Statistics: Discrete Methods

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Fall 2012
Statistics Discrete Methods
STAT 453/653
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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
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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)
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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
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Karl Pearson (March 27, 1857 April 27, 1936)
established the discipline of mathematical
statistics
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George Udny Yule
(18 Feb 1871, Scotland -- 26 June 1951, England)
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Sir Ronald Aylmer Fisher (17 February 1890 29
July 1962)
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Origin of discrete data
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Socio-economic statistics, 2009
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Socio-economic statistics, 2012
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Patterns in complex systems
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El-Nino
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Prediction problem
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Complex networks
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Map of the blogosphere
http//datamining.typepad.com/gallery/blog-map-gal
lery.html
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Sample problem
Aspirin
Placebo
0
100
Heart attack
No Heart attack
100
0
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Sample problem
Aspirin
Placebo
60
40
Heart attack
No Heart attack
40
60
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Sample problem
Aspirin
Placebo
60
40
Heart attack
No Heart attack
400
600