STATISTICS (MA 6963)
MATHEMATICAL STATISTICS (MATH 2962)
Spring 2021
Instructor
Mike O'Neil (oneil@cims.nyu.edu)
Teaching assistant
Paul Beckman (pgb8409@nyu.edu)
Description
The course is a graduate-level introduction to the mathematical theory of statistics, including statistical modelling, parameter inference, hypothesis testing, Bayes theory, and an introduction to some computational methods (e.g. MCMC and bootstrap). A working knowledge of probability at an advanced undergraduate or graduate level is assumed for the course. View the syllabus.
Lecture
Wednesday 11:00am - 1:30pm
Office hours
Instructor: By appointment, nyu.zoom.us/my/mike.oneil
TA: Tuesday 11:00am - 12:00pm
Announcements
None.
Mike O'Neil (oneil@cims.nyu.edu)
Teaching assistant
Paul Beckman (pgb8409@nyu.edu)
Description
The course is a graduate-level introduction to the mathematical theory of statistics, including statistical modelling, parameter inference, hypothesis testing, Bayes theory, and an introduction to some computational methods (e.g. MCMC and bootstrap). A working knowledge of probability at an advanced undergraduate or graduate level is assumed for the course. View the syllabus.
Lecture
Wednesday 11:00am - 1:30pm
Office hours
Instructor: By appointment, nyu.zoom.us/my/mike.oneil
TA: Tuesday 11:00am - 12:00pm
Announcements
None.
Materials
The course will work off of the material from three textbooks:
- Wasserman, All of Statistics, Springer 2004
- Wasserman, All of Nonparametric Statistics, Springer 2006
- Casella and Berger, Statistical Inference, 2nd Ed., Cengage, 2011
The textbooks by Wasserman are available electronically on SpringerLink via NYU.
Grading
The final numerical grade will be computed basic on the following rubric:
The overall letter grade will be computed based on the overall numerical grade.
The course will work off of the material from three textbooks:
- Wasserman, All of Statistics, Springer 2004
- Wasserman, All of Nonparametric Statistics, Springer 2006
- Casella and Berger, Statistical Inference, 2nd Ed., Cengage, 2011
The textbooks by Wasserman are available electronically on SpringerLink via NYU.
Grading
The final numerical grade will be computed basic on the following rubric:
| 15% | Engagement on Campuswire |
| 20% | Quizzes (every other week) |
| 20% | Exam 1 |
| 20% | Exam 2 |
| 25% | Final exam |
Schedule
Below is an updated list of discussion topics along with any documents that were distributed, notes, or relevant code.| Date | Topics | Materials |
|---|---|---|
| Feb 3 | Overview, Probability review Casella & Berger: Ch 1-4 Wasserman AoS: Ch 1-4 |
Notes Zoom recording |
| Feb 10 | Convergence of random variables, limit
theorems Casella & Berger: Ch 5.1-5.2, 5.3, 5.5 Wasserman AoS: Ch 5 |
Notes Zoom recording |
| Feb 17 | Quiz 1 Empiricial distribution function, method of moments Casella & Berger: Ch 7.1, 7.2.1 Wasserman AoS: Ch 6, 7, 9.1-9.2 |
Notes Zoom recording |
| Feb 24 | Method of maximum likelihood Casella & Berger: 7.2.2 Wasserman AoS: Ch 9.3-9.10 |
Notes Zoom recording |
| Mar 3 | Take-home exam 1 | |
| Mar 10 | Sufficiency, hypothesis testing Casella & Berger: 6.1, 6.2.1-6.2.2, 8.1, 8.3.1-8.3.2 Wasserman AoS: Ch 9.13.2, 10.0 |
Notes Zoom recording |
| Mar 17 | Hypothesis testing, p-values Casella & Berger: 8.2.1, 8.3.4 Wasserman AoS: 10.1-10.10 |
Notes Zoom recording |
| Mar 24 | Quiz 2 Bayesian inference Casella & Berger: 7.2.3, 8.2.2. 9.2.4 Wasserman AoS: Ch 11 |
Notes Zoom recording |
| Mar 31 | Regression, multivariate models, Gaussian
processes Casella & Berger: Ch 11.3, 4.6 Wasserman AoS: Ch 13, 14.1-14.3 Rasmussen & Williams: Ch 1, 2.2 |
Notes Zoom recording |
| Apr 7 | Take-home exam 2 | |
| Apr 14 |
Gaussian processes, non-parametric methods Rasmussen & Williams: Ch 1, 2.2-2.3, 4.1-4.2 Wasserman AoNPS: Ch 4, 5.0-5.1 |
Notes Zoom recording |
| Apr 21 | Quiz 3 Linear smoothers Wasserman AoNPS: Ch 5.0-5.4 |
Notes Zoom recording |
| Apr 28 |
Histograms, kernel density estimation Bootstrap, Newton's method Markov Chains Wasserman AoS: 8, 9.13.4, 20.1-20.3, 23.1-23.2 Wasserman AoNPS: 3, 6.1-6.3 Casella & Berger: 10.1.4, 10.6.5 |
Notes Zoom recording |
| May 5 | Quiz 4 Markov Chain Monte Carlo, Metropolis-Hastings Wasserman AoS: 23.2, 24.2, 24.4 Understanding the Metropolis-Hastings Algorithm |
Notes Zoom recording |
| May 12 | Final Exam | |