
A systematic development of the mathematical theory of statistical inference covering methods of estimation, hypothesis testing, and confidence intervals. An introduction to statistical decision theory. Undergraduate probability at the level of Statistics 241a assumed.

Instructor:

David Pollard

When: 
Tues, Thurs 10:30am  11:45am 
Where: 
24 Hillhouse, Rm 107 
Office hours: 
4:005:30 Tues, Wed 
TA: 
Chao Gao 
Problem session: 
to be arranged if needed 
Webpage: 
http://www.stat.yale.edu/~pollard/Courses/610.fall2013

Intended audience: 
Students (both graduate and
undergraduate) who are comfortable with introductory
probability (as covered in Stat 241/541).

Text: 
No single text. I find last year's text,
Young and Smith (2010) Essentials of Statistical Inference, Cambridge University Press,
a useful overview but I do not intend to cover the material in the same way or even in the same order.
Instead I will draw from multiple sources, many of which are available for free.

Topics
(tentative): 
Ideas to be explained, not necessarily in the following order:
 Statistical models
 sampling models
 models as an aid to thinking
 randomization
 Estimation and "margins of error"
 maximum likelihood and Mestimators
 asymptotic theory
 information inequality
 efficiency
 sufficiency
 confidence intervals
 robustness
 unbiasedness (Is it important?)
 Likelihood theory
 philosophy
 score function
 likelihood ratio tests
 Bayes theory
 independence vs. exchangeability
 Decision theory and related ideas
 hypothesis testing
 goodness of fit
 loss functions; risk; admissibility
 false discovery control
 Stein shrinkage
 sparsity
 Computation vs. theory

Grades: 
No exams.

The final grade will be based completely on the weekly homework.

Homework due each Thursday. All help received for the homework must be explicitly acknowledged.

Students who wish to work in teams (no more than 2 to a team)
should submit a single a solution set. All members of a team will be
expected to understand the team's solutions sufficiently well to
explain the reasoning at the blackboard. Occasional meetings with DP
will be arranged.

Other: 
Miscellaneous helpful materials.
 Handouts.

Class materials for an introductory probability course
(Stat
241/541,
Fall 2005), containing more extensive elementary discussion of
probabilistic ideas.
See, in particular, the first two chapters, on (conditional) probability and (conditional) expectations.
