Geodesic
The Dawning of the Age of Stochasticity
Atti della Accademia nazionale dei Lincei. Rendiconti Lincei. Matematica e applicazioni, Série 9, Tome 11 (2000) no. S1, pp. 107-125.

Voir la notice de l'article provenant de la source Biblioteca Digitale Italiana di Matematica

For over two millennia, Aristotle's logic has ruled over the thinking of western intellectuals. All precise theories, all scientific models, even models of the process of thinking itself, have in principle conformed to the straight-jacket of logic. But from its shady beginnings devising gambling strategies and counting corpses in medieval London, probability theory and statistical inference now emerge as better foundations for scientific models, especially those of the process of thinking and as essential ingredients of theoretical mathematics, even the foundations of mathematics itself. We propose that this see change in our perspective will affect virtually all of mathematics in the next century. 
@article{RLIN_2000_9_11_S1_a6,
     author = {Mumford, David},
     title = {The {Dawning} of the {Age} of {Stochasticity}},
     journal = {Atti della Accademia nazionale dei Lincei. Rendiconti Lincei. Matematica e applicazioni},
     pages = {107--125},
     publisher = {mathdoc},
     volume = {Ser. 9, 11},
     number = {S1},
     year = {2000},
     zbl = {1149.00309},
     mrnumber = {1845667},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/RLIN_2000_9_11_S1_a6/}
}
TY  - JOUR
AU  - Mumford, David
TI  - The Dawning of the Age of Stochasticity
JO  - Atti della Accademia nazionale dei Lincei. Rendiconti Lincei. Matematica e applicazioni
PY  - 2000
SP  - 107
EP  - 125
VL  - 11
IS  - S1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/RLIN_2000_9_11_S1_a6/
LA  - en
ID  - RLIN_2000_9_11_S1_a6
ER  - 
%0 Journal Article
%A Mumford, David
%T The Dawning of the Age of Stochasticity
%J Atti della Accademia nazionale dei Lincei. Rendiconti Lincei. Matematica e applicazioni
%D 2000
%P 107-125
%V 11
%N S1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/RLIN_2000_9_11_S1_a6/
%G en
%F RLIN_2000_9_11_S1_a6
Mumford, David. The Dawning of the Age of Stochasticity. Atti della Accademia nazionale dei Lincei. Rendiconti Lincei. Matematica e applicazioni, Série 9, Tome 11 (2000) no. S1, pp. 107-125. http://geodesic.mathdoc.fr/item/RLIN_2000_9_11_S1_a6/

[1] P. J. Davis - R. Hersh, The Mathematical Experience. Birkhäuser Boston, Cambridge Mass. 1980. | Zbl

[2] Weinan E. - K. Khanin - A. Mazel - Ya Sinai, Probability distribution fonctions for the random forced Burger's equation. Phys. Rev. Letters, 78, 1997, 1904-1907.

[3] C. Freiling, Axioms of symmetry: throwing darts at the real line. J. Symb. Logic, 51, 1986, 190-200. | Zbl

[4] N. Gordon - D. Salmond - A. Smith, Novel Approach to non-linear/non-Gaussian Bayesian State Estimation. IEEE Proc. F, 140, 1993, 107-113.

[5] U. Grenander - Y. Chow - D.M. Keenan , HANDS: A Pattern Theoretic Study of Biological Shapes. Springer-Verlag, New York 1991. | Zbl

[6] C. Gross, Aristotle on the Brain. The Neuroscientist, 1, 1995, 245-250.

[7] P. W. Hallinan - G. Gordon - A. L. Yuille - P. Giblin - D. Mumford, Two and Three-dimensional Patterns of the Face. AKPeters 1999. | Zbl

[8] M. Isard - A. Blake, Contour tracking by stochastic propagation of conditional density. Proc. European Conference on Computer Vision. Vol. 1, Cambridge UK 1996, 343-356.

[9] E.T. Jaynes, Probability Theory: The Logic of Science. Available at http://bayes.wustl.edu/etj/prob.html. To be published by Camb. Univ. Press, 1996-2000.

[10] K. Kanazawa - D. Koller - S. J. Russel, Stochastic simulation algorithms for dynamic probabilistic networks. Proc. of the 11th Annual Conference on Uncertainty in AI (UAI). Montreal, Canada, August 1995,346-351.

[11] S. Lauritzen - D. Spiegelhalter, Local computations with probabilities on graphical structures. J. Royal Stat. Soc., B50, 1988, 157-224. | Zbl

[12] A. A. Mumford - M. Young, The interrelationships of the physical measurements and the vital capacity. Biometrika, 15, 1923, 109-115.

[13] J. Pearl, Probabilistic Reasoning in Intelligent Systems. Morgan Kaufman Publ., San Mateo, Calif., 1988. | Zbl

[14] B. Russell - A. N. Whitehead, Principia Mathematica, vol. 2. Cambridge Univ. Press, 1912.

[15] S. Shelah - W. H. Woodin, Large cardinals imply that every reasonable definable set is Lebesgue measurable. Israel J. Math., 70, 1990, 381-394. | Zbl

[16] J. Spencer, Ten Lectures on the Probabilistic Method. SIAM, 2nd ed., Philadelphia 1994. | Zbl

[17] B. Widrow, The rubber mask technique. Pattern Recognition, 5, 1973, 175-211.