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Bibliography

1
Hadamard, J.: Lectures on the Cauchy Problem in Linear Partial Differential Equations. New Haven: Yale University Press 1923

2
Tikhonov, A.N.: Solution of incorrectly formulated problems and the regularization method. Soviet Math. Dokl. 4, 1035-1038 (1963)

3
Tikhonov, A.N., Arsenin, V.: Solution of Ill-posed Problems. New York: Wiley 1977

4
Vapnik, V.N.: Estimation of dependencies based on empirical data. New York: Springer 1982

5
Keller, J.B.: Ann. Math. Mon. 83, 107-118 (1976)

6
Louis, A.K.: Inverse und schlecht gestellte Probleme. Stuttgart: Teubner 1989

7
Kirsch, A.: An Introduction to the Mathematical Theory of Inverse Problems. New York: Springer 1996

8
Hofmann, B.: Mathematik inverser Probleme. Leibzig: Teubner 1999

9
Gel'fand, I.M., Levitan, B.M.: Trans. Amer. Soc. 1, 253-302 (1951)

10
Kac, M.: Am. Math. Mon. 73, 1-23 (1966)

11
Marchenko, V.A.: Sturm-Liouville Operators and Applications. Basel: Birkhauser 1986

12
Chadan, K., Colton, D., Päivärinta, L., Rundell, W.: An Introduction to Inverse Scattering and Inverse Spectral Problems. Philadelphia: SIAM, 1997

13
Zakhariev, B.N., Chabanov, V.M.: Inverse Problems. 13, R47-R79 (1997)

14
Newton, R.G.: Inverse Schrödinger Scattering in Three Dimensions. New York: Springer 1989

15
Chadan, K., Sabatier, P.C.: Inverse Problems in Quantum Scattering Theory. Berlin: Springer 1989

16
Wahba, G.: Spline Models for Observational Data. Philadelphia: SIAM 1990

17
Vapnik, V.N.: The Nature of Statistical Learning Theory. New York: Springer 1995

18
Vapnik, V.N.: Statistical Learning Theory. New York: Wiley 1998

19
Hastie,T.J., Tibshirani, R.J.: Generalized Additive Models. London: Chapman & Hall 1990

20
Huber, P-J.: Ann. Statist. 13(2), 435-475 (1985)

21
Breiman, L., Friedman, J.H., Olshen, R.A., Stone, C.J.: Classification and Regression Trees, New York: Chapman & Hall 1993

22
Bishop, C.M.: Neural Networks for Pattern Recognition. Oxford: Oxford University Press 1995

23
Lauritzen, S.L.: Graphical Models. Oxford: Clarendon Press, 1996

24
Michie, D., Spiegelhalter, D.J., Taylor, C.C. (eds.): Machine Learning, Neural and Statistical Classification. New York: Ellis Horwood 1994

25
Box, G.E.P., Tiao, G.C.: Bayesian Inference in Statistical Analysis. New York: Wiley 1992 (Originally published in 1973 by Addison-Wesley, Reading, MA)

26
Berger, J.O.: Statistical Decision Theory and Bayesian Analysis. New York: Springer-Verlag 1980

27
Loredo T.: From Laplace to Supernova SN 1987A: Bayesian Inference in Astrophysics. In Fougère, P.F. (ed.) Maximum-Entropy and Bayesian Methods, Dartmouth, 1989, 81-142. Dordrecht: Kluwer 1990. Available at http://bayes.wustl.edu/gregory/gregory.html.

28
Bernado, J.M., Smith, A.F.: Bayesian Theory. New York: John Wiley 1994

29
Robert, C.P.: The Bayesian Choice. New York: Springer 1994

30
Gelman, A., Carlin, J.B., Stern, H.S., Rubin, D.B.: Bayesian Data Analysis. New York: Chapman & Hall 1995

31
Sivia, D.S.: Data Analysis: A Bayesian Tutorial. Oxford: Oxford University Press 1996

32
Lemm, J.C.: Prior Information and Generalized Questions. A.I.Memo No. 1598, C.B.C.L. Paper No. 141, Massachusetts Institute of Technology 1996.
Available at http://pauli.uni-muenster.de/${}^\sim$lemm.

33
Lemm, J.C.: How to Implement A Priori Information: A Statistical Mechanics Approach. Technical Report, MS-TP1-98-12, Münster University 1998, arXiv:cond-mat/9808039.

34
Lemm, J.C.: Bayesian Field Theory. Nonparametric approaches to density estimation, regression, classification, and inverse quantum problems. Technical Report, MS-TP1-99-1, Münster University 1999, arXiv: physics/9911077.

35
Jeffrey, R.: Probabilistic Thinking. 1999.
Available at http://www.princeton.edu/${}^\sim$bayesway/.

36
Jaynes, E.T.: Probability Theory: The Logic Of Science. (In preparation)
Available at http://bayes.wustl.edu/etj/prob.html.

37
Doob, J.L: Stochastic Processes. New York: Wiley 1953 (New edition 1990)

38
Lemm, J.C., Uhlig, J., Weiguny, A.: Phys. Rev. Lett. 84, 2068 (2000)

39
Schulman, L.S.: Techniques and Applications of Path Integration. New York: Wiley 1981

40
Glimm, J., Jaffe, A.: Quantum Physics. A Functional Integral Point of View. (2nd ed.) New York: Springer 1987

41
Hammersley, J.M., Handscomb, D.C.: Monte Carlo Methods. London: Chapman & Hall 1964

42
Binder, K. (ed.): The Monte Carlo Method in Condensed Matter Physics. Berlin: Springer 1992

43
Winkler, G.: Image Analysis, Random Fields and Dynamic Monte Carlo Methods. Berlin: Springer Verlag 1995

44
Neal, R.M.: Technical Report No. 9702, Dept. of Statistics, Univ. of Toronto, Canada 1997

45
de Bruijn, N.G.: Asymptotic Methods in Analysis. Amsterdam: North-Holland, 1961.

46
Bleistein, N. , Handelsman, N.: Asymptotic Expansions of Integrals. New York: Dover 1986 (Originally published in 1975 by Holt, Rinehart and Winston, New York)

47
Honerkamp, J: Statistical Physics. Berlin: Springer-Verlag 1998

48
Williams, C.K.I., Rasmussen, C.E.: Gaussian Processes for Regression. In Advances in Neural Information Processing Systems 8, D.S. Touretzky et al (eds.), 515-520, Cambridge, MA: MIT Press 1996

49
MacKay, D.J.C.: Introduction to Gaussian processes. In Bishop, C., (ed.) Neural Networks and Machine Learning. NATO Asi Series. Series F, Computer and Systems Sciences, Vol. 168, 1998

50
Whittaker, E.T.: Proc. Edinborough Math. Assoc. 78, 81-89 (1923)

51
Shiller, R.: Econometrica 41, 775-778 (1973)

52
Akaike, H.: In Bayesian Statistics. J.M. Bernanda, M.H. De Groot, D.V. Lindley, A.F.M. Smith (eds.), 143-166, Valencia: Valencia University Press 1980

53
Green, P.J., Silverman, B.W.: Nonparametric Regression and Generalized Linear Models. A roughness penalty approach. London: Chapman & Hall 1994

54
Girosi, F., Jones, M., Poggio, T.: Neural Computation 7 (2), 219-269 (1995)

55
Kitagawa, G., Gersch, W.: Smoothness Priors Analysis of Time Series. New York: Springer 1996

56
Honerkamp, J., Weese J.: Cont. Mech. Thermodyn. 2, 17-30 (1990)

57
Messiah, A.: Quantum Mechanics. Amsterdam: North-Holland, 1961

58
Balian, R.: From Microphysics to Macrophysics. Vol. I. Berlin: Springer 1991

59
Choquet-Bruhat, Y., DeWitt-Morette, C., Dillard-Bleick, M.: Analysis, Manifolds and Physics. (rev. ed.) Amsterdam: North-Holland 1982

60
Lifshits, M.A.: Gaussian Random Functions. Kluwer Academic Publ. 1995

61
Neal, R.M.: Bayesian Learning for Neural Networks. New York: Springer 1996

62
Williams, C.K.I., Barber, D.: IEEE Trans. on Pattern Analysis and Machine Intelligence. 20(12), 1342-1351 (1998)

63
Lemm, J.C.: Mixtures of Gaussian Process Priors. In Proceedings of the Ninth International Conference on Artificial Neural Networks (ICANN99), IEEE Conference Publication No. 470. London: Institution of Electrical Engineers 1999

64
Hochstadt, H., Lieberman, B.: SIAM J. Appl. Math. 34, 676-680 (1976)

65
Zhu, W., Rabitz, H.: J. Chem. Phys. 111, 472-480 (1999)

66
Lemm, J.C.: Inverse Time-Dependent Quantum Mechanics. Technical Report, MS-TP1-00-1, Münster University 2000, arXiv:quant-ph/0002010.

67
Lemm, J.C.: Quadratic Concepts. In: Niklasson; L., Bodén, M., Ziemke, T. (eds.) Proceedings of the 8th International Conference on Artificial Neural Networks, Skövde, Sweden, 2-4 September 1998., 579-584, London: Springer 1998

68
Pierre, D.A.: Optimization Theory with Applications. New York: Dover 1986. (Original edition Wiley, 1969).

69
Fletcher, R.: Practical Methods of Optimization. New York: Wiley 1987

70
Press, W.H., Teukolsky, S.A., Vetterling, W.T., & Flannery, B.P.: Numerical Recipes in C. Cambridge: Cambridge University Press 1992

71
Bazaraa, M.S., Sherali, H.D., & Shetty, C.M.: Nonlinear Programming. (2nd ed.) New York: Wiley 1993

72
Bertsekas, D.P.: Nonlinear Programming. Belmont, MA: Athena Scientific 1995

73
Airapetyan, R.G., Puzynin, I.V.: Comp. Phys. Comm. 102, 97-108 (1997)

74
Eisenberg, J.M., Greiner, W.: Microscopic Theory of the Nucleus. Amsterdam: North-Holland 1972

75
Ring, P., Schuck, P.: The Nuclear Many-Body Problem. New York: Springer Verlag 1980

76
Blaizot, J.-P., Ripka, G.: Quantum Theory of Finite Systems. Cambridge, MA: The MIT Press 1986

77
Negele, J.W., Orland, H.: Quantum Many-Particle Systems. Frontiers In Physics Series, Vol. 68, Redwood City, CA: Addison-Wesley 1988

78
Lemm, J. C.: Annals of Physics 244 (1), 136-200 (1995)

79
Lemm, J.C., Uhlig, J.: Phys. Rev. Lett. 84, 4517 (2000)

80
Lemm, J. C., Giraud, B.G., Weiguny A.: Phys. Rev. Lett. 73, 420-423 (1994)



Joerg_Lemm 2000-06-06