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Statistics: Discrete Methods

Fall 2012. Statistics: Discrete Methods. STAT 453/653. The probability theory begins in attempts to describe gambling (how to win, how to divide the stakes, etc.), probability theory mainly considered discrete events, and its methods were mainly combinatorial. Gerolamo Cardano

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Statistics: Discrete Methods

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  1. Fall 2012 Statistics: Discrete Methods STAT 453/653

  2. The probability theory begins in attempts to describe gambling (how to win, how to divide the stakes, etc.), probability theory mainly considered discrete events, and its methods were mainly combinatorial Gerolamo Cardano (September 24, 1501 – September 21, 1576) Author of the first book on probability “De Ludo Aleae” ~ “On the dice game” written in 1560s, published in 1663

  3. … eventually, analytical considerations motivated the incorporation of continuous variables into the theory. The foundations of modern theory of probability were laid by Andrey Nikolaevich Kolmogorov, who combined the notion of sample space, introduced by Richard von Mises, and Lebesgue measure theory and presented his axiom system for probability theory in 1933 (Grundbegrie der Wahrscheinlichkeitsrechnung, by A. Kolmogorov, Julius Springer, Berlin, 1933, 62 pp.) Andrei Kolmogorov (1903-1987): A founder of modern theory of probabilities (1933) Henri Léon Lebesgue (June 28, 1875 – July 26, 1941) Richard Edler von Mises (19 April 1883 - 14 July 1953)

  4. Having given the number of instances respectively in which things are both thus and so, in which they are thus but not so, in which they are so but not thus, and in which they are neither thus not so, it is required to eliminate the general quantitative relativity inhering in the mere thingness of the things, and so to determine the special quantitative relativity subsisting between the thusness and the soness of the things. M. H. Doolittle, 1887

  5. Karl Pearson (March 27, 1857 – April 27, 1936) established the discipline of mathematical statistics

  6. George Udny Yule (18 Feb 1871, Scotland -- 26 June 1951, England)

  7. Sir Ronald Aylmer Fisher (17 February 1890 – 29 July 1962)

  8. Origin of discrete data

  9. Socio-economic statistics, 2009

  10. Socio-economic statistics, 2012

  11. Patterns in complex systems

  12. El-Nino

  13. Prediction problem

  14. Complex networks

  15. Map of the blogosphere http://datamining.typepad.com/gallery/blog-map-gallery.html

  16. Sample problem Aspirin Placebo 0 100 Heart attack No Heart attack 100 0

  17. Sample problem Aspirin Placebo 60 40 Heart attack No Heart attack 40 60

  18. Sample problem Aspirin Placebo 60 40 Heart attack No Heart attack 400 600

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