A Person Indexed Survey of Statistics
James R. Thompson
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First Statistician. Moses?
Moses's Census of 1452 B.C.____________________________________________________
Tribe Number of warriors
Judah 74,600Issachar 54,400Zebulun 57,400Reuben 46,500Simeon 59,300Gad 45,650 Ephraim 40,500Manasseh32,200Benjamin 35,400Dan 62,700 Asher 41,500Naphtali 53,400
Total 601,370
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Aristotle 384-322 BC
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Thucydides 460-395 BC
History of the Peloponnesian War
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St. Paul 3-65 AD
For now we see through a glass darkly, but then face to face.Now I know in part, but then shall I know even as also I am known.
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St. Thomas Aquinas 1225-1274.
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William of Ockham. 1288-1347
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Thomas Cromwell (c. 1485 - 1540)
1538 Parish registers began. Thomas Cromwell, Earl of Essex, ordered priests in every parish to keep a weekly record of baptisms, marriages and deaths occurring within their parish.
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Sir William Petty 1623-1687
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John Graunt (1620-1674)
Graunt's Life Table____________________________________________________ Age interval P(death in interval)
0-6 0.366-16 0.2416-26 0.1526-36 0.0936-46 0.0646-56 0.0456-66 0.0366-76 0.0276-86 0.01
Dimensionality Reduction
-.01
0
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0 10 20 30 40 50 60 70 80 90t=age
f(t) = Prob(death in year)
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0 10 20 30 40 50 60 70 80 90t=age
f(t)/[1-F(t)]
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Daniel Bernoulli, 1700-1782
St. Petersburg Paradox
Utility Theory
An Attempt at the ReductionOf Dimensionality
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Rev. Thomas Bayes 1702-1761
P(A^H) = P(A)P(H|A) = P(H)P(A|H)
P(A1|H) = P(H| A1)P(A1 )/[(H| Aj)P(Aj )]
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Marquis Pierre Simon Laplace 1749-1827Probability the sun will rise.Binomial approximated by normal
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Siméon Denis Poisson1781-1840
Poisson Process
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Carl Friedrich Gauss1777-1855
Least Squares
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Vilfredo Pareto 1848-1923
Systems fail due to a few assignable causes rather than due toa general mailaise across the system.
Contaminated Distributions (Mixtures)
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Charles Darwin. 1809-1882.
I have called this principle, by whicheach slight variation, if useful, is preserved, by the term Natural Selection.
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Sir Francis Galton F.R.S 1822 - 1911
IQ Test
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Karl Pearson. 1857-1936.
Goodness of Fit
Method of Moments
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Sir Ronald Aylmer Fisher. 1890-1962.
Maximum LikelihoodSufficiency (Dimensionality Reduction)
Significance Tests
Random Design of Experiments
Pot Crossed Self-Fertilized Difference I 23.500 17.375 6.125 I 12.000 20.375 -8.375 I 21.000 20.000 1.000 II 22.000 20.000 2.000 II 19.124 18.375 0.749 II 21.500 18.625 2.875 III 22.125 18.625 3.500 III 20.375 15.250 5.125 III 18.250 16.500 1.750 III 21.625 18.000 3.625 III 23.250 16.250 7.000 IV 21.000 18.000 3.000 IV 22.125 12.750 9.375 IV 23.000 15.500 7.500 IV 12.000 18.000 -6.000
Darwin’s Zea Mays Data
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Abraham Wald 1902-1950
The Likelihood Ratio Test
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Johann von Neumann 1903-1957
Computer Based Simulation
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Samuel S. Wilks, 1906-1964.
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John W. Tukey, 1915-2000.
Far better an approximate answer to the right question,which is often vague,than an exact answer to the wrong question,which can always be made precise.
Robustness, Exploratory Data Analysis
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Suggested Topics
• Gauss and Least Squares• Bayesian Analysis• Laplace• Poisson Process• Maximum Likelihood vs. Method of Moments• The Estimation of the Standard Deviation MAD vs s• Likelihood Ratio Tests• Analysis of Darwin’s Zea Mays Data• Sufficiency• Likelihood