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A Person Indexed Survey of Statistics

A Person Indexed Survey of Statistics. James R. Thompson. First Statistician. Moses?. Moses's Census of 1452 B.C. ____________________________________________________ Tribe Number of warriors Judah 74,600 Issachar 54,400 Zebulun 57,400 Reuben 46,500 Simeon 59,300

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A Person Indexed Survey of Statistics

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  1. A Person Indexed Survey of Statistics James R. Thompson

  2. First Statistician. Moses?

  3. Moses's Census of 1452 B.C. ____________________________________________________ Tribe Number of warriors Judah 74,600 Issachar 54,400 Zebulun 57,400 Reuben 46,500 Simeon 59,300 Gad 45,650 Ephraim 40,500 Manasseh32,200 Benjamin 35,400 Dan 62,700 Asher 41,500 Naphtali 53,400 Total 601,370

  4. Aristotle 384-322 BC

  5. Thucydides 460-395 BC History of the Peloponnesian War

  6. 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.

  7. St. Thomas Aquinas 1225-1274.

  8. William of Ockham. 1288-1347

  9. 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.

  10. Sir William Petty 1623-1687 John Graunt (1620-1674)

  11. Graunt's Life Table ____________________________________________________ Age interval P(death in interval) 0-6 0.36 6-16 0.24 16-26 0.15 26-36 0.09 36-46 0.06 46-56 0.04 56-66 0.03 66-76 0.02 76-86 0.01 Dimensionality Reduction

  12. St. Petersburg Paradox Utility Theory An Attempt at the Reduction Of Dimensionality Daniel Bernoulli, 1700-1782

  13. 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 )/[S(H| Aj)P(Aj )]

  14. Marquis Pierre Simon Laplace 1749-1827 Probability the sun will rise. Binomial approximated by normal

  15. Siméon Denis Poisson 1781-1840 Poisson Process

  16. Carl Friedrich Gauss 1777-1855 Least Squares

  17. Vilfredo Pareto 1848-1923 Systems fail due to a few assignable causes rather than due to a general mailaise across the system. Contaminated Distributions (Mixtures)

  18. Charles Darwin. 1809-1882. I have called this principle, by whicheach slight variation, if useful, is preserved, by the term Natural Selection.

  19. Sir Francis Galton F.R.S 1822 - 1911 IQ Test

  20. Karl Pearson. 1857-1936. Goodness of Fit Method of Moments

  21. Sir Ronald Aylmer Fisher. 1890-1962. Significance Tests Maximum Likelihood Sufficiency (Dimensionality Reduction) Random Design of Experiments

  22. Darwin’s Zea Mays Data 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

  23. Abraham Wald 1902-1950 The Likelihood Ratio Test

  24. Johann von Neumann 1903-1957 Computer Based Simulation

  25. Samuel S. Wilks, 1906-1964.

  26. 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

  27. 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

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