### ORIE 6700 Statistical Principles (Fall 2018)

1. Basic info

2. Syllabus

3. Prerequisites

4. Textbooks

5. Homework

6. Exams

7. Website

8. Grading

9. Academic Integrity

Lectures: Mon/Wed/Fri 10:10am--11:00am,
Hollister Hall 320

Recitations: Thu 2:55--4:30pm,
Phillips Hall 307

Instructor:

Prof. Christina Lee Yu
(cleeyu at cornell edu, Rhodes 226)

Office hours: Monday 11am--12pm

TA:

Raul Astudillo (ra598 at cornell edu)

Office hours: Wednesday 2-3pm in 419 Rhodes Hall

The course is about how to think rationally about the scientific
extraction of information from data. This is a “theory” course, but
mathematical formulations will be motivated by applications.

- • Basic concepts and models: sufficient statistics, completeness, exponential families, conjugate priors.
- • Statistical decision theory: risk, optimality, admissibility, Bayesian framework.
- • Hypothesis testing: likelihood ratio test, most powerful tests, Neyman-Pearson and Karlin-Rubin, Bayesian hypothesis testing.
- • Parameter estimation: uniform minimum variance unbiased estimators, Fisher Information, Cramer-Rao bounds, Rao-Blackwell and Lehmann-Scheffe, maximum likelihood estimators, asymptotic efficiency, linear regression.
- • Interval estimation: duality with testing, Bayesian credible intervals, p-values.
- • Error analysis: consistency, asymptotic efficiency, concentration inequalities, non-asymptotic analysis.
- • Computational statistics: Expectation-Maximization (EM), gradient descent, Markov chain Monte Carlo.

- • Multivariate calculus including epsilon-delta proofs as taught
in
advanced calculus or mathematical analysis courses, such as Math 4130
at Cornell.

- • Linear algebra and matrices (including eigenvalues/vectors, SVD)
- • One semester of undergraduate probability, including:

- - Probabilities,
random
variables and vectors, probability mass functions and probability
density functions. Cumulative distribution functions. Joint probability
mass/density functions, independence.

- - Expected values, moments, moment generating functions, (co)variance.
- - Modes of convergence (in distribution, in probability, and almost surely).
- - The law of large numbers, the central limit theorem, basic concentration inequalities (Markov, Chebyshev).
- - Basic distributions (normal, uniform, exponential, gamma, beta, chi-square, t, F, binomial, Poisson, geometric, hypergeometric, negative binomial).

- Probability prerequisites can mostly be found in Casella & Berger:
Sections 1.1-6, 2.1-3, 3.1-3 & 3.6.1, 4.1-3, 4.5-4.6, 5.1-5. You
should read these sections carefully in the first week of class. They
may give a more formal treatment of these topics than you have seen
before. For a more basic reference, you may consult the textbook, “A First Course in Probability,” by
Sheldon Ross, although you are required to understand the material at
the level of Casella & Berger.

- • Required: Casella, G. and Berger, R. (2002, 2nd ed.). Statistical Inference.
- • Helpful: Shao, J. (2003, 2nd edition). Mathematical Statistics. The proofs of some of the technical results in the course can be found in this book.
- • Helpful: Keener, R. (2010). Theoretical Statistics: Topics for a Core Course.

Casella and Berger will be on reserve at the library, and the latter two books are available online via the Cornell library website.

Homework assignments will be posted weekly on Thursday, and are due the following Thursday by noon (12:00pm) to the course dropbox in 411 Rhodes Hall. The first homework will be assigned by Aug 30. No HWs accepted late or to any other location. At the end of semester, your lowest two homework grades will be dropped.

While you should do all the assigned problems, only a randomly chosen subset will actually be graded. You will find some problems in the problem sets marked as "practice". These are not required, but you might find it helpful to work through them if you are looking for more practice working with the concepts introduced in class. Don't be misled by the relatively few points assigned to homework grades in the final grade calculation! While the grade you get on your homework is only a minor component of your final grade, working through the homework is a crucial part of the learning process and will invariably have a major impact on your understanding of the material. Some of the problem sets will involve a coding component, to help you explore different aspects of the material.

You may discuss problems if you find this educational but solutions must be written up individually. Copying is a violation of the honor code.

- • Prelim (Midterm): Tuesday 10/16, 7:30--9:30PM, in Phillips 403. You are allowed to bring one double-sided, letter-sized sheet of notes.
- • Final: Tuesday, 12/11, 2:00--4:30PM, in Phillips 403. You can bring two
double-sided, letter-sized sheets of notes.

Please contact Prof. Yu if you have an existing conflict with the exam times.

Log in to Blackboard to access course materials. You should be automatically given access to the course Blackboard site when you enroll in the course. All course communication is via Blackboard.

Your final grade will be determined according to the weights of Homework 20%, Midterm 40%, and Final 40%, with the two lowest homework grades dropped. In addition, if you do better on the Final than the Midterm, and you have done all the problem sets, then I will override your Midterm score with your Final score.

In case of a grading error you may resubmit the homework (to your TA, with permission) or exam (to Prof., with permission) within one week of when it was returned to you, with a written explanation of the grading error. The entire assignment or exam is carefully regraded, so the final grade may be lower due to our finding additional mistakes.

Each student in this course is expected to abide by the Cornell
University Code of Academic Integrity. Any work submitted by a student
in this course for academic credit will be the student’s own work. See above for the policy regarding homework. The Code is available here.