605b, Foundations of Statistics,

Fall 2004

Class Times: TBA

Dana House, 24 Hillhouse Avenue

Instructor: John Hartigan


Office hours: 3.30-5 Fridays

24 Hillhouse Avenue

Course Description

Statistics 605b, the Foundations of Statistics, will examine the evolution of modern probabilistic reasoning. Since right action, based on experience, circumstances, and uncertain consequences, is of concern in many fields, the emphasis will be on learning about the different ways of choosing action and handling uncertainty in the various fields. The fields studied will include Religion, Philosophy, Astronomy, Law, Insurance, Psychology, Sociology, Economics, and Physics. Some attention will be paid to the familiar schism between Bayesian and frequentist views on Statistical Inference.

People taking the course should have had at least two courses in theoretical statistics at the 241-242 level. The format of the course

is one lecture and one discussion section per week. Participants will be expected to read widely in a diverse literature, to join in the discussions, to prepare a short report for leading a discussion, and to prepare a paper on which a lecture will be given.


1 Divination, lots, dice, cards, the I Ching.

2 Gambling: Cardano, Fermat, Pascal, Huygens

3 The alchemy of the Law of Large Numbers: Bernoulli and DeMoivre

4 Inverse probability: Bayes and Laplace

5 Least squares: Euler, Legendre, Gauss, Laplace

6 Taxation and conscription: Censuses in Europe and China

7 Demographics: Graunt, Quetelet, Galton

8 The old fashioned way: Keynes, Jeffreys

9 Frequency: Venn, Boole, Von Mises

10 Statistical Mechanics: Maxwell, Boltzmann, Gibbs, Jaynes

11 Quantum mechanics: Bohr, Heisenberg, Shrodinger, Feynman

12 The Fisherian revolution: Edgeworth, Pearson, Fisher

13Another turn of the wheel: Neyman, Pearson, Wald

14 Castles in the sand: De Finetti, Savage, Good, Lindley

15 Rational choice: Von Neumann and Morgenstern

16 Irrational choice: Kahneman and Tversky

17 Let no new thing arise: evidence in law

18 Attractive nuisances: Casinos and insurance

19 The back of my hand: astrology, fuzzy sets, chaos


If you were to buy one book, I would suggest Stigler, the best modern History of Statistics, and an excellent source of other readings.

The History of Statistics : The Measurement of Uncertainty Before 1900 Stephen M. Stigler

The Empire of Chance : How Probability Changed Science and Everyday Life (Ideas in Context); Gerd Gigerenzer, et al

Games, Gods and Gambling : A History of Probability and Statistical Ideas; F. N. David

Creating Modern Probability : Its Mathematics, Physics and Philosophy in Historical Perspective (Cambridge Studies in Probability, Induction and decision; Jan Von Plato,

Emergence of Probability; A Philosophical Study of Early Ideas about Probability, Induction, and Decision; Ian Hacking

Logic of Statistical Inference: Ian Hacking

Theory of Probability: H. Jeffreys

The Foundations of Statistics: L.J.Savage

Induction and Probability: Bruno De Finetti