605b,
Foundations of Statistics,
Fall 2004
Class Times: TBA
Dana House,
Instructor:
John Hartigan
john.hartigan@yale.edu
Office hours: 3.30-5
Fridays
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.
Topics
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
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
Texts
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