## STA732: Statistical Inference

 Prof: Robert L. Wolpert wolpert@stat.duke.edu (684-3275) Office Hours: Old Chem 211c, Mon 4:15-5:00pm or by appointment TA: Zhenglei Gao zhenglei@stat.duke.edu (684-9390) Office Hours: Old Chem 214D, Tue 4-6pm or by appointment Class: Mon & Wed 1:15-2:30pm Old Chem 025 Text: Peter Bickel & Kjell Doksum, Mathematical Statistics: Basic Ideas and Selected Topics (2nd edn) Recc: George Casella & Roger Berger, Statistical Inference (Chaps 3.3, 6-9) Larry Wasserman, All of Statistics (Chaps 6,7,9-12) Opt'l: James Berger & Robert Wolpert, The Likelihood Principle (2nd edn) Andrew Gelman, John Carlin, Hal Stern, & Don Rubin, Bayesian Data Analysis Erich Lehmann, Theory of Point Estimation and Testing Statistical Hypotheses

### Description

This is a course about making inference using statistics, or functions of observed data: this includes the (point and interval) estimation of uncertain parameters and the testing of statistical hypotheses. All three contemporary paradigms of inference (Likelihood, Classical, Bayesian) are presented and compared; traditional properties of estimators (bias, consistency, efficiency, sufficiency, etc.) and tests (size, power, probability) are considered in detail. The emphasis is perhaps 60% on frequentist methods, 30% on Bayesian methods, and 10% on likelihoodist methods.

Students are assumed to be familiar with random variables and their distributions from a calculus-based introduction to probability theory, at the level of the first five chapters of Statistical Inference by Casella & Berger or Probability and Statistics by DeGroot, or the first nine chapters of A First Course in Probability by Ross. Some problems and projects will require computation; students should be or become familiar with either R (some notes and an intro are available, also in an older but nice form (Contents, 1-29, 30-64, 65-85, Examples)) or Matlab (a primer and intro are available), both easier to use than compiled languages like FORTRAN or C.

Not all homework sets will be graded, but they should be turned in for comment; Monday classes will often begin with a class solution of one or two of the preceeding week's problems. Here is at least a tentative schedule, containing most of the topics below.

OUTLINE -- course topics will include: (look here for a tentative schedule)

• Review of Probability (e.g. dist'ns)
• Likelihood Functions (notes)
• Likelihoodist, Bayes, & Frequentist (incl. Classical) Paradigms
• Exponential Families
• Sufficiency
• Observed & Expected (Fisher) Information
• Nuisance Parameters
• The Likelihood Principal
• Point & Interval Estimation
• Consistency
• Confidence & Credible Intervals
• Coverage Probability
• Frêchet (Cramér-Rao) Lower Bound
• Efficiency & Robustness
• Testing Statistical Hypotheses
• P-Values
• Posterior Probabilities
• Size & Power
• Neyman-Pearson Lemma

Note on Auditing:

My rules about auditors are that a student can sit in on or (preferably) audit a course if:

1. There are enough seats in the room,
2. He/she is willing to commit to active participation:
1. turn in about a third or a half of the homeworks (or a few problems on each of most HW assignments)
2. take either the final or the midterm
3. come regularly to lectures, and ask or answer questions now and then.
I expect all students to participate actively. It hurts the class atmosphere and lowers students' expectations when some attenders only spectate. I try to discourage that by requiring active participation of everyone, including auditors, to make the classes more fun and productive for us all.