STA-215 Statistical Inference

Spring 99

Links to: Problems

STA 215 STATISTICAL INFERENCE. Credits: 1.00, Hours: 3.0. 
Areas: QR. 
      Section 01. Call No. 141336. Limit: 18. Instructor:
      MUELLER, P. 
            TTh, 3:50PM- 5:05 in Old Chemistry, room 025.

STA 213 or equivalent is a prerequisite for this class. If you are in doubt, please make a self test.

Instructor

Peter Müller ; office: 219 Old Chemistry Bldg.;
office hours: Friday from 2:00 to 3:00 and by appointment;

e-mail: pm@stat.duke.edu; telephone: 684-3437.

TA: Kern, John . office: 211B Old Chemistry Bldg.
e-mail:kern@stat.duke.edu, phone: 684-8088.

Midterms and Problems

Two midterms: Midterms will be open book and open notes.

Weekly problem sets: around 10 problems. Group work is ok and encouraged. Solutions and hints will be posted regularily.

Exercises: occasional exercises to prepare class discussion for the next lecture. Excercises will not be collected.

Computing

Some problems will require statistical computing. Splus is recommended. Any other software (Gauss, Xlisp-Stat etc) is ok.

Grading

Grading will be based on homework problems (30%), midterms (30% each) and class participation (10%).

Textbooks

GCSR: Gelman, Carlin, Stern and Rubin, Bayesian Data Analysis. Main course text for Bayesian inference. Most problem sets for the first half of the semester will come from GCSR.
BC: Berger and Casella, Statistical Inference. Main course text for classical inference.
Most problem sets for the first half of the semester will come from GCSR.
Spector: An Introductioon to S and S-plus. Reference for Splus, optional course text.

Reading List

BS: Bernardo and Smith, Bayesian Theory. Alternative to GCSR. More formal presentation. Will use chapters 4.2-4.5 and 6.
OH: O'Hagan, Bayesian Inference. Alternative to GCSR.
S: Schervish, M., Theorey of Statistics .
Those of you who are interested in a mathematically more rigorous discussion than GCSR will like this book to complement the more informal discussion in GCSR.
B: Berger, Bayesian Analysis and Statstical Decision Theory Some decision theoretic foundations (Chapters 1 and 2).
R: Robert, The BAyesian choice. Alternative to GCSR. More decision theoretic.
BD: Bickel and Docksum, Mathematical Statistics. Frequentist optimality criteria (Ch 4), Hyptothesis testing (Ch 6).
Berger and Wolpert, The Likelihood Principle.

If, beyond this course, you want to read more on statistics see the Duke Statistics reading list.

Part I: Basic Concepts

Introduction: Prior, likelihood, posterior (GCSR Ch 1 and 2).
Foundations: The Bayesian paradigm (B Ch 1; CB Ch 6). Likelihood principle and sufficiency principle.
Multiparameter models: Marginal posteriors, mv normal, multinomial (GCSR Ch 3).
Analytic posterior approximations (GCSR Ch 4 and 9).

Part II: More Modelling

Hierarchical models (GCSR Ch 5). Empirical Bayes (B Ch. 4.5).
Model checking and model comparison (GCSR Ch 6; BS 6).
Regression (GCSR Ch 8 and 12).
General principles (may be skipped): Exchangeability (BS 4.2); invariance (BS 4.3); sufficiency (BS 4.4); nonidentifiability; sequential decisions.

Part III: Classical Inference

Point estimation (CB Ch 7)
Hypothesis testing (CB Ch 8)
Interval estimation (CB Ch 9)

Part IV: Comparison of classical, likelihood and Bayesian approaches

Decision theoretic foundations (R Ch 2, 6; CB Ch 10). Utility and loss; Admissibility; Admissibility of BAyes estimators.
P-values and Bayes Factors Significance testing. p-values. Contrast with Bayes factors. Testing point null hypothesis. Bayesian vs. Classical perspectives.

pm@stat.duke.edu