A Person Indexed Survey of Statistics James R. Thompson

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

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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