A Person Indexed Survey of Statistics

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A Person Indexed Survey of Statistics

• James R. Thompson

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First Statistician. Moses?
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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 Ga
d 45,650 Ephraim 40,500 Manas
seh32,200 Benjamin 35,400 Dan 62,700
Asher 41,500 Naphtali 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
John Graunt (1620-1674)
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Graunt's Life Table _____________________________
_______________________ Age interval
P(death in interval) 0-6 0.36 6-16 0.24 16-2
6 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
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St. Petersburg Paradox
Utility Theory
An Attempt at the Reduction Of Dimensionality
Daniel Bernoulli, 1700-1782
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Rev. Thomas Bayes 1702-1761
P(AH) P(A)P(HA) P(H)P(AH)
P(A1H) P(H A1)P(A1 )/S(H Aj)P(Aj )
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Marquis Pierre Simon Laplace 1749-1827
Probability the sun will rise.
Binomial approximated by normal
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Siméon Denis Poisson 1781-1840
Poisson Process
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Carl Friedrich Gauss 1777-1855
Least Squares
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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)
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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.
Significance Tests
Maximum Likelihood Sufficiency (Dimensionality
Reduction)
Random Design of Experiments
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Darwins 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

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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 Darwins Zea Mays Data
• Sufficiency
• Likelihood