### ORIE 6700 Statistical Principles (Fall 2018)

1. Basic Info

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

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: 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.

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, 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.

4. Textbooks

• 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.

5. Homework

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.

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 (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.

7. Website

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.