### ORIE 6700 Statistical Principles (Fall 2020)

1. Basic Info

Lectures: Mon/Wed 11:30a–12:45p, Olin 255. Zoom link on Canvas.
Sessions: Fri 3:00p--4:15p, Olin 255. Zoom link on Canvas.

Instructor:
Yudong Chen (yudong.chen at cornell edu, Rhodes 223)
Office hours: Monday 5:15-6:15pm. Zoom link on Canvas. Or by appointment.

TA:
Lijun Ding (ld446 at cornell edu)
Office hours: Tuesday 5:15-6:15pm. Zoom link on Canvas. Or by appointment.

2. Syllabus

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: exponential families, location/scale families, mixture models, order statistics, sufficient statistics, completeness.
• • Statistical decision theory: risk, optimality, admissibility, Bayesian framework.
• • Point estimation: uniform minimum variance unbiased estimators, Fisher Information, Cramer-Rao bounds, Rao-Blackwell and Lehmann-Scheffe, maximum likelihood estimators, asymptotic efficiency, linear regression.
• • Hypothesis testing: most powerful tests, Neyman-Pearson and Karlin-Rubin, z/t-tests, Bayesian hypothesis testing.
• • Interval estimation: duality with testing, Bayesian credible intervals, p-values.
• • Computational statistics: Expectation-Maximization (EM), gradient descent, Markov chain Monte Carlo, Gibbs sampler, model checking.
• • Minimax theory: from estimation to testing, LeCam, Fano, Assouad
• • Selected topics: high dimensional statistics, concentration, random matrices, sequential tests, non-parametric estimation, bandits, Markov Decision Processes.

3. Prerequisites

• • 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, spectral theorem, Singular Value Decomposition)
• • 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, (co)variance, moments, moment generating functions.
• - Modes of convergence (in distribution, in probability, and almost surely).
• - The law of large numbers and the central limit theorem.
• - Basic distributions (multivariate normal, uniform, exponential, Poisson, gamma, beta, chi-square, t, F, binomial, Poisson, geometric, hypergeometric, negative binomial).
• - Product, convolution and mixture of distributions.
• 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.

4. Textbooks

• Recommended: 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.
• • Helpful: Bickel, P.J. & Doksum, K.A. (2007, 2nd ed.). Mathematical Statistics.
• • Helpful: Wasserman, L. (2003). All of Statistics: A Concise Course in Statistical Inference.

5. Homework

Homework assignments will be posted weekly on Wednesday, and are due the Wednesday following week by 11:59pm, unless otherwise noticed. No HWs accepted late or to any other location. Homework should be submitted electronally on Canvas. You are encouraged to typeset your homework using LaTeX.

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

6. Exams

• Prelim: TBD. You are allowed to bring one double-sided, letter-sized sheet of notes.
• Final: TBD. You can bring two double-sided, letter-sized sheets of notes.

7. Website

Log in to Canvas 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.

• • Homework 20%, Midterm 30%, Final 50%, with the two lowest homework grades dropped.
• • Homework 40%, Midterm 30%, Final 30%, with no homework grade dropped.

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.

9. Academic Integrity and Behavior Compact

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.

It’s critical for everyone to abide by the Behavioral Compact. Doing so protects students, staff, faculty, and the wider Ithaca community, including people who have underlying health conditions that may not be apparent. It also helps keep the campus open.