. R. Ade, J. J. Bock, J. R. Bond, and J. A. Brevik, 2009, Astrophys. J. 694, 1200.
  374. Richardson, S., and P. Green, 1997, J. R. Stat. Soc. Ser. B 59, 731.
  375. Richardson, S., and P. Green, 1998, J. R. Stat. Soc. Ser. B 60, U3.
  376. Ripley, B., 1987, Stochastic Simulation (Wiley, New York).
  377. Robert, C. P., and G. Casella, 2010, Introducing Monte Carlo Methods with R (Springer, New York).
  378. Robert, C. P., 1994, The Bayesian Choice (Springer, Berlin).
  379. Robert, C. P., and G. Casella, 1999, Monte Carlo Statistical Methods (Springer, New York).
  380. Gelman, A., W. R. Gilks, and G. O. Roberts, 1997, Ann. Appl. Probab. 7, 110.
  381. Roberts, G. O., and J. S. Rosenthal, 2001, Stat. Sci. 16, 351.
  382. Roberts, G. O., and J. S. Rosenthal, 2009, J. Comput. Graph. Stat. 18, 349.
  383. Roth, J., 1999, J. Nucl. Mater. 266–269, 51.
  384. Roth, J., and C. Garcia-Rosales, 1996, Nucl. Fusion 36, 1647.
  385. Roweis, S., and Z. Ghahramani, 1999, Neural Comput. 11, 305.
  386. Rudoy, D., S. G. Yuen, R. D. Howe, and P. J. Wolfe, 2010, J. Roy. Stat. Soc. Ser. C 59, 573.
  387. Russell, S., and P. Norvig, 2003, Artifical Intelligence: A Modern Approach (Prentice-Hall, Englewood Cliffs, NJ).
  388. Ryan, K. J., 2003, J. Comput. Graph. Stat. 12, 585.
  389. Sacks, J., W. J. Welch, T. J. Mitchell, and H. P. Wynn, 1989, Stat. Sci. 4, 409.
  390. Saltelli, A., S. Tarantola, and F. Campolongo, 2000, Stat. Sci. 15, 377.
  391. Schwarz, G., 1978, Ann. Stat. 6, 461.
  392. Schwarz-Selinger, T., R. Preuss, V. Dose, and W. von der Linden, 2001, J. Mass Spectrom. 36, 866.
  393. Sebastiani, P., and H. P. Wynn, 2000, J. R. Stat. Soc. Ser. B 62, 145.
  394. Seifert, U., 2005, Phys. Rev. Lett. 95, 040602.
  395. Sellke, T., M. J. Bayarri, and J. O. Berger, 2001, The American Statistician 55, 62.
  396. Shachter, R. D., and M. Peot, 1989, in Proceedings of the Fifth Conference on Uncertainty in Artificial Intelligence (UAI-89) (Morgan and Kaufmann, Windsor, Ontario, Canada).
  397. Shaw, J., M. Bridges, and M. Hobson, 2007, Mon. Not. R. Astron. Soc. 378, 1365.
  398. Sheffield, J., 1975, Plasma Scattering of Electromagnetic Radiation (Academic Press, New York).
  399. Sisson, S., 2005, J. Am. Stat. Assoc. 100, 1077.
  400. Sivia, D., 2006, Data Analysis—A Baysian Tutorial (Oxford University Press, Oxford).
  401. Sivia, D., and W. David, 1994, Acta Crystallogr. Sect. A 50, 703.
  402. Skellam, J. G., 1946, J. R. Stat. Soc. 109, 296.
  403. Skilling, J., 1991, in Fundamentals of Maxent in Data Analysis, edited by B. Buck and V. Macauley (Clarendon Press, Oxford), p. 19.
  404. Skilling, J., 2004a, in Bayesian Inference and Maximum Entropy Methods in Science and Engineering, edited by G. Erickson, J. Rychert, and C. Smith, AIP Conf. Proc. No. 735 (AIP, Melville, NY), p. 395.
  405. Skilling, J., 2004b, in Bayesian Inference and Maximum Entropy Methods in Science and Engineering, edited by G. Erickson and Y. Zhai, AIP Conf. Proc. No. 707 (AIP, Melville, NY), p. 388.
  406. Skilling, J., 2006, Bayesian Analysis 1, 833.
  407. Skilling, J., 2010, in Bayesian Methods in Cosmology, edited by M. P. Hobson, A. H. Jaffe, A. R. Liddle, P. Mukherjee, and D. Parkinson (Cambridge University Press, Cambridge, UK), p. 3.
  408. Skilling, J., and D. MacKay, 2003, Ann. Stat. 31, 753.
  409. Skinner, C. H., et al., 2008, Fusion Sci. Technol. 54, 891.
  410. Smith, A. F. M., and D. J. Spiegelhalter, 1980, J. R. Stat. Soc. Ser. B 42, 213 [http://www.jstor.org/stable/2984964].
  411. Smith, R., M. Self, and P. Cheeseman, 1990, in Autonomous Robot Vehicles, edited by I. J. Cox and G. T. Wilfon (Springer, New York), p. 167.
  412. Sollom, I., A. Challinor, and M. P. Hobson, 2009, Phys. Rev. D 79, 123521.
  413. Spergel, D. N., et al., 2007, Astrophys. J. Suppl. Ser. 170, 377.
  414. Spiegelhalter, D. J., 2002, J. R. Stat. Soc. Ser. B 64, 583.
  415. Spirtes, P., C. Glymour, and R. Scheines, 2000, Causation, Prediction, and Search (MIT Press, Cambridge, MA), 2nd ed.
  416. Starobinsky, A. A., 1982, Phys. Lett. 117B, 175.
  417. Steinerg, D. M., and W. G. Hunter, 1984, Technometrics 26, 71.
  418. Stephens, D. A., 1994, Appl. Statist. 43, 159 [http://www.jstor.org/stable/2986119].
  419. Stephens, M., 2000, J. R. Stat. Soc. Ser. B 62, 795.
  420. Stewart, L., 1987, J. R. Stat. Soc. Series D 36, 211 [http://www.jstor.org/stable/2348514].
  421. Stoica, P., and Y. Selén, 2004, IEEE Signal Process. Mag. 21, 36.
  422. Stone, M., 1959, Ann. Math. Stat. 30, 55.
  423. Stone, M., 1961, Ann. Math. Stat. 32, 1339.
  424. Svensson, J., A. Dinklage, J. Geiger, A. Werner, and R. Fischer, 2004, Rev. Sci. Instrum. 75, 4219.
  425. Svensson, J., and A. Werner, 2007, in Proceedings of the IEEE International Symposium on Intelligent Signal Processing (IEEE, New York), p. 1.
  426. Tanner, M. A., and W. H. Wong, 1987, J. Am. Stat. Assoc. 82, 528.
  427. Tarantola, A., 2005, Inverse Problem Theory and Methods for Model Parameter Estimation (SIAM, Philadelphia).
  428. Ter Braak, C. J., and J. A. Vrugt, 2008, Stat. Comput. 18, 435.
  429. Tesmer, J., and M. Nastasi, 1995, Eds., Handbook of Modern Ion Beam Analysis (Material Research Society, Pittsburgh, PA).
  430. Thomas, A., D. Spiegelhalter, and W. Gilks, 1992, in Bayesian Statistics, edited by J. Bernardo, J. Berger, A. Dawid, and A. Smith (Oxford University Press, Oxford), Vol. 4, p. 837.
  431. Thomopoulos, S., 1990, Journal of Robotic Systems 7, 337.
  432. Thrun, S., and D. Fox, 2005, Probabilistic Robotics (MIT Press, Cambridge, MA).
  433. Thrun, S., W. Burgard, and D. Fox, 1998, Autonomous Robots 5, 253.
  434. Thrun, S., and M. Montemerlo, 2006, Int. J. Robotics Res. 25, 403.
  435. Tierney, L., 1994, Ann. Stat. 22, 1701.
  436. Tierney, L., and J. Kadane, 1986, J. Am. Stat. Assoc. 81, 82.
  437. Tierney, L., and A. Mira, 1999, Stat. Med. 18, 2507.
  438. Tinney, C. G., R. P. Butler, G. W. Marcy, H. R. A. Jones, G. Laughlin, B. D. Carter, J. A. Bailey, and S. O’Toole, 2006, Astrophys. J. 647, 594.
  439. Tinney, C. G., R. P. Butler, G. W. Marcy, H. R. A. Jones, A. J. Penny, C. McCarthy, B. D. Carter, and J. Bond, 2003, Astrophys. J. 587, 423.
  440. Toman, B., 1999, in Encyclopedia of Statistical Sciences Update, edited by S. Kotz, and N. L. Johnson (Wiley, New York), Vol. 3, p. 35.
  441. Toman, B., 1996, J. Am. Stat. Assoc. 91, 185.
  442. Toussaint, D., 1989, Comput. Phys. Commun. 56, 69.
  443. Trotta, R., 2007a, Mon. Not. R. Astron. Soc. 378, 72.
  444. Trotta, R., 2007b, Mon. Not. R. Astron. Soc. 378, 819.
  445. Trotta, R., 2008, Contemp. Phys. 49, 71.
  446. Tynan, G., 1998, New Orleans, APS Meeting.
  447. Uson, J. M., and D. T. Wilkinson, 1984, Astrophys. J. 277, L1.
  448. van Eeden, C., 1995, Can. J. Stat. 23, 245.
  449. von der Linden, W., 1995, Appl. Phys. A 60, 155.
  450. von der Linden, W., V. Dose, N. Memmel, and R. Fischer, 1998, Surf. Sci. 409, 290.
  451. von der Linden, W., V. Dose, J. Padayachee, and V. Prozesky, 1999, Phys. Rev. E 59, 6527.
  452. von der Linden, W., R. Preuss, and V. Dose, 1999b, in Maximum Entropy and Bayesian Methods, edited by W. von der Linden, V. Dose, R. Fischer, and R. Preuss (Kluwer Academic Publishers, Dordrecht).
  453. von Keudell, A., 2002, Thin Solid Films 402, 1.
  454. von Toussaint, U., 2011 (unpublished).
  455. von Toussaint, U., and V. Dose, 2005, Appl. Phys. A 82, 403.
  456. von Toussaint, U., V. Dose, and A. Golan, 2004, J. Vac. Sci. Technol. A 22, 401.
  457. von Toussaint, U., R. Fischer, K. Krieger, and V. Dose, 1999, New J. Phys. 1, 11.
  458. von Toussaint, U., S. Gori, and V. Dose, 2004, Appl. Opt. 43, 5356.
  459. von Toussaint, U., K. Krieger, R. Fischer, and V. Dose, 1999, in Maximum Entropy and Bayesian Methods, edited by W. von der Linden, V. Dose, R. Fischer, and R. Preuss (Kluwer Academic Publishers, Dordrecht).
  460. von Toussaint, U., T. Schwarz-Selinger, and S. Gori, 2008, in Bayesian Inference and Maximum Entropy Methods in Science and Engineering, edited by M. S. Lauretto, C. A. B. Pereira, J. M. Sternand , AIP Conf. Proc. No. 1073 (AIP, Melville, NY), p. 348.
  461. Wainwright, M. J., and M. I. Jordan, 2003, Graphical Models, Exponential Families, and Variational Inference, Technical Report No. 649, Department Statistics, UC Berkeley.
  462. Wald, L., 1998, in Proceedings EARSeL Symposium 1997: Future Trends in Remote Sensing, edited by P. Gudmansen (A. A. Balkema, Rotterdam), p. 385.
  463. Weiss, Y., 2000, Neural Comput. 12, 1.
  464. Whyte, D., G. Tynan, R. Doerner, and J. Brooks, 2001, Nucl. Fusion 41, 47.
  465. Wolpert, R. L., and K. Ickstadt, 2004, Inverse Probl. 20, 1759.
  466. Wright, J. T., 2005, Publ. Astron. Soc. Pac. 117, 657.
  467. Wright, J. T., and A. W. Howard, 2009, Astrophys. J. Suppl. Ser. 182, 205.
  468. Y. Wu, H. Tjelmeland, and M. West, 2007, J. Comput. Graph. Stat. 16, 44.
  469. Zhao, X., and P. Chu, 2010, J. Clim. 23, 1034.

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Rev. Mod. Phys. 83, 943– Published 19 September, 2011
  • Received 8 December 2009

© 2011 American Physical Society

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