COMPUTATIONAL STATISTICS (MA 6973, MATH 2080)
Fall 2021
Instructor
Mike O'Neil (oneil@cims.nyu.edu)
Teaching assistant
Paul Beckman (pgb8409@nyu.edu)
Description
This course aims to cover topics needed to develop a broad working knowledge of modern computational statistics. We seek to develop a practical understanding of how and why existing methods work, enabling effective use of modern statistical methods. Achieving these goals requires familiarity with diverse topics in statistical computing, computational statistics, computer science, and numerical analysis. View the syllabus for more detailed information.
Lecture
Wednesday 11:00am - 1:30pm, 2 MTC 804
(In person)
Office hours
By appointment
Announcements
None.
Mike O'Neil (oneil@cims.nyu.edu)
Teaching assistant
Paul Beckman (pgb8409@nyu.edu)
Description
This course aims to cover topics needed to develop a broad working knowledge of modern computational statistics. We seek to develop a practical understanding of how and why existing methods work, enabling effective use of modern statistical methods. Achieving these goals requires familiarity with diverse topics in statistical computing, computational statistics, computer science, and numerical analysis. View the syllabus for more detailed information.
Lecture
Wednesday 11:00am - 1:30pm, 2 MTC 804
(In person)
Office hours
By appointment
Announcements
None.
Materials
The course will work off of the material from two textbooks:
- Efron and Hastie, Computer Age Statistical Inference, Cambridge, 2016
- Gentle, Computational Statistics, Springer, 2009
Both texts are available for free via NYU Libraries.
Grading
A 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 two textbooks:
- Efron and Hastie, Computer Age Statistical Inference, Cambridge, 2016
- Gentle, Computational Statistics, Springer, 2009
Both texts are available for free via NYU Libraries.
Grading
A final numerical grade will be computed basic on the following rubric:
| 10% | Homework 1 |
| 10% | Homework 2 |
| 10% | Homework 3 |
| 10% | Homework 4 |
| 30% | Midterm |
| 30% | Final project |
Schedule
Below is an updated list of discussion topics along with any documents that were distributed, notes, or relevant code.| Date | Topics | Materials |
|---|---|---|
| Sep 8 | Probability and statistics review | Notes Efron & Hastie: Ch 1-5 Gentle: Ch 1 |
| Sep 15 | Root finding, optimization | Notes Gentle: Ch 6.1-6.2 |
| Sep 22 | BFGS Numerical linear algebra: Operation counts, norms, and conditioning |
Notes Gentle: 6.2 Steven Johnson Notes Gentle: Ch 2, 3, 5.1 |
| Sep 29 | Numerical linear algebra: LU, Cholesky, least squares, QR |
Notes Gentle: Ch 5.2-5.3, 5.6 |
| Oct 6 | Singular value decomposition Principal component analysis |
Notes Gentle: Ch 1.2, 16.3 |
| Oct 13 | Gaussian processes |
Notes Rasmussen and Williams |
| Oct 20 | Midterm (In class) | |
| Oct 27 | Function interpolation, approximation |
Notes Gentle: Ch 4.1-4.3 |
| Nov 3 | Numerical integration |
Notes Gentle: Ch 4.6 |
| Nov 10 | Monte Carlo integration Inverse CDF method |
Notes Gentle: Ch 4.7, 7.1-7.2 |
| Nov 17 |
Stochastic processes Markov Chain Monte Carlo |
Notes Gentle: Ch 7.3 Understanding the Metropolis-Hastings Algorithm |
| Nov 24 |
Bayes + MCMC, Gibbs sampling, variance reduction Kernel density estimation |
Notes Gentle: Ch 4.7, 7.2-7.4, 11.5, 15.3-15.4 Efron & Hastie: Ch 13 Wasserman AoS: Ch 20.3 |
| Dec 1 |
Kernel density estimation Jackknife, bootstrap |
Notes Gentle: Ch 12, 13 Wasserman AoS: Ch 20.3 |
| Dec 8 | Project presentations |