Advanced Statistics II: Statistics 36-756
Department of Statistics, Carnegie Mellon University
Fall, 2006
- Office : BH 132G, telephone: x8-2723
- Office hours: by appointment.
Lectures: TR 10:30-11:50am BH 232Q
(Conference Room)
(We will occasionally meet on Mondays or Wednesdays to make up classes
when I need to be away. See tentative schedule and topics below.)
Syllabus
Class
Topics and Readings
August 29:
Introduction; Discussion of Bayesian versus
frequentist inference
August 31:
Readings: Chapter 1 of Schervish, Theory of
Statistics, Sections 1.1 and 1.2
September 5: Bayesian
History paper. For a copy click
here.
September 6 and 7 (note that we are
meeting Wed. this week):
Readings: Continuation from Chapter 1 of Schervish, Theory of
Statistics; Ramsay (1926) [for a copy click here], and de
Finetti (1937) 1983 English
translation by Kyburg.
September 12 and 14: No
Classes
September 19 and 21:
Continuation of discussion of exchangeability, with readings from de
Finetti and Schervisah Chapter 1. Introduction to Dirichlet
processes.
September 26: Dirichlet
processes and their properties. Schervish, Section 1.6 and
Ferguson (1973,
1974).
September 27: (yes, we are
meeting on Wednesday too this week): Schervish, Chapter 2,
Sufficiency. Ancilarity, and Exponential families from both frequentist
and Bayesian perspectives. See also Degroot
and Fienberg (1983) and Seidenfeld
(1985).
September 28: Continuation of Chapter 2
Schervish from Wedwesday. See also, Reid
(1995).
October 3: The Behrens-Fisher
Problem (see Welch,
(1937)) and the Fieller-Creasy Problems (see Creasy
(1954) and Fieller
(1954) and the discussion
of their papers following the paper by David, especially the
comments of R.A. Fisher.
October 4 (another Wednesday class): Continuation
from Tuesday on the Fieller-Creasy Problem
October 5: Objective
vs. subjective Bayesian methods. Begin by reading Section2.3.4 of
Schervish on Jeffreys' prior, and look at review of rules for formal
priors by Kass
and Wasserman (1996).
Papers
by Berger and Goldstein presented at the Bayesian Case Studies Workshop
(2005), and published with discussion in Bayesian Analysis
(2006). Go to: http://ba.stat.cmu.edu/vol01is03.php
October 10:
Dutch books, Axiomatics, and
the
Sure-Thing Principle and Simpson's Paradox.
Schervish, Section 3.3 on
axiomatic decision theory.
Richard
Jeffrey, Subjective
Probability: The Real Thing (chapter 1 on
Dutch books). For a copy click
here.
Colin
Blyth (1972) "On Simpson's Paradox and the Sure-Thing Principle,"
JASA, 67, 364-366. For a copy
click here.
October 12: No regular class. Instead,
studewnts will be attending a lecture at the universit yof Pittsburgh
on Friday Oct. 13 by James Joyce:
"Rational Belief and Reasonable Belief, a Ramseyian
Distinction"
James Joyce, Department of Philosophy, University of
Michigan
Friday, October 13, 2006, 3:30 pm
817R Cathedral of Learning
http://www.pitt.edu/~pittcntr/Events/All/Conferences/others/other_conf_2006-07/bayesianism_fundamentally.htm
October 17: Graphical
Models, Darroch,
Lauritzen and Speed (1980). Markov Random Fields and
Log-Linear Models for Contingency Tables. Annals of Statistics, 8, 522-539.
October 19: Graphical
Models
October 24: HyperMarkov
Laws (Dawid
and Lauritzen, 1993) and Bayesian model search with graphical
models (Madigan
and Raftery 1994).
October 26: No
class.
October 31: David Huang:
Missing Data, EM and variational inference.
Rubin
(1976)
Dempster,
Laird, and Rubin (1977)
November 2: David Huang:
Missing Data, EM and variational inference. Continuation from Oct. 31.
C. F. Jeff Wu "On the Convergence Properties of the EM
Algorithm," The Annals of Statistics, Vol. 11, No. 1. (Mar., 1983),
95-103.
http://www.jstor.org/view/00905364/di983917/98p04132/0?frame=noframe&dpi=3&userID=80ede88a@cmu.edu/01cc99331300501b10825&config=jstor>
http://links.jstor.org/sici?sici=0090-5364%28198303%2911%3A1%3C95%3AOTCPOT%3E2.0.CO%3B2-M
BEAL, M.J. and GHAHRAMANI, Z. (2003).
The Variational Bayesian EM Algorithm for Incomplete Data: With Application
to Scoring Graphical
Model Structures. Bayesian Statistics 7, 453-463. To be
distributed.
November 7: Eric
Huang- Causal Inference
Judea
Pearl "Causal Inference in Statistics: A Gentle Introduction"
Don Rubin "Direct and Indirect Causal Effects via Potential Outcomes"
Steffen
Lauritzen Discussion on Don Rubin's paper
Don
Rubin "Bayesian Inference for Causal Effects: The Role of Randomization"
November 9: Eric Huang: Causal
Inference (cont.)
November 14: Charles
Lee: The Bootstrap
Brad
Efron (1979) Bootstrap Methods: Another Look ast the Jackknife, Annals of Statistics, 7.
Rupert
Miller (1974) The Jackknife: A Review. Biometrika, 61.
Brad
Efron (2003) Second Thoughts on the Bootstrap, Statistical Science, 18.
November 16: Charles
Lee: The Bootstrap (cont)
November 21: no class
November 23: Thanksgiving
-- no class
November 28: Cindy Yang:
Elicitation
Garthwaite_Kadane_review2005.pdf
Shephard_caseStudy.pdf
Edwards_Lindman1963.pdf
November 30: Cindy Yang:
Elicitation (cont.)
December 5: Dan Heinz:
Dirichlet Prosses
Teh, Jordan, Beal, Blei. "Hierarchical Dirichlet Processes".
Available here:
http://www.cs.berkeley.edu/~jordan/publications.html
- Persi
Diaconis; David Freedman:On
the Consistency of Bayes Estimates, Annals of Statistics,
(1986), vol. 14 pp. 1-26
- Stable URL: http://links.jstor.org/sici?sici=0090-5364%28198603%2914%3A1%3C1%3AOTCOBE%3E2.0.CO%3B2-U
See also the extended discussion including the that by Bergsr, and by
Lindley, and the response as well as the followup paper.
- Discussion:
On the Consistency of Bayes Estimates, pp. 30-37
- James Berger
- Stable URL: http://links.jstor.org/sici?sici=0090-5364%28198603%2914%3A1%3C30%3ADOTCOB%3E2.0.CO%3B2-O
- Discussion:
On the Consistency of Bayes Estimates, p. 48
- J. A. Hartigan
- Stable URL: http://links.jstor.org/sici?sici=0090-5364%28198603%2914%3A1%3C48%3ADOTCOB%3E2.0.CO%3B2-D
- Discussion:
On the Consistency of Bayes Estimates, pp. 55-58
- William S. Krasker; John W. Pratt
- Stable URL: http://links.jstor.org/sici?sici=0090-5364%28198603%2914%3A1%3C55%3ADOTCOB%3E2.0.CO%3B2-D
- Discussion:
On the Consistency of Bayes Estimates, pp. 60-63
- Dennis V. Lindley
- Stable URL: http://links.jstor.org/sici?sici=0090-5364%28198603%2914%3A1%3C60%3ADOTCOB%3E2.0.CO%3B2-F
- Rejoinder:
On the Consistency of Bayes Estimates, pp. 63-67
- P. Diaconis; D. Freedman
- Stable URL: http://links.jstor.org/sici?sici=0090-5364%28198603%2914%3A1%3C63%3AROTCOB%3E2.0.CO%3B2-Z
On
Inconsistent Bayes Estimates of Location, pp. 68-87
P. Diaconis; D. Freedman
Stable URL:
http://links.jstor.org/sici?sici=0090-5364%28198603%2914%3A1%3C68%3AOIBEOL%3E2.0.CO%3B2-X
December 7:
Dan Heinz (contnutation from Dec 5)
Last Updated: December 4, 2006.