Bayesian field theory

Bayesian Field Theory

Volumn , Issue , 2003, Pages 1-411

  Lemm, Jörg C ^a  

^a NONE

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EID: 84906591582     PISSN: None     EISSN: None     Source Type: Book    
DOI: None     Document Type: Book

References (541)

1. E. Aarts and J. Korts. Simulated Annealing and Boltzmann Machines. Wiley, New York, 1989.
2. Y. Abu Mostafa. Learning from hints in neural networks. Journal of Complexity, 6:192-198, 1990.
3. Y. Abu Mostafa. Hints and the VC dimension. Neural Computation, 5:278-288, 1993.
4. Y. Abu Mostafa. A method for learning from hints. In S. J. Hanson, J. D. Cowan, and C. L. Giles, editors, Advances in Neural Information Processing Systems 5, pages 73-80. Morgan Kaufmann, San Mateo, CA, 1993.
5. A. Agresti. Categorical Data Analysis. Wiley, New York, 2nd edition, 2002.
6. T. Aida. Field theoretical analysis of on-line learning of probability distributions. Phys. Rev. Lett, 83:3554-3557, 1999. arXiv:condmat/9911474.
7. R. G. Airapetyan and I. V. Puzynin. Newtonian iterative scheme with simultaneous iterations of inverse derivative. Comp. Phys. Comm., 102:97-108, 1997.
8. H. Akaike. Likelihood and the Bayes procedure. In J. M. Bernanda, M. H. De Groot, D. V. Lindley, and A. F. M. Smith, editors, Bayesian Statistics, pages 143-166. Valencia University Press, Valencia, 1980.
9. I. Aleksander, editor. Neural Computing Architectures. North Oxford Academic, London, 1989.
10. I. Aleksander and H. Morton. An Introduction to Neural Computing. Chapman & Hall, London, 1990.
11. I. Aleksander and H. Morton. Neurons and Symbols. Chapman & Hall, London, 1993.
12. D. M. Allen. The relationship between variable selection and data augmentation and a method of prediction. Technometrics, 16:125, 1974.
13. S.I. Amari. Differential Geometrical Methods in Statistics, volume 28 of Springer Lecture Notes in Statistics. Springer-Verlag, New York, 1985.
14. S.I. Amari. Information geometry of the EM and em algorithms for neural networks. Neural Networks, 8(9):1379-1408, 1995.
15. S.I. Amari, O. E. Barndorff Nielsen, R. E. Kass, S. L. Lauritzen, and C. R. Rao, editors. Differential Geometry in Statistical Inference, volume 10 of Lecture Notes-Monograph Series. Institute of Mathematical Statistics, Hayward, CA, 1987.
16. S.I. Amari, A. Cichocki, and H. H. Yang. A new learning algorithm for blind signal separation. In D. S. Touretzky, M. C. Mozer, and M. E. Hasselmo, editors, Advances in Neural Information Processing Systems 8, pages 757-763. MIT Press, Cambridge, MA, 1996.
17. W. F. Ames. Numerical Methods for Partial Differential Equations. Academic Press, New York, 2nd edition, 1977.
18. T. G. Andersen and B. Sorensen. GMM estimation of a stochastic volatility model: A Monte Carlo study. Journal of Business and Economic Statistics, 14:328-352, 1996.
19. N. Aronszajn. Theory of reproducing kernels. Trans. Amer. Math. Soc., 686:337-404, 1950.
20. G. Auletta. Foundations and Interpretations of Quantum Mechanics. World Scientific, Singapore, 2000.
21. A. Baddeley and R. Turner. Practical maximum pseudolikelihood for spatial point patterns. Research report 98-16, Department of Mathematics, University of Western Australia, August 1998. To appear in Australian and New Zealand Journal of Statistics as a discussion paper.
22. V. Balasubramanian. Statistical inference, Occam's razor, and statistical mechanics on the space of probability distributions. Neural Computation, 9(2):349-368, 1997.
23. R. Balian. From Microphysics to Macrophysics, volume 1. Springer- Verlag, Berlin, 1991.
24. D. H. Ballard. An Introduction to Natural Computation. MIT Press, Cambridge, MA, 1997.
25. K. Banaszek, G. M. D'Ariano, M. G. A. Paris, and M. F. Sacchi. Maximum likelihood estimation of the density matrix. Phys. Rev. A, 61:R10304, 1999.
26. O. E. Barndorff Nielsen. Information and Exponential Families in Statistical Theory. Wiley, New York, 1978.
27. T. R. Bayes. An essay towards solving a problem in the doctrine of chances. Philosophical Transactions of the Royal Society London, 53:370, 1763. Reprinted in Biometrika 45:293, 1958.
28. M. S. Bazaraa, H. D. Sherali, and C. M. Shetty. Nonlinear Programming. Wiley, New York, 2nd edition, 1993.
29. C. Beck and F. Schlogl. Thermodynamics of Chaotic Systems. Cambridge University Press, Cambridge, 1993.
30. A. J. Bell and T. J. Sejnowski. An information-maximization approach to blind separation and blind deconvolution. Neural Computation, 7(6):1129-1159, 1995.
31. J. S. Bell. Speakable and Unspeakable in Quantum Mechanics. Cambridge University Press, Cambridge, 1987.
32. A. Ben Israel and T. N. E. Greville. Generalized Inverses: Theory and Applications. Wiley, New York, 1974.
33. J. O. Berger. Statistical Decision Theory and Bayesian Analysis. Springer-Verlag, New York, 2nd edition, 1985.
34. J. O. Berger and L. M. Berliner. Robust Bayes and empirical Bayes analysis with e-contaminated priors. Ann. Statist., 14:461-486, 1986.
35. J. O. Berger and R. Wolpert. The Likelihood Principle, volume 9 of Monograph Series. IMS Lecture Notes, Hayward, CA, 2nd edition, 1988.
36. P. L. Berger and T. Luckmann. Die gesellschaftliche Konstruktion der Wirklichkeit. S. Fischer Verlag, Frankfurt/Main, 1969.
37. J. M. Bernado. Reference posterior distributions for Bayesian inference (with discussion). Journal of the Royal Statistical Society A, 41:113-147, 1979.
38. J. M. Bernado and A. F. Smith. Bayesian Theory. Wiley, New York, 1994.
39. M. Bertero, T. Poggio, and V. Torre. Ill-posed problems in early vision. In Proceedings of the IEEE, volume 76, pages 869-889, 1988.
40. D. P. Bertsekas. Nonlinear Programming. Athena Scientific, Belmont, MA, 1995.
41. J. Besag. Spatial interaction and the statistical analysis of lattice systems. Journal of the Royal Statistical Society B, 36:192-236, 1974.
42. J. Besag. Statistical analysis of non-lattice data. The Statistician, 24:179-195, 1975.
43. J. Besag. Some methods of statistical analysis for spatial data. Bulletin of the International Statistical Institute, 47:77-92, 1977.
44. D. Beymer, A. Shashua, and T. Poggio. Example based image analysis and synthesis. Artificial Intelligence Laboratory Memo 1431, Massachusetts Institute of Technology, Cambridge, MA, 1993.
45. W. Bialek, C. G. Callan, and S. P. Strong. Field theories for learning probability distributions. Phys. Rev. Lett., 77:4693-4697, 1996. arXiv:cond-mat/9607180.
46. B. M. Bibby and M. Srensen. Martingale estimation functions for discretely observed diffusion processes. Bernoulli, 1:17-39, 1995.
47. K. Binder, editor. Monte Carlo Method in Condensed Matter Physics. Springer-Verlag, Berlin, 1988.
48. K. Binder and D. W. Heermann. Monte Carlo Simulation in Statistical Physics: An Introduction. Springer-Verlag, Berlin, 2nd edition, 1988.
49. K. Binder and D. W. Heermann. Monte Carlo Simulation in Statistical Physics. Springer-Verlag, Berlin, corr. 2nd edition, 1992.
50. S. J. Biondo. Fundamentals of Expert Systems Technology: Principles and Concepts. Ablex, Norwood, NJ, 1990.
51. C. M. Bishop. Curvature-driven smoothing: A learning algorithm for feedforward networks. IEEE Transactions on Neural Networks, 4(5):882-884, 1993.
52. C. M. Bishop. Neural Networks for Pattern Recognition. Oxford University Press, Oxford, 1995.
53. C. M. Bishop. Training with noise is equivalent to Tikhonov regularization. Neural Computation, 7(1):108-116, 1995.
54. E. Bishop and D. Bridges. Constructive Analysis, volume 279 of Grundlehren der Mathematischen Wissenschaften. Springer-Verlag, Berlin, 1985.
55. M. J. Black and A. Rangarajan. On the unification of line processes, outlier rejection, and robust statistics with applications in early vision. Intjl J. Computer Vision, 19(1), 1996.
56. J.P. Blaizot and G. Ripka. Quantum Theory of Finite Systems. MIT Press, Cambridge, MA, 1986.
57. A. Blake and A. Zisserman. Visual Reconstruction. MIT Press, Cambridge, MA, 1987.
58. P. Blanchard and E. Bruening. Variational Methods in Mathematical Physics. Springer-Verlag, Berlin, 1982.
59. N. Bleistein and N. Handelsman. Asymptotic Expansions of Integrals. Dover, New York, 1986. Originally published in 1975 by Holt, Rinehart, and Winston, New York.
60. P. Boehner, editor. Ockham: Philosophical Writings. Nelson, Edinburgh, 1957.
61. G. E. P. Box and G. C. Tiao. Bayesian Inference in Statistical Analysis. Addison-Wesley, Reading, MA, 1973. Wiley Classics Library Edition published 1992.
62. L. Breiman. Probability. Classics in Applied Mathematics. Society for Industrial and Applied Mathematics, Philadelphia, 1992. Originally published by Addison-Wesley, Reading, MA, 1968.
63. L. Breiman. Hinging hyperplanes for regression, classification, and function approximation. IEEE Trans. Inform. Theory, 39(3):999-1013, 1993.
64. L. Breiman, J. H. Friedman, R. A. Olshen, and C. J. Stone. Classification and Regression Trees. Chapman & Hall, New York, 1993.
65. G. L. Bretthorst. Bayesian Spectrum Analysis and Parameter Estimation, volume 48 of Lecture Notes in Statistics. Springer-Verlag, Berlin, 1988. Available at http://bayes.wustl.edu/glb/book.pdf.
66. R. Brunelli and T. Poggio. Template matching: Matched spatial filters and beyond. Artificial Intelligence Laboratory Memo 1549, Massachusetts Institute of Technology, Cambridge, MA, 1995.
67. B. Buck and V. A. Macaulay, editors. Maximum Entropy in Action. Oxford University Press, Oxford, 1991.
68. W. Buntine and A. Weigend. Bayesian back-propagation. Complex Systems, 5:603, 1991.
69. C. J. C. Burges. A tutorial on support vector machines for pattern recognition. Data Mining and Knowledge Discovery, 2(2): 121-167, 1998.
70. K. Burrage, A. Willimas, J. Erhel, and B. Pohl. Implementation of a generalized cross validation algorithm using deflation techniques for systems of linear equations. Appl. Num. Math., 19:17-31, 1995.
71. V. Buzek, G. Drobny, R. Derka, G. Adam, and H. Wiedemann. Reconstruction of quantum states from incomplete data. Chaos, Solitons, and Fractals, 10:981-1074, 1999. arXiv:quant-ph/9805020.
72. J. Cardy. Scaling and Renormalization in Statistical Physics. Cambridge University Press, Cambridge, 1996.
73. B. P. Carlin and T. A. Louis. Bayes and Empirical Bayes Methods for Data Analysis, volume 69 of Monographs on Statistics and Applied Probability. Chapman & Hall/CRC, Boca Raton, FL, 1996.
74. N. Cartwright. How the Laws of Physics Lie. Clarendon Press, Oxford, 1983.
75. N. Cartwright. Nature's Capacities and Their Measurement. Clarendon Press, Oxford, 1989.
76. K. Chadan, D. Colton, L. Paivarinta, and W. Rundell. An Introduction to Inverse Scattering and Inverse Spectral Problems. SIAM, Philadelphia, 1997.
77. K. Chadan and P. C. Sabatier. Inverse Problems in Quantum Scattering Theory. Springer-Verlag, New York, 1989.
78. G. Chamberlain. Asymptotic efficiency in estimation with conditional moment restrictions. Journal of Econometrics, 34:305-334, 1987.
79. C. B. Chiu, E. C. G. Sudarshan, and B. Misra. Time evolution of unstable quantum states and a resolution of Zeno's paradox. Phys. Rev. D, 16(2):520-529, 1976.
80. Y. Choquet Bruhat, C. DeWitt Morette, and M. Dillard Bleick. Analysis, Manifolds, and Physics. Part I: Basics. North Holland, Amsterdam, 1982.
81. A. Cichocki and R. Unbehauen. Neural Networks for Optimization and Signal Processing. Wiley, Chichester, 1993.
82. B. S. Clarke and A. R. Barron. Information-theoretic asymptotics of Bayes methods. IEEE Transactions on Information Theory, 36(3) :453- 471, 1990.
83. P. Clifford. Markov random fields in statistics. In G. R. Grimmet and D. J. A. Welsh, editors, Disorder in Physical Systems. A Volume in Honour of John M. Hammersley, pages 19-32. Clarendon Press, Oxford, 1990.
84. J. Collins. Renormalization. Cambridge University Press, Cambridge, 1984.
85. C. Cortes and V. Vapnik. Support vector networks. Machine Learning, 20:1-25, 1995.
86. D. R. Cox and D. V. Hinkley. Theoretical Statistics. Chapman & Hall, London, 1974.
87. R. T. Cox. Probability, frequency, and reasonable expectation. Am. J. Phys., 14:1, 1946.
88. R. T. Cox. The Algebra of Probable Inference. Johns Hopkins University Press, Baltimore, 1961.
89. P. Craven and G. Wahba. Smoothing noisy data with spline functions: estimating the correct degree of smoothing by the method of generalized cross-validation. Numer. Math., 31:377-403, 1979.
90. N. A. C. Cressie. Statistics for Spatial Data. Wiley, New York, 1993.
91. M. Creutz. Quarks, gluons, and lattices. Cambridge University Press, Cambridge, 1983.
92. N. Cristianini, C. Campbell, and J. Shawe Taylor. Dynamically adapting kernels in support vector machines. In M. S. Kearns, S. S. Solla, and D. A. Cohn, editors, Advances in Neural Information Processing Systems 11, pages 204-210. MIT Press, Cambridge, MA, 1999.
93. N. Cristianini and J. Shawe Taylor. An Introduction to Support Vector Machines and Other Kernel-Based Learning Methods. Cambridge University Press, Cambridge, 2000.
94. F. Cucker and S. Smale. On the mathematical foundation of learning. Bulletin of the American Mathematical Society, 39(1):l-39, 2002.
95. G. D'Agostini. Bayesian reasoning in high energy physics: Principles and applications. Yellow Report 99-03, CERN, 1999. Available at http://www-zeus. romal.infn.it/~agostini/prob+stat.html.
96. A. P. David. Applications of a general propagation algorithm for probabilistic expert systems. Statistics and Computing, 2:25-36, 1992.
97. R. Davidson and J. G. MacKinnon. Estimation and Inference in Econometrics. Oxford University Press, New York, 1993.
98. L. Davis, editor. Genetic Algorithms and Simulated Annealing. Morgan Kaufmann, San Mateo, CA, 1987.
99. L. Davis, editor. Handbook of Genetic Algorithms. Van Nostrand Reinhold, New York, 1991.
100. P. Dayan, G. E. Hinton, R. M. Neal, and R. S. Zemel. The Helmholtz machine. Neural Computation, 7:889-904, 1995.
101. N. G. de Bruijn. Asymptotic Methods in Analysis. Dover, New York, 1981. Originally published by North-Holland Publishing Co., Amsterdam, 1958.
102. B. de Finetti. Probability, Induction, and Statistics. Wiley, New York, 1972.
103. G. Deco and D. Obradovic. An Information-Theoretic Approach to Neural Computing. Springer-Verlag, New York, 1996.
104. A. P. Dempster, N. Laird, and D. B. Rubin. Maximum likelihood from incomplete data via the EM algorithm. Journal of the Royal Statistical Society, B, 39:1-38, 1977.
105. H.P. Deutsch. Derivate und Interne Modelle. Schaffer-Poeschel, Stuttgart, 2nd edition, 2001.
106. L. Devroye, L. Gyorfi, and G. Lugosi. A Probabilistic Theory of Pattern Recognition. Springer-Verlag, New York, 1996.
107. C. Di Castro and G. Jona Lasinio. The renormalization group approach to critical phenomena. In C. Domb and M. S. Green, editors, Phase Transitions and Critical Phenomena, volume 6. Academic Press, London, 1976.
108. P. Diaconis and D. Preedman. Asymptotic of graphical projection pursuit. The Annals of Statistics, 12(3):793-815, 1984.
109. R. Dietrich, M. Opper, and H. Sompolinsky. Statistical mechanics of support vector networks. Phys. Rev. Lett, 82(14):2975-2978, 1999.
110. D. L. Donoho and I. M. Johnstone. Projection-based approximation and a duality with kernel methods. Ann. Statist., 17(1):58-106, 1989.
111. J. L. Doob. Stochastic Processes. Wiley, New York, 1953. New edition published 1990.
112. V. Dose and W. von der Linden. Outlier tolerant parameter estimation. In W. von der Linden, V. Dose, R. Fischer, and R. Preuss, editors, Maximum Entropy and Bayesian Methods. Kluwer Academic Publishers, Dordrecht, 1999.
113. R. M. Dudley. A Course on Empirical Processes, volume 1097 of Lecture Notes in Mathematics, pages 2-142. Springer-Verlag, New York, 1984.
114. J. Durbin and S. J. Koopman. Monte Carlo maximum likelihood estimation for non-Gaussian state space models. Biometrika, 84(3):669-684, 1997.
115. W. Ebeling, J. Preund, and F. Schweitzer. Komplexe Strukturen: Entropie und Information. Teubner, Stuttgart, 1998.
116. E. Eells. Probabilistic Causality. Cambridge University Press, Cambridge, 1991.
117. K. B. Efetov. Supersymmetry and theory of disordered metals. Advances in Physics, 32:53-127, 1983.
118. B. Efron. Bootstrap methods: Another look at the jacknife. Ann. Statist., 7:1-26, 1979.
119. B. Efron. Nonparametric estimates of the standard error: The jackknife, the bootstrap, and other methods. Biometrika, 68:589-599, 1981.
120. B. Efron and R. J. Tibshirani. An Introduction to the Bootstrap, volume 57 of Monographs on Statistics and Applied Probability. Chapman & Hall, New York, 1993.
121. J. M. Eisenberg and W. Greiner. Microscopic Theory of the Nucleus. North-Holland, Amsterdam, 1972.
122. H. Engl, M. Hanke, and A. Neubauer. Regularization of Inverse Problems. Kluwer, Cordrecht, 1996.
123. B. S. Everitt and D. J. Hand. Finite Mixture Distributions. Chapman & Hall, New York, 1981.
124. T. Evgeniou, M. Pontil, and T. Poggio. Regularization networks and support vector machines. Advances in Computational Mathematics, 13:1-50, 2000.
125. R. Fernandez, J. Frohlich, and A. D. Sokal. Random Walks, Critical Phenomena, and Triviality in Quantum Field Theory. Springer-Verlag, Berlin, 1992.
126. H. Feshbach. Theoretical Nuclear Physics: Nuclear Reactions. Wiley, New York, 1992.
127. M. W. Firebaugh. Artificial Intelligence: A Knowledge-Based Approach. PWS-Kent, Boston, MA, 1989.
128. K. H. Fischer and J. A. Hertz. Spin Glasses. Cambridge University Press, Cambridge, 1991.
129. M. C. Fischer, B. Gutierrez Medina, and M. G. Raizen. Observation of the quantum Zeno and Anti-Zeno effects in an unstable system. Phys. Rev. Lett, 87(4):040402, 2001.
130. R. Fischer, K. M. Hanson, V. Dose, and W. von der Linden. Background estimation in experimental spectra. Phys. Rev. E, 61:1152, 2000.
131. R. A. Fisher. On the mathematical foundations of theoretical statistics. Philosophical Transactions of the Royal Society A, 222:309, 1922.
132. R. A. Fisher. Inverse probability. Proc. Camb. Phil. Soc., 26:528, 1930.
133. R. A. Fisher. Statistical Methods and Scientific Inference. Oliver and Boyd, London, 2nd edition, 1965.
134. R. Fletcher. Practical Methods of Optimization. Wiley, New York, 1987.
135. L. Fonda, G. C. Ghirardi, and A. Rimini. Decay theory of unstable quantum systems. Rep. Prog. Phys., 41:587-631, 1978.
136. I. Fredholm. Sur une classe d'equations fonctionelles. Acta Math., 27:365-390, 1903.
137. D. J. Freedman, M. Riesenhuber, T. Poggio, and E. K. Miller. Categorical representation of visual stimuli in the primate prefrontal cortex. Science, 291:312-316, 2001.
138. J. H. Friedman and W. Stuetzle. Projection pursuit regression. J. Am. Statist. Assoc., 76(376):817-823, 1981.
139. J. H. Friedman and J. W. Tukey. A projection pursuit algorithm for exploratory data analysis. IEEE Trans. Comput., 24:1000-1006, 1974.
140. K. Fukunaga. Statistical Pattern Recognition. Academic Press, Boston, 1990.
141. S. I. Gallant. Neural Network Learning. MIT Press, Cambridge, MA, 1993.
142. C. W. Gardiner. Handbook of Stochastic Methods. Springer-Verlag, Berlin, 2nd edition, 1990.
143. E. Gardner. Maximum storage capacity in neural networks. Europhysics Letters, 4:481-485, 1987.
144. E. Gardner. The space of interactions in neural network models. Journal of Physics A, 21:257-270, 1988.
145. E. Gardner and B. Derrida. Optimal storage properties of neural network models. Journal of Physics A, 21:271-284, 1988.
146. D. Geiger and F. Girosi. Parallel and deterministic algortihms for MRFs: Surface reconstruction. IEEE Trans, on Pattern Analysis and Machine Intelligence, 13(5):401-412, 1991.
147. D. Geiger and A. L. Yuille. A common framework for image segmentation. Int'l J. Computer Vision, 6(3):227-243, 1991.
148. I. M. GePfand and B. M. Levitan. On the determination of a differential equation from its spectral function. Trans. Amer. Soc., 1:253-302, 1951.
149. S. B. Gelfand and S. K. Mitter. On Sampling Methods and Annealing Algorithms. Markov Random Fields - Theory and Applications. Academic Press, New York, 1993.
150. A. Gelman, J. B. Carlin, H. S. Stern, and D. B. Rubin. Bayesian Data Analysis. Chapman & Hall, New York, 1995.
151. D. Geman and G. Reynolds. Constraint restoration and the recover of discontinuities. IEEE Trans, on Pattern Analysis and Machine Intelligence, 14:367-383, 1992.
152. S. Geman and D. Geman. Stochastic relaxation, Gibbs distributions, and the Bayesian restoration of images. IEEE Trans, on Pattern Analysis and Machine Intelligence, 6:721-741, 1984. Reprinted in Shafer & Pearl, editors, 1990. Readings in Uncertainty Reasoning. Morgan Kaufmann, San Mateo, CA, 1990.
153. C. Geyer. Practical Markov chain Monte Carlo (with discussion). Statistical Science, 7:473-511, 1992.
154. M. Gibbs and D. J. C. MacKay. Efficient implementation of Gaussian processes. Cavendish Laboratory, Cambridge, 1997. Draft manuscript, available from http://www.cs.toronto.edu/mackay/gpros.ps.gz.
155. F. J. Giessibl, S. Hembacher, H. Bielefeld, and J. Mannhart. Subatomic features on the silicon (Ill)-(7x7) surface observed by atomic force microscopy. Science, 289:422-425, 2000.
156. T. Gilovich, D. Griffin, and D. Kahnemann, editors. Heuristics and Biases. Cambridge University Press, Cambridge, 2002.
157. B. G. Giraud, A. Lapedes, L. C. Liu, and J. C. Lemm. Lorentzian neural nets. Neural Networks, 8(5):757-767, 1995.
158. F. Girosi. Models of noise and robust estimates. Artificial Intelligence Laboratory Memo 1287, Massachusetts Institute of Technology, Cambridge, MA, 1991.
159. F. Girosi. Some extensions of radial basis functions and their applications in artificial intelligence. Computers Math. Applic., 24(12):61-80, 1992.
160. F. Girosi. An equivalence between sparse approximation and support vector machines. Artificial Intelligence Laboratory Memo 1606, Massachusetts Institute of Technology, Cambridge, MA, 1997.
161. F. Girosi and N. T. Chan. Prior knowledge and the creation of virtual examples for rbf networks. In IEEE Workshop on Neural Networks for Signal Processing, Cambridge, MA, 1995.
162. F. Girosi, M. Jones, and T. Poggio. Regularization theory and neural network architectures. Neural Computation, 7(2):219-269, 1995.
163. F. Girosi, T. Poggio, and B. Caprile. Extensions of a theory of networks for approximations and learning: Outliers and negative examples. In R. Lippmann, J. Moody, and D. Touretzky, editors, Advances in Neural Information Processing Systems 3. Morgan Kaufmann, San Mateo, CA, 1991.
164. D. Giulini, E. Joos, C. Kiefer, I.O. Stamatescu, and H. D. Zeh. Decoherence and the Appearance of a Classical World in Quantum Theory. Springer-Verlag, Berlin, 1996.
165. J. Glimm and A. Jaffe. Quantum Physics. A Functional Integral Point of View. Springer-Verlag, New York, 1987.
166. K. Goeke, R. Y. Cusson, F. Griimmer, P.G. Reinhard, and H. Reinhardt. Time dependent Hartree-Fock and beyond: A review. Prog. Theor. Phys. (Suppl), 74 & 75:33, 1983.
167. D. E. Goldberg. Genetic Algorithms in Search, Optimization, and Machine Learning. Addison-Wesley, Redwood City, CA, 1989.
168. R. M. Golden. Mathematical Methods for Neural Network Analysis and Design. MIT Press, Cambridge, MA, 1996.
169. G. H. Golub, M. Heath, and G. Wahba. Generalized cross validation as a method for choosing a good ridge parameter. Technometrics, 21:215- 224, 1979.
170. G. H. Golub and C. F. van Loan. Matrix Computations. Johns Hopkins University Press, Baltimore, 3rd edition, 1996.
171. G. H. Golub and U. von Matt. Generalized cross-validation for large scale problems. Journal of Computational and Graphical Statistics, 6(1):l-34, 1997.
172. J. Gomes and L. Velho. Image Processing for Computer Graphics. Springer-Verlag, New York, 1997.
173. R. C. Gonzales and R. E. Woods. Digital Image Processing. Addison- Wesley, Reading, MA, 1993.
174. I. J. Good. Some history of the hierachical Bayesian methodology. In J. M. Bernardo, M. H. DeGroot, D. V. Lindley, and A. F. M. Smith, editors, Bayesian Statistics II. North-Holland, Amsterdam, 1980.
175. I. J. Good. Good Thinking: The Foundations of Probability and Its Applications. University of Minnesota Press, Minneapolis, 1983.
176. I. J. Good and R. A. Gaskins. Nonparametric roughness penalties for probability densities. Biometrika, 58:255-277, 1971.
177. C. Goodall. M-estimators of location: An outline of the theory. In D. C. Hoaglin, F. Mosteller, and J. W. Tukey, editors, Understanding Robust and Exploratory Data Analysis, pages 339-403. Wiley, New York, 1983.
178. G. Gorz, editor. Einfuhrung in die kunstliche Intelligenz. Addison- Wesley, Bonn, Paris, 1993.
179. C. Gourieroux. ARCH Models and Financial Applications. Springer- Verlag, New York, 1997.
180. C. Gourieroux, A. Monfort, and A. Trognon. Pseudo maximum likelihood methods: Theory. Econometrica, 52:681-700, 1984.
181. W. P. Gouveia and J. A. Scales. Resolution of seismic waveform inversion: Bayes versus Occam. Inverse Problems, 13:323-349, 1997.
182. I. Gradstein and I. Ryshik. Tables of Series, Products, and Integrals. Harry Deutsch, 1981.
183. P. J. Green and B. W. Silverman. Nonparametric Regression and Generalized Linear Models, volume 58 of Monographs on Statistics and Applied Probability. Chapman & Hall, London, 1994.
184. C. Grofiman and H.G. Roos. Numerik partieller Differentialgleichungen. Teubner, Stuttgart, 1994.
185. S. F. Gull. Bayesian data analysis straight line fitting. In J. Skilling, editor, Maximum Entropy and Bayesian Methods, pages 511-518. Kluwer Academic Publishers, Dordrecht, 1989.
186. S. F. Gull. Developments in maximum entropy data analysis. In J. Skilling, editor, Maximum Entropy and Bayesian Methods, pages 53- 71. Kluwer Academic Publishers, Dordrecht, 1989.
187. S. F. Gull and G. J. Daniell. The maximum entropy method. In C. Van Schooneveld, editor, Image formation from coherence functions in astronomy, pages 219-225. Reidel, Dordrecht, 1979.
188. H. Gumin and Meier H., editors. Einfuhrung in den Konstruktivismus. Piper, Miinchen, Zurich, 1992.
189. W. Hackbusch. Multi-grid Methods and Applications. Springer-Verlag, New York, 1985.
190. W. Hackbusch. Integralgleichungen. Teubner, Stuttgart, 1989.
191. W. Hackbusch. Iterative Losung grofter schwachbesetzter Gleichungssysteme. Teubner, Stuttgart, 1993.
192. J. Hadamard. Lectures on the Cauchy Problem in Linear Partial Differential Equations. Yale University Press, New Haven, 1923.
193. P. Hall. The Bootstrap and Edgeworth Expansion. Springer-Verlag, New York, 1992.
194. Hammersley J.M. and Clifford P. Markov fields on finite graphs and lattices. Unpublished, 1971.
195. J. M. Hammersley and D. C. Handscomb. Monte Carlo Methods, volume 3 of Monographs on Statistics and Applied Probability. Chapman & Hall, London, 1964.
196. F. R. Hampel, E. M. Ronchetti, P. J. Rousseeuw, and W. A. Stahel. Robust Statistics. The Approach Based on Influence Functions. Wiley, New York, 1986.
197. L. Hansen. Large sample properties of generalized method of moments estimators. Econometrica, 50:1029-1054, 1982.
198. W. Hardle. Applied nonparametric regression. Cambridge University Press, Cambridge, 1990.
199. J. Hartung. Statistik. Oldenbourg, Miinchen, 13th edition, 2002.
200. A. C. Harvey, E. Ruiz, and N. Shepard. Multivariate stochastic volatility models. Review of Econometric Studies, 61:247-264, 1994.
201. T. J. Hastie and R. J. Tibshirani. Generalized additive models. Statist. Sci., 1:297-318, 1986.
202. T. J. Hastie and R. J. Tibshirani. Generalized additive models: Some applications. J. Am. Statist. Assoc., 82:371-386, 1987.
203. T. J. Hastie and R. J. Tibshirani. Generalized Additive Models, volume 43 of Monographs on Statistics and Applied Probability. Chapman & Hall, London, 1990.
204. W. K. Hastings. Monte Carlo sampling methods using Markov chains and their applications. Biometrika, 57:97-109, 1970.
205. F. Hayes Roth. The knowledge based expert system: A tutorial. IEEE Computer, 17(9): 11-28, 1984.
206. R. Hecht Nielsen. Neurocomputing. Addison-Wesley, Reading, MA, 1990.
207. C. W. Helstrom. Quantum Detection and Estimation Theory. Academic Press, New York, 1976.
208. R. Herbrich, T. Graepel, and C. Campell. Bayesian learning in reproducing kernel Hilbert spaces. Technical Report TR 99-11, Technische Universitat Berlin, 1999. Available from http://stat.cs.tu-berlin.de/~ralfh/publications. html.
209. J. Hertz, A. Krogh, and R.G. Palmer. Introduction to the Theory of Neural Computation. Addison-Wesley, Redwood City, CA, 1991.
210. D. Hilbert and R. Courant. Methods of Mathematical Physics, volumes 1 & 2. Wiley, New York, 1989. First German editions published by Springer-Verlag, Berlin, 1924, 1937.
211. G. E. Hinton, P. Dayan, B. J. Frey, and R. M. Neal. The cwake-sleep' algorithm for unsupervised neural networks. Science, 268:1158-1161, 1995.
212. G. E. Hinton and T. J. Sejnowski. Learning and relearning in Boltzmann machines. In D. E. Rumelhart, J. L. McClelland, and the PDP Research Group, editors, Parallel Distributed Processing, pages 282-317. MIT Press, Cambridge, MA, 1986.
213. D. C. Hoaglin, F. Mosteller, and J. W. Tukey, editors. Understanding Robust and Exploratory Data Analysis. Wiley, New York, 1983.
214. H. Hochstadt and B. Lieberman. An inverse Sturm-Liouville problem with mixed given data. SIAM J. Appl. Math., 34:676-680, 1976.
215. R. Hoffmann, V. I. Minkin, and B. K. Carpenter. Ockham's razor and chemistry. Bulletin de la Societe Chimique de France, 133:117-130, 1996. Available at http://www.rz.uni-karlsruhe.de/ed01/Hyle/Hyle3/hoffman.htm.
216. B. Hofmann. Mathematik inverser Probleme. Teubner Verlag, Stuttgart, Leibzig, 1999.
217. A. S. Holevo. Probabilistic and Statistical Aspects of Quantum Theory. North-Holland, Amsterdam, 1982.
218. J. H. Holland. Adaption in Natural and Artificial Systems. University of Michigan Press, Ann Arbor, MC, 1975. MIT Press, Cambridge, MA, second edition, 1992.
219. S. Holm. A simple sequentially rejective multiple test procedure. Scandinavian Journal of Statistics, 6:65-70, 1979.
220. J. Honerkamp. Stochastic Dynamical Systems. Concepts, Numerical Methods, Data Analysis. VCH Verlag, New York, 1994.
221. J. Honerkamp. Statistical Physics. Springer-Verlag, New York, 1998.
222. J. Honerkamp and J. Weese. Tikhonovs regularization method for illposed problems: A comparison of different methods. Cont. Mech. Thermodyn., 2:17-30, 1990.
223. R. Horst, M. Pardalos, and N. V. Thoai. Introduction to Global Optimization. Kluwer Academic Publishers, Dordrecht, 1995.
224. P. J. Huber. Robust estimation of location parameter. Ann. Math. Stat., 35(1):1753-1758, 1964.
225. P. J. Huber. Robust smoothing. In E. Launer and G. Wilkinson, editors, Robustness in Statistics. Academic Press, New York, 1979.
226. P. J. Huber. Robust Statistics. Wiley, New York, 1981.
227. P. J. Huber. Projection pursuit. Ann. Statist., 13(2):435-475, 1985.
228. J. Hull. Options, Futures, and Other Derivative Securities. Prentice Hall, Englewood Cliffs, NJ, 1989.
229. B. Iglewicz. Robust scale estimators and confidence intervals for location. In D. C. Hoaglin, F. Mosteller, and J. W. Tukey, editors, Understanding Robust and Exploratory Data Analysis, pages 405-431. Wiley, New York, 1983.
230. J. P. Ignizio. Introduction to Expert Systems: The Development and Implementation of Rule-Based Expert Systems. Prentice Hall, Englewood Cliffs, NJ, 1989.
231. W. M. Itano, D. J. Heinzen, J. J. Bellinger, and D. J. Wineland. Quantum Zeno effect. Phys. Rev. A, 41:2295-2300, 1990.
232. C. Itzkyson and J.M. Drouffe. Statistical Field Theory, volumes 1 & 2. Cambridge University Press, Cambridge, 1989.
233. B. Jahne. Digitale Bildverarbeitung. Springer-Verlag, Berlin, 4th edition, 1997.
234. E. T. Jaynes. Probability theory: The logic of science, 2000. Available at http://bayes. wustl. edu/et j/prob. html.
235. R. C. Jeffrey. The Logic of Decision. University of Chicago Press, Chicago, 1983.
236. R. C. Jeffrey. Probabilistic judgment, 1999. Available from http://www.princeton.edu/~bayesway/.
237. R. C. Jeffrey. Probabilistic thinking, 1999. Available fromhttp://www.princeton.edu/~bayesway/.
238. H. Jeffreys. Theory of Probability. Oxford University Press, Oxford, 3rd edition, 1961. First edition published 1939.
239. H. Jeffreys and J. O. Berger. Ockham's razor and Bayesian analysis. American Scientist, 80:468-477, 1992.
240. H. Jeggle. Nichtlineare Funktionalanalys. Teubner, Stuttgart, 1979.
241. F. V. Jensen. An Introduction to Bayesian Networks. Springer-Verlag, New York, 1996.
242. F. V. Jensen, S. L. Lauritzen, and K. G. Olesen. Bayesian updating in causal probabilistic networks by local computations. Computational Statistics Quarterly, 5:269-282, 1990.
243. M. C. Jones and R. Sibson. What is projection pursuit? Journal of the Royal Statistical Society A, 150:1-36, 1987.
244. M. J. Jones and T. Poggio. Model-based matching of line drawings by linear combinations of prototypes. In Proceedings of the IEEE 5th International Conference on Computer Vision, pages 531-536. IEEE Computer Society Press, Cambridge, MA, 1995.
245. M. Jordan, editor. Learning in Graphical Models. MIT Press, Cambridge, MA, 1999.
246. M. I. Jordan and R. A. Jacobs. Hierachical mixtures of experts and the EM algorithm. Neural Computation, 6:181-214, 1994.
247. M. Kac. Can one hear the shape of a drum? Am. Math. Mon., 73:1-23, 1966.
248. D. Kahneman, P. Slovic, and A. Tversky. Judgement Under Uncertainty: Heuristics and Biases. Cambridge University Press, New York, 1982.
249. L. Kahnemann and A. Tversky. Judgment under uncertainty: Heuristics and biases. Science, 182:1124-1131, 1974.
250. L. Kahnemann and A. Tversky. Prospect theory: An analysis of decision under risk. Econometrica, 47(263):269-291, 1979.
251. M. Kaku. Quantum Field Theory. Oxford University Press, Oxford, 1993.
252. A. Kandel. Fuzzy Techniques in Pattern Recognition. Wiley, New York, 1982.
253. I. Kant. Kritik der reinen Vernunft, volume 3 of Kants Werke. Koniglich PreuBische Akademie der Wissenschaften, Berlin, 2nd edition, 1787. Reprinted by Walter de Gruyter & Co, Berlin, 1968.
254. M. J. Kearns and U. V. Vazirani. An Introduction to Computational Learning Theory. MIT Press, Cambridge, MA, 1994.
255. J. B. Keller. Inverse problems. Ann. Math. Mon., 83:107-118, 1976.
256. D. F. Kerridge. Inaccuracy and inference. Journal of the Royal Statistical Society, 23:184-194, 1961.
257. J. M. Keynes. A Treatise on Probability. MacMillan, London, 1921.
258. S. Kim, N. Shephard, and S. Chib. Stochastic volatility: Likelihood inference and comparison with arch models. Review of Economic Studies, 65:361-393, 1998.
259. G. S. Kimmeldorf and G. Wahba. A correspondence between Bayesian estimation on stochastic processes and smoothing by splines. Ann. Math. Stat., 41:495-502, 1970.
260. G. S. Kimmeldorf and G. Wahba. Spline functions and stochastic processes. Sankhya Ser. A, 32(Part 2):173-180, 1970.
261. S. Kirkpatrick, C. D. Gelatt Jr., and M. P. Vecchi. Optimization by simulated annealing. Science, 220:671-680, 1983.
262. A. Kirsch. An Introduction to the Mathematical Theory of Inverse Problems. Springer-Verlag, New York, 1996.
263. G. Kitagawa and W. Gersch. Smoothness Priors Analysis of Time Series. Springer-Verlag, New York, 1996.
264. H. Kleinert. Pfadintegrale. Wissenschaftsverlag, Mannheim, 1993.
265. G. J. Klir and B. Yuan. Fuzzy Sets and Fuzzy Logic. Prentice Hall, Upper Saddle River, NJ, 1995.
266. G. J. Klir and B. Yuan, editors. Fuzzy Sets, Fuzzy Logic, and Fuzzy Systems. World Scientific, Singapore, 1996.
267. M. Koecher. Lineare Algebra und analytische Geometrie. Springer- Verlag, Berlin, 1985.
268. A. G. Kofrnan and G. Kurizki. Acceleration of quantum decay processes by frequent observations. Nature, 405:546-549, 2000.
269. T. Kohonen. Self-Organizing and Associative Memory. Springer, Berlin, 1984.
270. T. Kohonen. Self-Organizing Maps. Springer, Berlin, 1995.
271. P. Kontkanen, P. Myllymaki, and H. Tirri. Constructing Bayesian finite mixture models by the EM algorithm. Technical Report Series NC-TR- 97-003, NeuroCOLT, 1997.
272. H. Kopp. Bildverarbeitung interaktiv. Teubner, Stuttgart, 1997.
273. B. Kosko. Neural Networks for Signal Processing. Prentice-Hall, Englewood Cliffs, NJ, 1992.
274. J. R. Koza. Genetic Programming. MIT Press, Cambridge, MA, 1992.
275. S. Kullback. Information Theory and Statistics. Wiley, New York, 1951.
276. S. Kullback and R. A. Leibler. On information and sufficiency. Ann. Math. Statist, 22:79-86, 1951.
277. H. Kyburg Jr. and H. Smokier, editors. Studies in Subjective Probabilities. Robert E. Krieger, Huntington, NY, 1980.
278. D. P. Landau and K. Binder. A Guide to Monte Carlo Simulations in Statistical Physics. Cambridge University Press, Cambridge, 2000.
279. A. Lapedes and R. Farber. How neural nets work. In D. Z. Anderson, editor, Neural Information Processing Systems, pages 442-456. American Institute of Physics, New York, 1988.
280. P. S. Laplace. Theorie Analytique des Probabilites. Courcier, Paris, 1812.
281. P. S. Laplace. Philosophical Essay on Probability. Dover, New York, 1951.
282. S. L. Lauritzen. Graphical Models. Oxford University Press, Oxford, 1996.
283. C. L. Lawson and R. J. Hanson. Solving Least Squares Problems. Prentice Hall, Englewood Cliffs, NJ, 1974.
284. M. Le Bellac. Quantum and Statistical Field Theory. Oxford Science Publications, Clarendon Press, Oxford, 1991.
285. L. Le Cam. Asymptotic Methods in Statistical Decision Theory. Springer-Verlag, New York, 1986.
286. T. K. Leen. Prom data distributions to regularization in invariant learning. Neural Computation, 7(5):974-981, 1995.
287. J. C. Lemm. Lecture notes 'Econophysics'. Available at http://pauli.uni-muenster.de/~lemm/econoWS99/econo.ps.gz.
288. J. C. Lemm. Entscheidungsstrategien und Informationskosten. Diplomarbeit, Fachbereich Psychologie, Universitat Minister, 1984.
289. J. C. Lemm. Inhomogeneous random phase approximation: A solvable model. Annals of Physics, 244(1):201-238, 1995.
290. J. C. Lemm. Inhomogeneous random phase approximation for nuclear and atomic reactions. Annals of Physics, 244(1): 136-200, 1995.
291. J. C. Lemm. Prior information and generalized questions. Artificial Intelligence Laboratory Memo 1598, Massachusetts Institute of Technology, Cambridge, MA, 1996.
292. .C. Lemm. Fuzzy interface with prior concepts and non-convex regularization. In Wilfried Brauer, editor, Fazzy-Neuro Systems '98- Computational Intelligence. Proceedings of the 5. International Workshop 'Fuzzy-Neuro Systems '98' (FNS '98), March 19-20, 1998, Munich, Germany, Proceedings in Artificial Intelligence, pages 298-305. Infix, Sankt Augustin, 1998.
293. J. C. Lemm. Fuzzy rules and regularization theory. In ELITE European Laboratory for Intelligent Techniques Engineering, editor, 6th European Congress on Intelligent Techniques and Soft Computing (EUFIT '98). Mainz, Aachen, 1998.
294. J. C. Lemm. How to Implement a priori information: A statistical mechanics approach. Universitat Munster, Institut fur Theoretische Physik, MS-TP1-98-12, 1998. arXiv:cond-mat/9808039.
295. J. C. Lemm. Quadratic concepts. In L. Niklasson, M. Boden, and T. Ziemke, editors, ICANN 98. Proceedings of the 8th International Conference on Artificial Neural Networks, Skovde, Sweden, September 1-4, 1998, pages 579-584. Springer-Verlag, London, 1998.
296. J. C. Lemm. Bayesian field theory. Technical Report MS-TP1-99-1, Universitat Minister, 1999. arXiv:physics/9912005.
297. J. C. Lemm. Mixtures of Gaussian process priors. In ICANN 99. Proceedings of the 9th International Conference on Artificial Neural Networks, Edinburgh, UK, September 7-10, 1999. IEEE Conference Publication, London, 1999.
298. J. C. Lemm. Inverse time-dependent quantum mechanics. Phys. Lett. A, 276(1-4):19-24, 2000. arXiv:quant-ph/0002010.
299. J. C. Lemm. Nonparametric approaches to density estimation. In Proceedings of the International Joint Conference on Neural Networks, Como, Italy. IEEE Conference Publications, London, 2000.
300. J. C. Lemm. Bayesian field theory and approximate symmetries. In A. Mohammad-Djafari, editor, Bayesian Inference and Maximum Entropy Methods in Science and Engineering, International Workshop, Gif sur Yvette, France, 2000, volume 568 of AIP Conference Proceedings. American Institute of Physics, 2001. MS-TP1-00-10.
301. J. C. Lemm, V. Beiu, and J. G. Taylor. Density estimation as a preprocessing step for constructive algorithms. In Kappen B. and S. Gielen, editors, Neural Networks: Artificial Intelligence and Industrial Applications. Proceedings of the 3rd SNN Neural Network Symposium. The Netherlands, Nijmegen, September 14~15, 1995, pages 213-216. Springer-Verlag, Berlin, 1995.
302. J. C. Lemm, B. G. Giraud, and A. Weiguny. Beyond the timeindependent mean field theory for nuclear and atomic reactions: Inclusion of particle-hole correlations in a generalized random phase approximation. Phys. Rev. Lett., 73:420-423, 1994.
303. J. C. Lemm and J. Uhlig. Bayesian inverse quantum theory. Few-Body Systems, 29:25-52, 2000. arXiv:quant-ph/0006027.
304. J. C. Lemm and J. Uhlig. Hartree-Fock approximation for inverse many-body problems. Phys. Rev. Lett, 84:4517-4520, 2000. arXiv:nuclth/9908056.
305. J. C. Lemm, J. Uhlig, and A. Weiguny. A Bayesian approach to inverse quantum statistics. Phys. Rev. Lett, 84:2068-2071, 2000. arXivicondmat/9907013.
306. J. C. Lemm, J. Uhlig, and A. Weiguny. Bayesian reconstruction of approximately periodic potentials for quantum systems at finite temperatures. The European Physical Journal B, 20(3):349-366, 2001. MS TP1-00-4, arXiv:quant-ph/0005122.
307. H. Lenk. Interpretation und Realitat. Suhrkamp, Frankfurt a. M., 1995.
308. T. Leonard and J. S. J. Hsu. Bayesian Methods. Cambridge University Press, Cambridge, 1999.
309. M. A. Lifshits. Gaussian Random Functions. Kluwer Academic Publishers, Dordrecht, 1995.
310. D. V. Lindley. A statistical paradox. Biometrica, 44:187-192, 1957.
311. D. V. Lindley. Bayesian Statistics, A Review. SIAM, Philadelphia, 1972.
312. D. V. Lindley and L. D. Phillips. Inference for a Bernoulli process (a Bayesian view). Amer. Statist., 30:112-119, 1976.
313. N. K. Logothetis, T. Vetter, A. Hurlbert, and T. Poggio. View-based models of 3d object recognition and class-specific invariances. Artificial Intelligence Laboratory Memo 1472, Massachusetts Institute of Technology, Cambridge, MA, 1994.
314. T. Loredo. From Laplace to Supernova SN 1987A: Bayesian inference in astrophysics. In P. F. Fougere, editor, Maximum-Entropy and Bayesian Methods, Dartmouth, 1989, pages 81-142. Kluwer Academic Publishers, Dordrecht, 1990. Available from http://bayes.wustl.edu/gregory/gregory.html.
315. A. K. Louis. Inverse und schlecht gestellte Probleme. Teubner, Stuttgart, 1989.
316. D. R. Luce and H. Raiffa. Games and Decisions. Wiley, New York, 1957. Also published by Dover, New York, 1989.
317. D. J. C. MacKay. The evidence framework applied to classification networks. Neural Computation, 4(5):720-736, 1992.
318. D. J. C. MacKay. A practical Bayesian framework for backpropagation networks. Neural Computation, 4(3):448-472, 1992.
319. D. J. C. MacKay. Bayesian methods for backpropagation networks. In E. Domany, J. L. van Hemmen, and K. Schulten, editors, Models of Neural Networks III, pages 211-254. Springer-Verlag, New York, 1996.
320. D. J. C. MacKay. Bayesian non-linear modeling for the prediction competition. In G. Heidbreder, editor, Maximum Entropy and Bayesian Methods, Santa Barbara 1993, pages 221-234. Kluwer Academic Publishers, Dordrecht, 1996.
321. D. J. C. MacKay. Hyperparameters: Optimise or integrate out? In G. Heidbreder, editor, Maximum Entropy and Bayesian Methods, Santa Barbara 1993, pages 43-59. Kluwer Academic Publishers, Dordrecht, 1996. An extended version appeared in Neural Comp. 11:1035-1068, 1999 under the title 'Comparison of Approximate Methods for Handling Hyperparameters'.
322. D. J. C. MacKay. Introduction to Gaussian processes. In C. Bishop, editor, Neural Networks and Machine Learning, volume 168 of Series F, Computer and Systems Sciences. NATO ASI Series, 1998.
323. D. J. C. MacKay. Comparison of approximate methods for handling hyperparameters. Neural Computation, 11:1035-1068, 1999. A preprint version is available at http://wol.ra.phy.cam.ac.uk/mackay/alpha.ps.gz.
324. G. J. MacLachlan and K. E. Bashford. Mixture Models: Inference and Applications to Clustering. Marcel Dekker, New York, 1988.
325. G. Mahler and V. A. Weberrufi. Quantum Networks. Springer-Verlag, Berlin, 1995.
326. C. Mallows, Some comments on cp. Technometrics, 15:661-675, 1973.
327. B. B. Mandelbrot. The Fractal Geometry of Nature. Freeman and Company, New York, 1977.
328. B. B. Mandelbrot. Fractals and Scaling in Finance. Springer-Verlag, New York, 1997.
329. V. A. Marchenko. Sturm-Liouville Operators and Applications. Birkhauser, Basel, 1986.
330. D. W. Marquardt. Generalized inverses, ridge regression, biased linear estimation, and nonlinear regression. Technometrics, 12:591-613, 1970.
331. D. W. Marquardt and R. D. Snee. Ridge regression in practice. The American Statistician, 29:3-20, 1975.
332. J. L. Marroquin, S. Mitter, and T. Poggio. Probabilistic solution of illposed problems in computational vision. J. Am. Stat. Assoc., 82:76-89, 1987.
333. P. McCullagh and J. A. Nelder. Generalized Linear Models, volume 37 of Monographs on Statistics and Applied Probability. Chapman & Hall, London, 1989.
334. M. L. Mehta. Random Matrices. Academic Press, San Diego, 2nd edition, 1991.
335. M. Meila and M. L Jordan. Learning with mixtures of trees. J. of Machine Learning Research, 1:1-48, 2000.
336. A. Messiah. Quantum Mechanics. North-Holland, Amsterdam, 1961.
337. N. Metropolis, A. W. Rosenbluth, M. N. Rosenbluth, A. H. Teller, and E. Teller. Equation of state calculations by fast computing machines. Journal of Chemical Physics, 21:1087-1092, 1953.
338. M. Mezard, G. Parisi, and M. A. Virasoro. Spin Glass Theory and Beyond. World Scientific, Singapore, 1987.
339. Z. Michalewicz. Genetic Algorithms + Data Structures = Evolution Programs. Springer-Verlag, Berlin, 1992.
340. D. Michie, D. J. Spiegelhalter, and C. C. Taylor, editors. Machine Learning, Neural and Statistical Classification. Ellis Horwood, New York, 1994.
341. D. Miller. Critical Rationalism: A Restatement and Defence. Open Court Publishing Company, Chicago, IL, 1994.
342. R. G. Miller. Simultaneous Statistical Inference. McGraw-Hill, New York, 1966.
343. W. T. Miller III, R. S. Sutton, and P. J. Werbos, editors. Neural Networks for Control. MIT Press, Cambridge, MA, 1990.
344. M. L. Minski and S. A. Papert. Perceptrons. MIT Press, Cambridge, MA, expanded edition, 1990. Original edition published 1969.
345. A. R. Mitchell and D. F. Griffiths. The Finite Difference Method in Partial Differential Equations. Wiley, New York, 1980.
346. M. Mitchell. An Introduction to Genetic Algorithms. MIT Press, Cambridge, MA, 1996.
347. A. Mohammad Djafari. A full Bayesian approach for inverse problems. In K. M. Hanson and R. N. Silver, editors, Maximum Entropy and Bayesian Methods, Santa Fe, New Mexico, 1995. Kluwer Academic Publishers, Dordrecht, 1996.
348. A. Mohammad Djafari and J. Idier. A scale invariant Bayesian method to solve linear inverse problems. In G. Heidbreder, editor, Maximum Entropy and Bayesian Methods, Santa Barbara 1993, pages 121-134. Kluwer Academic Publishers, Dordrecht, 1996. An extended version can be found in the Santa Fe Institute Technical Report 94-07-001.
349. L. Molgedey and H. G. Schuster. Separation of a mixture of independent signals using time delayed correlations. Phys. Rev. Lett., 72(23):3634- 3637, 1994.
350. J. F. Monahan. Numerical Methods of Statistics. Cambridge University Press, Cambridge, 2001.
351. I. Montvay and G. Minister. Quantum Fields on a Lattice. Cambridge University Press, Cambridge, 1994.
352. E. H. Moore. On the reciprocal of the general algebraic matrix. Bull Amer. Math. Soc., 26:394-395, 1920.
353. V. A. Morozov. Methods for Solving Incorrectly Posed Problems. Springer-Verlag, New York, 1984.
354. C. Morris. Parametric empirical Bayes inference: Theory and applications. J. Amer. Statist. Assoc., 78:47-65, 1983.
355. P. M. Morse and H. Feshbach. Methods of Theoretical Physics. Part II. McGraw-Hill, New York, 1953.
356. F. Mosteller and D. Wallace. Inference in an authorship problem. A comparative study of discrimination methods applied to authorships of the disputed Federalist papers. J. Amer. Statist. Assoc., 58:275-309, 1963.
357. C. Mudry, C. Chamon, and X.G Wen. Two-dimensional conformal field theory for disordered systems at criticality. Nucl. Phys. J5, 466 [FS]:383-443, 1996.
358. B. Miiller and J. Reinhardt. Neural Networks. Springer-Verlag, Berlin, second printing, 1991.
359. D. Mumford and J. Shah. Optimal approximations by piecewise smooth functions and associated variational problems. Comm. Pure Applied Math., 42:577-684, 1989.
360. M. K. Murray and J. W. Rice. Differential Geometry and Statistics, volume 48 of Monographs on Statistics and Applied Probability. Chapman & Hall, London, 1993.
361. E. A. Nadaraya. On nonparametric estimates of density functions and regression curves. Theor. Prob. Appl, 10:186-190, 1965.
362. F. Natterer. The Mathematics of Computerized Tomography. Teubner and Wiley, Stuttgart, 1986.
363. R. M. Neal. Bayesian Learning for Neural Networks. Springer-Verlag, New York, 1996.
364. R. M. Neal. Monte Carlo implementation of Gaussian process models for Bayesian regression and classification. Technical Report 9702, Department of Statistics, University of Toronto, Canada, 1997.
365. J. W. Negele and H. Orland. Quantum Many-Particle Systems, volume 68 of Frontiers in Physics Series. Addison-Wesley, Redwood City, CA, 1988.
366. R. G. Newton. Scattering Theory of Waves and Particles. Springer- Verlag, Berlin, second edition, 1982.
367. R. G. Newton. Inverse Schrodinger Scattering in Three Dimensions. Springer-Verlag, Berlin, 1989.
368. M. Nitzberg and T. Shiota. Nonlinear image filtering with edge and corner enhancement. IEEE Trans, on Pattern Analysis and Machine Intelligence, 14(8):862-833, 1992.
369. P. Niyogi, F. Girosi, and T. Poggio. Incorporating prior information in machine learning by creating virtual examples. In IEEE Proceedings on Intelligent Signal Processing, volume 86, pages 2196-2209, 1998.
370. J. J. K. 0 Ruanaidh and W. J. Fitzgerald. Numerical Bayesian Methods Applied to Signal Processing. Springer-Verlag, New York, 1996.
371. A. O'Hagen. Bayesian Inference, volume 2B of Kendall's Advanced Theory of Statistics. Edward Arnold, London, 1994.
372. B. A. Olshausen and D. J. Field. Natural image statistics and efficient coding. Network, 7:333-339, 1995. Proceedings of the Workshop on Information Theory and the Brain, September 4-5, 1995, University of Stirling.
373. B. A. Olshausen and D. J. Field. Emergence of simple-cell receptive field properties by learning a sparse code for natural images. Nature, 381:607-609, 1996.
374. M. Opper. Gaussian processes for classification: Mean field algorithms. Technical Report NCRG/1999/030, Neural Computing Research Group at Aston University, 1999.
375. M. Opper and D. Haussler. Generalization performance of Bayes optimal classification algorithm for learning a perceptron. Phys. Rev. Lett., 66:2677, 1991.
376. M. Opper and W. Kinzel. Statistical mechanics of generalization. In E. Domany, J. L. van Hemmen, and K. Schulten, editors, Models of Neural Networks III, pages 151-210. Springer-Verlag, New York, 1996.
377. M. Opper and O. Winther. Mean field methods for classification with Gaussian processes. In M.S. Kearns, S. S. Solla, and D. A. Cohn, editors, Advances in Neural Information Processing Systems 11, pages 309-315. MIT Press, Cambridge, MA, 1999.
378. M. Opper and O. Winther. Gaussian process classification and SVM: Mean field results and leave-one-out estimator. In A. J. Smola, P. Bartlett, B. Scholkopf, and D. Schuurmans, editors, Advances in Large Margin Classifiers, pages 43-65. MIT Press, Cambridge, MA, 2000.
379. Y. Pao. Adaptive Pattern Recognition and Neural Networks. Addison- Wesley, Reading, MA, 1989.
380. G. Parisi. Field Theory, Disorder, and Simulations. World Scientific, Singapore, 1992.
381. E. Parzen. An approach to time series analysis. Ann. Math. Statist., 32:951-989, 1962.
382. E. Parzen. On the estimation of a probability function and mode. Ann. Math. Statist., 33:3, 1962.
383. E. Parzen. Probability density functional and reproducing kernel Hilbert spaces. In M. Rosenblatt, editor, Proc. Symposium on Time Series Analysis, pages 155-169. Wiley, New York, 1963.
384. E. Parzen. Statistical inference on time series by rkhs methods. In R. Pyke, editor, Proc. 12th Biennal Seminar, Montreal, Canada: Canadian Mathematical Congress, pages 1-37, 1970.
385. W. Paul and J. Baschnagel. Stochastic Processes: From Physics to Finance. Springer-Verlag, Berlin, 1999.
386. J. Pearl. Probabilistic Reasoning in Intelligent Systems. Morgan Kaufmann, San Mateo, CA, 1988.
387. J. Pearl. Causal diagrams for empirical research. Biometrika, 82(4):669- 710, 1995.
388. J. Pearl. On the identification of nonparametric structural models. In M. Berkane, editor, Latent Variable Modelling with Application to Causality, Lecture Notes in Statistics, pages 29-68. Springer-Verlag, New York, 1997. Available from http://Singapore.cs.ucla.edu/csl.papers.html.
389. J. Pearl. Causality: Models, Reasoning, and Inference. Cambridge University Press, New York, 2000.
390. J. Pearl. Bayesianism and causality, or, why I am only a half-Bayesian. In D. Corfield and J. Williamson, editors, Foundations of Bayesianism, Kluwer Applied Logic Series. Kluwer Academic Publishers, Dordrecht, 2001. Available from http://Singapore.cs.ucla.edu/csl-papers.html.
391. H.O. Peitgen, H. Jiirgens, and D. Saupe. Chaos and Fractals. Springer- Verlag, New York, 1992.
392. R. Penrose. A generalized inverse for matrices. Proceedings of the Cambridge Philosophical Society, 51:406-413, 1955.
393. R. Penrose. On best approximate solutions of linear matrix equations. Proceedings of the Cambridge Philosophical Society, 52:17-19, 1956.
394. V. Periwal. Reparametrization invariant statistical inference and gravity. Phys. Rev. Lett., 78:4671-4674, 1997.
395. V. Periwal. Geometric statistical inference. Nucl. Phys. B, 554:719-730, 1999.
396. P. Perona and J. Malik. Scale-space and edge detection using anisotropic diffusion. IEEE Trans, on Pattern Analysis and Machine Intelligence, 12(7):629-639, 1990.
397. M. E. Perskin and D. V. Schroeder. An Introduction to Quantum Field Theory. Addison-Wesley, Reading, MA, 1995.
398. D. A. Pierre. Optimization Theory with Applications. Dover, New York, 1986. Original edition published by Wiley, New York, 1969.
399. T. Poggio and F. Girosi. A theory of networks for approximation and learning. Artificial Intelligence Laboratory Memo 1140, Massachusetts Institute of Technology, Cambridge, MA, 1989.
400. T. Poggio and F. Girosi. Networks for approximation and learning. In Proceedings of the IEEE, volume 78, pages 1481-1497, 1990.
401. T. Poggio, V. Torre, and C. Koch. Computational vision and regularization theory. Nature, 317:314-319, 1985.
402. E. Polak. Optimization. Springer-Verlag, New York, 1997.
403. D. Pollard. Convergence of Stochastic Processes. Springer-Verlag, New York, 1984.
404. D. A. Pomerleau. ALVINN: An autonomous land vehicle in a neural network. In D. Touretzky, editor, Advances in Neural Information Processing Systems 1, pages 305-313. Morgan Kaufmann, San Mateo, CA, 1989.
405. M. Pontil, S. Mukherjee, and F. Girosi. On the noise model of support vector machine regression. In Proceedings of Algorithmic Learning Theory 2000 Conference, Sydney, Australia, December 11-13, 1998.
406. K. Popper. Logik der Forschung. Julius Springer Verlag, Vienna, 1935. English translation: The Logic of Scientific Discovery. Hutchinson, London, 1959.
407. K. Popper. Conjectures and Refutations: The Growth of Scientific Knowledge. Routledge, London, 1963.
408. A. Pordt. Random walks in field theory. In H. Meyer-Ortmanns and A. Kliimper, editors, Field Theoretical Tools for Polymer and Particle Physics. Springer-Verlag, Berlin, 1998.
409. J. Preskill. Quantum information and computation. A course on quantum computation at Caltech, 1998. Available from http://www.theory.caltech.edu/ people/preskill.
410. W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery. Numerical Recipes in C. Cambridge University Press, Cambridge, 1992.
411. F. P. Ramsey. Truth and probability. In R. B. Braithwaite, editor, The Foundations of Mathematics and Other Logical Essays. Routledge and Kegan Paul, London, 1931.
412. M. Reed and B. Simon. Functional Analysis I. Academic Press, Boston, 1980.
413. P. Ring and P. Schuck. The Nuclear Many-Body Problem. Springer- Verlag, New York, 1980.
414. B. D. Ripley. Modelling spatial patterns (with discussion). Journal of the Royal Statistical Society £, 39:172-212, 1977.
415. B. D. Ripley. Stochastic Simulation. Wiley, New York, 1987.
416. B. D. Ripley. Pattern Recognition and Neural Networks. Cambridge University Press, Cambridge, 1996.
417. J. Rissanen. Modeling by shortest data description. Automatica, 14:465- 471, 1978.
418. J. Rissanen. Stochastic complexity and modeling. Annals of Statistics, 14:1080-1100, 1986.
419. H. Ritter, T. Martinetz, and K. Schulten. Neuronale Netze. Addison- Wesley, Bonn, second edition, 1991.
420. H. Robbins. Asymptotically subminimax solutions of compound statistical decision problems. In Proc. Second Berkely Symp. Math. Statist. Probab., volume 1, pages 131-148. University of Berkeley Press, Berkeley, 1951.
421. H. Robbins. An empirical Bayes approach to statistics. In Proc. Third Berkely Symp. Math. Statist. Probab., volume 1, pages 157-164. University of Berkeley Press, Berkeley, 1955.
422. H. Robbins. The empirical Bayes approach to statistical decision problems. Ann. Math. Statist., 35:1-20, 1964.
423. H. Robbins. Some thoughts on empirical Bayes estimation. Ann. Statist., 1:713-755, 1964.
424. C. P. Robert. The Bayesian Choice. Springer-Verlag, New York, 1994.
425. R. T. Rockafellar. Convex Analysis. Princeton University Press, Princeton, NJ, 1970.
426. C. C. Rodriguez. Cross validated non parametric Bayesianism by Markov chain Monte Carlo, 1997. arXiv:physics/9712041.
427. R. Rojas. Theorie der neuronalen Netze. Springer, Berlin, 1993.
428. K. Rose, E. Gurewitz, and G. C. Fox. Statistical mechanics and phase transitions in clustering. Phys. Rev. Lett, 65:945-948, 1990.
429. F. Rosenblatt. Principles of Neurodynamics. Spartan, New York, 1962.
430. H. J. Rothe. Lattice Gauge Theories. World Scientific, Singapore, 1992.
431. T. Roths, D. Maier, C. Friedrich, M. Marth, and J. Honerkamp. Determination of the relaxation time spectrum from dynamic moduli using an edge preserving regularization method. Rheol. Ada, 39(2):163-173, 2000.
432. P. J. Rousseeuw and A. M. Leroy. Robust Regression and Outlier Detection. Wiley, New York, 1987.
433. D. E. Rumelhart, J. L. McClelland, and the PDF Research Group. Parallel Distributed Processing, volumes 1 & 2. MIT Press, Cambridge, MA, 1986.
434. P. A. Ruud. An Introduction to Classical Econometric Theory. Oxford University Press, Oxford, 2000.
435. L. H. Ryder. Quantum Field Theory. Cambridge University Press, Cambridge, 1996.
436. L. J. Savage. Foundations of Statistics. Wiley, New York, 1954. Also published by Dover, New York, 1972.
437. H. Scheffe. The Analysis of Variance. Wiley, New York, 1959.
438. M. J. Schervish. Theory of Statistics. Springer-Verlag, New York, 1995.
439. S. J. Schmidt, editor. Der Diskurs des Radikalen Konstruktivismus. Suhrkamp, Frankfurt a. M., 1996.
440. B. Scholkopf, P. L. Bartlett, A. Smola, and R. Williamson. Shrinking the tube: A new support vector regression algorithm. In M.S. Kearns, S. S. Solla, and Cohn D. A., editors, Advances in Neural Information Processing Systems 11, pages 330-336. MIT Press, Cambridge, MA, 1999.
441. B. Scholkopf, C. Burges, and A. Smola, editors. Advances in Kernel Methods: Support Vector Machines. MIT Press, Cambridge, MA, 1998.
442. B. Scholkopf and A. Smola. Learning with Kernels. MIT Press, Cambridge, MA, 2001.
443. L. L. Schumaker. Spline Functions: Basic Theory. Wiley, New York, 1981.
444. H.P. Schwefel. Evolution and Optimum Seeking. Wiley, New York, 1995.
445. H. S. Seung. Annealed theories of learning. In Neural Networks: The Statistical Mechanics Perspective. Proceedings of the CTP-PBSRI Joint Workshop on Theoretical Physics. World Scientific, Singapore, 1995.
446. G. Shafer. Constructive probability. Synthese, 48:1-60, 1981.
447. G. Shafer and P. Shenoy. Probability propagation. Annals of Mathematics and Artificial Intelligence, 2:327-352, 1990.
448. C. E. Shannon. A mathematical theory of communication. Bell System Tech. J., 26:379-423, 623-656, 1948.
449. J. Shawe Taylor, P. L. Bartlett, R. C. Williamson, and M. Anthony. A framework for structural risk minimization. Technical Report NCTR- 96-032, NeuroColt Technical Report Series, 1996.
450. J. Shawe Taylor, P. L. Bartlett, R. C. Williamson, and M. Anthony. Structural risk minimization over data-dependent hierachies. Technical Report NC-TR-96-053, NeuroColt Technical Report Series, 1996.
451. P. P. Shenoy and G. Shafer. Axioms for probability and belief-function propagation. In G. Shafer and J. Pearl, editors, Readings in Uncertain Reasoning, pages 575-609. Morgan Kaufmann, San Mateo, CA, 1990.
452. N. Shephard and M. K. Pitt. Likelihood analysis of non-Gaussian measurement time series. Biometrika, 84(3):653-667, 1997.
453. R. Shiller. A distributed lag estimator derived from smoothness priors. Econometrica, 41:775-778, 1973.
454. A. Shleifer. Inefficient Markets. Oxford University Press, Oxford, 2000.
455. B. W. Silverman. Spline smoothing: The equivalent variable kernel method. Ann. Statist., 12:898-916, 1984.
456. B. W. Silverman. Density Estimation for Statistics and Data Analysis, volume 26 of Monographs on Statistics and Applied Probability. Chapman & Hall, London, 1986.
457. D. S. Sivia. Data Analysis: A Bayesian Tutorial. Oxford University Press, Oxford, 1996.
458. J. Skilling. Fundamentals of maxent in data analysis. In B. Buck and V. A. Macaulay, editors, Maximum Entropy in Action, pages 19-40. Oxford University Press, Oxford, 1991.
459. J. Skilling. On parameter estimation and quantified maxent. In W. T. Grandy and L. H. Schick, editors, Maximum Entropy and Bayesian Methods. Laramie, 1990, pages 267 -273. Kluwer Academic Publishers, Dordrecht, 1991.
460. A. F. M. Smith and G. O. Roberts. Bayesian computation via Gibbs sampler and related Markov chain Monte Carlo methods (with discussion). Journal of the Royal Statistical Society B, 55:3-23, 1993.
461. A. J. Smola, P. Bartlett, B. Scholkopf, and D. Schuurmans, editors. Advances in Large Margin Classifiers. MIT Press, Cambridge, MA, 2000.
462. A. J. Smola and B. Scholkopf. Prom regularization operators to support vector kernels. In M. I. Jordan, M. J. Kearns, and S. A. Solla, editors, Advances in Neural Information Processing Systems 10. MIT Press, Cambridge, MA, 1998.
463. A. J. Smola and B. Scholkopf. A tutorial on support vector machines. Technical Report TR-1998-030, Neuro COLT, 1998. Available from http//svm.first.gmd.de.
464. A. J. Smola, B. Scholkopf, and K.R. Miiller. The connection between regularization operators and support vector kernels. Neural Networks, 11:637-649, 1998.
465. R. Snieder and A. Tarantola. Imaging of quantum mechanical potentials. Phys. Rev. A, 39:3303-3309, 1989.
466. P. Sollich. Probabilistic interpretation and Bayesian methods for support vector machines. In Proceedings of ICANN 1999, pages 91-96, 1999.
467. P. Sollich. Probabilistic methods for support vector machines. In S. A. Solla, T. K. Leen, and K.-R-Miiller, editors, Advances in Neural Information Processing Systems 12, pages 349-355. MIT Press, Cambridge, MA, 2000.
468. P. Sollich. Bayesian methods for support vector machines: Evidence and predictive class probabilities. Machine Learning, 46(1-3):21-52, 2002.
469. R. G. Staudte and S. J. Sheather. Robust Estimation and Testing. Wiley, New York, 1990.
470. A. Steane. Quantum computing. Rep. Prog. Phys., 61:117-173, 1998. arXiv:quant-ph/9708022.
471. M. Stone. Cross-validation choice and assessment of statistical predictions. Journal of the Royal Statistical Society B, 36:111-147, 1974.
472. M. Stone. An asymptotic equivalence of choice of model by crossvalidation and Akaike's criterion. Journal of the Royal Statistical Society B, 39:44, 1977.
473. M. Stone. Additive regression and other nonparametric models. Ann. Statist., 13:689-705, 1985.
474. C. E. M. Strauss, D. H. Wolpert, and D. R. Wolf. Alpha, evidence, and the entropic prior. In A. Mohammad-Djafari, editor, Maximum Entropy and Bayesian Methods. Kluwer Academic Publishers, Dordrecht, 1992.
475. K. K. Sung and T. Poggio. Finding human faces with a Gaussian mixture distribution-based face model. In Recent Progress in Computer Vision, LNCS Series. Springer-Verlag, New York, 1995.
476. M. Tan. An inverse problem approach to optical homodyne tomography. J. Mod. Opt, 44:2233, 1997.
477. M. A. Tanner. Tools for Statistical Inference. Springer-Verlag, New York, second edition, 1993.
478. A. Tarantola. Inverse Problem Theory: Methods for Data Fitting and Model Parameter Estimation. Elsevier, Amsterdam, 1987.
479. J. R. Taylor. Scattering Theory. Krieger, Malabar, FL, 1972.
480. C. J. Thompson. Mathematical Statistical Mechanics. Princeton University Press, Princeton, NJ, 1972.
481. L. Tierney. Markov chains for exploring posterior distributions (with discussion). Annals of Statistics, 22:1701-1762, 1994.
482. A. N. Tikhonov. Solution of incorrectly formulated problems and the regularization method. Soviet Math. Dokl, 4:1035-1038, 1963.
483. A. N. Tikhonov and V. Arsenin. Solution of El-posed Problems. Wiley, New York, 1977.
484. J. Timmer. Parameter estimation in nonlinear stochastic differential equations. Chaos, Solitons, and Fractals, 11:2571-2578, 2000.
485. D. M. Titterington, A. F. M. Smith, and U. E. Makov. Statistical Analysis of Finite Mixture Distributions. Wiley, New York, 1985.
486. G. F. Trecate, C. K. I. Williams, and M. Opper. Finite-dimensional approximation of Gaussian processes. In M.S. Kearns, S. S. Solla, and D. A. Cohn, editors, Advances in Neural Information Processing Systems 11, pages 218-224. MIT Press, Cambridge, MA, 1999.
487. A. Tversky. Elimination by aspects. Psychological Review, 79(4):281- 301, 1972.
488. A. Tversky and D. Kahnemann. The framing of decisions and the psychology of choice. Science, 211:453-458, 1981.
489. J. Uhlig. Bayessches Lernen in der Quantentheorie. Ph.D. Thesis, Universitat Miinster, 2000.
490. B. C. van Fraassen. The Scientific Image. Clarendon Press, Oxford, 1980.
491. N. G. van Kampen. Stochastic Processes in Physics and Chemistry. North-Holland, Amsterdam, 1992.
492. V. N. Vapnik. Estimation of Dependencies Based on Empirical Data. Springer-Verlag, New York, 1982.
493. V. N. Vapnik. The Nature of Statistical Learning Theory. Springer- Verlag, New York, 1995.
494. V. N. Vapnik. Statistical Learning Theory. Wiley, New York, 1998.
495. V. N. Vapnik and A. Y. Chervonenkis. On the uniform convergence of relative frequencies of events to their probabilities. Th. Prob. and Its Application, 17(2):264-280, 1971.
496. V. N. Vapnik and A. Y. Chervonenkis. The necessary and sufficient conditions for consistency in the empirical risk minimization method. Pattern Recognition and Image Analysis, 1(3):283-305, 1991.
497. W. N. Venables and B. D. Ripley. Modern Applied Statistics with SPlus. Springer-Verlag, New York, 1994.
498. G. Vico. De antiquissima Italorum sapientia. Stamperia de' Classici Latini, Naples, 1858. Originally published in 1710.
499. W. von der Linden, V. Dose, J. Padayachee, and V. Prozesky. Signal and background separation. Phys. Rev. E, 59:6527-6534, 1999.
500. W. von der Linden, R. Fischer, and V. Dose. Evidence integrals. In R. N. Silver and K. M. Hanson, editors, Maximum Entropy and Bayesian Methods, page 443. Kluwer Academic Publishers, Dordrecht, 1996.
501. W. von der Linden, R. Fischer, and V. Dose. On the importance of a-marginalization in maximum entropy. In R. N. Silver and K. M. Hanson, editors, Maximum Entropy and Bayesian Methods, page 229. Kluwer Academic Publishers, Dordrecht, 1996.
502. E. von Glasersfeld. Radikaler Konstruktivismus. Suhrkamp, Frankfurt a. M., second edition, 1998.
503. J. von Neumann. Mathematical Foundations of Quantum Mechanics. Princeton University Press, Princeton, NJ, 1955.
504. J. von Neumann and O. Morgenstern. Theory of Games and Economic Behavior. Princeton University Press, Princeton, NJ, 1947.
505. G. Wahba. A comparison of GCV and GML for choosing the smoothing parameter. Numer. Math., 24:383-393, 1975.
506. G. Wahba. Bayesian confidence intervals for the cross-validated smoothing spline. Journal of the Royal Statistical Society B, 45, 1983.
507. G. Wahba. Spline Models for Observational Data. SIAM, Philadelphia, 1990.
508. G. Wahba. Support vector machines, reproducing kernel Hilbert spaces and the randomized GACV. In B. Scholkopf, C. Burges, and A. J. Smola, editors, Advances in Kernel Methods: Support Vector Machines, pages 69-88. MIT Press, Cambridge, MA, 1998.
509. G. Wahba and S. Wold. A completely automatic French curve. Commun. Statist, 4:1-17, 1975.
510. P. D. Wasserman. Advanced Methods in Neural Computing. Van Nostrand Reinhold, New York, 1993.
511. T. L. H. Watkin, A. Rau, and M. Biehl. The statistical mechanics of learning a rule. Rev. Mod. Phys., 65:499-556, 1993.
512. P. Watzlawick, editor. How Real Is Real? Random House, New York, 1976.
513. P. Watzlawick, editor. The Invented Reality. Norton, New York, 1984.
514. A. R. Webb. Functional approximation by feed-forward networks: A least-squares approach to generalization. IEEE Trans. Neural Networks, 5:363-371, 1994.
515. S. Weinstein. The Quantum Theory of Fields, volume 1. Cambridge University Press, Cambridge, 1995.
516. S. Weinstein. The Quantum Theory of Fields, volume 2. Cambridge University Press, Cambridge, 1996.
517. M. West and J. Harrison. Bayesian Forecasting and Dynamic Models. Springer-Verlag, New York, 1997.
518. H. White. Maximum likelihood estimation of misspecified models. Econometrica, 50:1-25, 1981.
519. E. T. Whittaker. On a new method of graduation. Proc. Edinborough Math. Assoc., 78:81-89, 1923.
520. C. K. I. Williams. Gaussian processes. In M. A. Arbib, editor, The Handbook of Brain Theory and Neural Networks. MIT Press, Cambridge, MA, second edition, 2002.
521. C. K. I. Williams and D. Barber. Bayesian classification with Gaussian processes. IEEE Trans, on Pattern Analysis and Machine Intelligence, 20:1342-1351, 1998.
522. C. K. I. Williams and C. E. Rasmussen. Gaussian processes for regression. In D. S. Touretzky, M. C. Mozer, and M. E. Hasselmo, editors, Advances in Neural Information Processing Systems 8, pages 514-520. MIT Press, Cambridge, MA, 1996.
523. P. Wilmott, J. Dewynne, and S. Howison. Option Pricing: Mathematical Models and Computation. Oxford Financial Press, Oxford, 1993.
524. G. Winkler. Image Analysis, Random Fields, and Dynamic Monte Carlo Methods. Springer-Verlag, Berlin, 1995.
525. D. H. Wolpert. A rigorous investigation of 'evidence' and 'Occam factors' in Bayesian reasoning. Working Paper SFI 92-03-013, Santa Fe Institute, 1992. Available from http//www.santafe.edu/sfi/publications.
526. D. H. Wolpert. On the use of evidence in neural networks. In Stephen Jose Hanson, Jack D. Cowan, and C. Lee Giles, editors, Advances in Neural Information Processing Systems 5, pages 539-546. Morgan Kaufmann, San Mateo, CA, 1993.
527. D. H. Wolpert, editor. The Mathematics of Generalization. The Proceedings of the SFI/CNLS Workshop on Formal Approaches to Supervised Learning. Santa Fe Institute, Studies in the Sciences of Complexity. Addison-Wesley, Reading, MA, 1995.
528. D. H. Wolpert. The existence of a priori distinctions between learning algorithms. Neural Computation, 8(7):1391-1420, 1996.
529. D. H. Wolpert. The lack of a priori distinctions between learning algorithms. Neural Computation, 8(7): 1341-1390, 1996.
530. D. H. Wolpert and C. E. M. Strauss. What Bayes has to say about the evidence procedure. In G. Heidbreder, editor, Maximum Entropy and Bayesian Methods, Santa Barbara 1993, pages 61-78. Kluwer Academic Publishers, Dordrecht, 1996. An extended version can be found in the Santa Fe Institute Technical report 94-07-001.
531. S. J. Yakowitz and F. Szidarovsky. A comparison of kriging with nonparametric regression methods. J. Multivariate Analysis, 16:21-53, 1985.
532. A. L. Yuille. Generalized deformable models, statistical physics and matching problems. Neural Computation, 2(1):l-24, 1990.
533. A. L. Yuille and J. J. Kosowski. Statistical physics algorithm that converge. Neural Computation, 6(3):341-356, 1994.
534. A. L. Yuille, P. Stolorz, and J. Utans. Statistical physics, mixtures of distributions, and EM algorithm. Neural Computation, 6(2):334-340, 1994.
535. B. N. Zakhariev and V. M. Chabanov. New situation in quantum mechanics. Inverse Problems, 13:R47-R79, 1997.
536. H. Zhu, C. K. I. Williams, R. Rohwer, and M. Morciniec. Gaussian regression and optimal finite dimensional linear models. Technical Report NCRG/97/011, Aston University, Birmingham, 1997.
537. S. C. Zhu and D. Mumford. Prior learning and Gibbs reactiondiffusion. IEEE Trans, on Pattern Analysis and Machine Intelligence, 19(11):1236-1250, 1997.
538. S. C. Zhu, Y. N. Wu, and D. Mumford. Minimax entropy principle and its application to texture modeling. Neural Computation, 9(8):1627- 1660, 1997.
539. S. C. Zhu and A. L. Yuille. Region competition: Unifying snakes, region growing, and Bayes/MDL for multiband image segmentation. IEEE Trans, on Pattern Analysis and Machine Intelligence, 18(9):884-900, 1996.
540. W. Zhu and H. Rabitz. Potential surfaces from the inversion of time dependent probability density data. J. Chem. Phys., 111:472-480, 1999.
541. J. Zinn Justin. Quantum Field Theory and Critical Phenomena. Oxford Science Publications, Oxford, 1989.