STA532: Theory of Statistical Inference

Prof:Robert L. Wolpert wolpert@stat.duke.edu OH: Wed 1:30-2:30pm, 211c Old Chem
TA:TBD TBD@duke.edu  OH: Wed 4:00-6:00pm, 211a Old Chem
Class: Wed Fri 8:30-9:45am, 123 Old Chem
Text:Larry Wasserman, All of Statistics (errata, website)
Opt'l:G Young & R Smith, Essentials of Statistical Inference
G Casella & R Berger, Statistical Inference (2/e)
A Gelman, J.B. Carlin, et al. Bayesian Data Analysis (3/e)

Syllabus

WeekTopicHomework
I. Foundations & Estimation ProblemsDue
Jan     -09 Models & Inference hw1Jan 16
Jan 14-16 Estimating CDFs and Statistical Functionals hw2Jan 23
Jan 21-23 Parametric Inference I: MoM & MLEs hw3Jan 30
Jan 28-30 Parametric Inference II: Properties & Asymptotics hw4Feb 06
Feb 04-06 Bayesian & Objective Bayes Estimation hw5Feb 11
Feb 11-13 Review & in-class Midterm Exam I (pdf sheet) Hists: Exam, Course
Feb 18-20 Confidence and Credible Interval Estimates hw6Mar 06
Feb 25-27 Winter storm
II. Testing Statistical Hypotheses
Mar 04-06 P-values, Significance, & Hypothesis Tests hw7Mar 20
--- Spring Recess (Mar 07-15) ---
Mar 18-20 Likelihood Ratios & Neyman-Pearson Tests hw8 Mar 27
Mar 25-27 Bayes Factors & Bayesian Testing hw9 Apr 01
Apr 01-03 Review & in-class Midterm Exam II Hists: Exam, Course
III. Models & Methods
Apr 08-10 Empirical and Hierarchical Bayes hw10 Apr 15
Apr 15- Review for Final Exam
Apr 29 7-10pm Wed: In-class Final Examination Hists: exam, course

Description

This is a course about statistical inference, concentrating on the two leading contemporary paradigms (Frequentist and Bayesian), and introducing others (fiducial, likelihoodist, etc.). Theories of point and interval estimation and testing are introduced, and their properties (efficiency, consistency, sufficiency, robustness) are studied. Maximum likelihood, moments and non-parametric methods based on exact or large sample distribution theory; associated EM, asymptotic normality and bootstrap computational techniques. Theoretical aspects of objective Bayesian inference, prediction, and testing. Selected additional topics drawn from, for example, multiparameter testing, contingency tables, multiplicity studies.

Lecture notes are available on-line (click on the "Week" column if it's blue or green). If you bring a copy of these to lectures you can spend more time understanding and less time writing. These notes are a work-in-progress, and will evolve as I try to improve them by adding material, correcting errors, and clarifying difficult points. If something in the notes looks wrong or confusing, first check to see if the website has a more recent version (refresh your browser, and look at the "Last edited" date at the bottom of the last page). If it still looks puzzling, please e-mail me with a question or comment so I can fix it if it's wrong, try to explain better or add an example if it's confusing, or help you understand if it was just a difficult issue.

This is syllabus is also tentative, last revised , and will almost surely be superseded— reload your browser for the current version.

Note on Background:

Statistical modeling and inference depend on the mathematical theory of probability, and solving practical problems usually requires integration or optimization in several dimensions, either analytically or numerically. Thus this course requires a solid mathematical background: multivariate calculus at the level of Duke's MTH212 or MTH222 and linear algebra at the level of Duke's MTH221 or MTH216. Students must be proficient in calculus-based probability theory at the level of MTH230/STA230.

Some questions will be computational, and will require skill in any one of the computing environments commonly used in statistical analysis such as R, Matlab, or Python. Students without strong preparation in these will need to invest significant additional time to fill in the gaps. Don't expect spreadsheets or calculators to be sufficient.

Note on Homework:

This is a demanding course. The homework exercises are difficult, and the problem sets are long. The only way to learn this material is to solve problems, and for most students this will take a substantial amount of time outside class— six to ten hours for many students. Be prepared to commit the time it will take to succeed, and don't expect the material to come easily. Working with one or more classmates is fine; but write up your own solutions in your own way, don't copy someone else's solutions. Students who rely too much on others for homework tend to do badly on the exams, which count far more.

Weekly problem sets are assigned on the class website here. Homeworks are collected at the start of each Friday class (so I can answer questions about them in class) and are returned at the following Wednesday class. LaTeX'd homework assignments can also be submitted electronically as pdf attachments to an e-mail sent to sta532@stat.duke.edu. Until solutions are posted, late homeworks are accepted but are penalized 10% per day. The lowest homework score will be dropped. Exam week homeworks are due on Wednesday, so you can ask questions about them and get feedback before the test.

Homework problems are awarded points based on your success in communicating a correct solution. For full credit the solution must be clear, concise, and correct; even a correct solution will lose points or be returned ungraded if it is not clear and concise. Neatness counts. Consider using LaTeX and submitting your work in pdf form if necessary (it's good practice anyway).

Note on Evaluation:

Course grade is based on homework (10%), in-class midterm exams (25% each), and final exam (40%). Most years grades range from B- to A, with a median grade near the B+/A- boundary. Grades of C+ or lower are possible (best strategy: skip some homeworks, skip several classes, tank an exam or two), as is A+ (given about once every two or three years for exceptional performance).

Note on Enrollment:

Spaces in this course are reserved for Statistical Science Masters students. Other well-prepared students are welcome, but space in the course is limited and in most years it is over-subscribed.

Note on Auditing:

Unregistered students are welcome to sit in on or (preferably) audit this course if:
  1. There are enough seats in the room, and
  2. They are willing to commit to active participation:
    1. turn in about a third or so of the homeworks (or a few problems on each of most HW assignments)
    2. take either the final exam or a 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 are just spectators. I try to discourage that by requiring active participation of everyone, including auditors, to make the classes more fun and productive for us all. Past experiences suggests that most auditors stop attending midway through the semester, when they have to balance competing demands on their time; if this course material is important to you, it is better to take the class for credit.

Note on Absence:

No excuse is needed for missing class. Class attendance is entirely optional. You remain responsible for turning in homework on time and for material presented in class that is not in the readings. Try not to get sick at scheduled examination times.

Academic Integrity

You may discuss and collaborate in solving homework problems, but you may not copy— each student should write up his or her solution. Cheating on exams, copying or plagiarising homeworks or projects, lying about an illness or absence and other forms of academic dishonesty are a breach of trust with classmates and faculty, and will not be tolerated. They also violate Duke's Community Standard and will be referred to the Graduate School Judicial Board or the Dean of the Graduate School.