625.726.81 - Theory of Statistics II
Description
This course is a continuation of 626.725. The course further deepens your understanding of mathematical foundations of statistical methods through an analysis of standard and contemporary methods. This course starts with decision theory, and then continues with density estimation, nonparametric regression methods (kernels, local polynomials), nonparametric classification (density based, kernels, trees), high dimensional methods (lasso, ridge regression), statistical analysis of graphical models, minimax theory, causality, dimensionality reduction, mixture models, boosting, conformal methods, M-estimation, U-statistics, empirical processes and semiparametric models, use of concentration inequalities, bias and variance, the central limit theorem, likelihood and sufficiency, point estimation (MLE, method of moments and Bayes), asymptotic theory, confidence intervals, bootstrap methods, high dimensional statistics, and model selection.
Instructors
Thomas Woolf
Burhan Sadiq
Course Structure
The course materials are divided into modules which can be accessed by clicking Modules on the course menu. A module will have several sections including the overview, readings, lectures, group activity, and assignments. You are encouraged to preview all sections of the module before starting. Most modules run for a period of seven (7) days, exceptions are noted in the Course Outline. You should regularly check the Calendar and Announcements for assignment due dates.
Course Topics
Statistical Decision Theory
Linear and Logistic Regression / Density Estimation / M-Estimators
Multivariate Models / U-statistics and Optimal Estimators
Inference about Independence
Causal Inference
Statistical Analysis of Graphical Models
Mixture Models / Minimax Theory / Dimensionality Reduduction
Log-Linear Models
Nonparametric Curve Estimation
Smoothing / High Dimensional Models
Classification / Conformal Methods
Kernels / Empirical Processes
Stochastic Process / Semiparametric Models
Simulation Methods
Course Goals
To deepen your understanding of the mathematical foundations of statistics
Textbooks
- Cassella, G. and Berger, R. (2002). Statistical Inference. (2nd edition) Wadsworth, Inc., Belmont, CA.
- Wasserman, L. (2010). All of Statistics. Springer Nature, Switzerland.
- Larsen, R.J. and Marx M.L. (2018) An Introduction to Mathematical Statistics and Its Applications (6th edition), Prentice Hall
- Optional Reference: Rice, J.A. (2007) Mathematical Statistics and Data Analysis (3rd edition) Duxbury, Thomson Brooks/Cole, Belmont CA)
Student Coursework Requirements
Weekly group problem sets (30% of final grade)
- Group problem sets begin from Module 1 and will be completed collaboratively on Overleaf.
- You can create a free Overleaf account here: https://www.overleaf.com/
- Each week, you will be randomly placed into a Canvas group.
- See here on how to access your group page: https://vimeo.com/58553577
- Your Canvas group page will contain the Overleaf link exclusive to your group for collaborative completion
- We strongly recommend that each group meets online to collaboratively complete the group exercise
- Each part of problem is answered (20%)
- The course content is correctly applied to arrive at the solutions (40%)
- Intermediate derivations and calculations are provided (20%)
- Solution is technically correct and is clearly indicated (20%)
100–90%—All parts of problem are addressed; The course material is correctly applied to arrive at the solution; All intermediate derivations and calculations are provided; Solution is technically correct and is clearly indicated.
89–80%—All parts of problem are addressed; The course material is correctly applied; Some intermediate derivations and calculations are provided; Solution is technically correct and is indicated.
79–70%—Most parts of problem are addressed; Some course material is not correctly applied; Few intermediate derivations and calculations are provided; Some solutions are not technically correct but are indicated.
<70%—Some parts of the problem are addressed; Some course material is not correctly applied; Intermediate derivations and calculations are not provided; Some answers are incorrect or missing.
Two cumulative quizzes (30% of final grade)
- Module 7 (covering Modules 1-6)
- Module 12 (covering Modules 7-11)
Term project with interim deliverables throughout semester (40% of final grade)
- Full introduction in module 1.
- Project concept: Four running data examples and project choices based on the same data: Census, Cars, Housing, heart-disease, and NHANES
- Module 2 - Students submit preferences for data sets to work on (5%)
- Module 6 - Pseudo code and outline (5%)
- Module 9 – Bibliography (10%)
- Module 10 - Full Methods (20%)
- Module 13 – Report & Code (60%) [includes a short Powerpoint to be posted for others to comment on]
- Module 14 - Comment on Projects
Grading Policy
Here is a grading curve for the overall course score:
| Score Range | Letter Grade |
|---|---|
| 100-97 | = A+ |
| 96-93 | = A |
| 92-90 | = A− |
| 89-87 | = B+ |
| 86-83 | = B |
| 82-80 | = B− |
| 79-77 | = C+ |
| 76-73 | = C |
| 72-70 | = C− |
| 69-67 | = D+ |
| 66-63 | = D |
| <63 | = F |
It is possible that the grading curve for the overall course score will be relaxed, but it won’t be made tougher.
Academic Policies
Deadlines for Adding, Dropping and Withdrawing from Courses
Students may add a course up to one week after the start of the term for that particular course. Students may drop courses according to the drop deadlines outlined in the EP academic calendar (https://ep.jhu.edu/student-services/academic-calendar/). Between the 6th week of the class and prior to the final withdrawal deadline, a student may withdraw from a course with a W on their academic record. A record of the course will remain on the academic record with a W appearing in the grade column to indicate that the student registered and withdrew from the course.
Academic Misconduct Policy
All students are required to read, know, and comply with the Johns Hopkins University Krieger School of Arts and Sciences (KSAS) / Whiting School of Engineering (WSE) Procedures for Handling Allegations of Misconduct by Full-Time and Part-Time Graduate Students.
This policy prohibits academic misconduct, including but not limited to the following: cheating or facilitating cheating; plagiarism; reuse of assignments; unauthorized collaboration; alteration of graded assignments; and unfair competition. Course materials (old assignments, texts, or examinations, etc.) should not be shared unless authorized by the course instructor. Any questions related to this policy should be directed to EP’s academic integrity officer at ep-academic-integrity@jhu.edu.
Students with Disabilities - Accommodations and Accessibility
Johns Hopkins University values diversity and inclusion. We are committed to providing welcoming, equitable, and accessible educational experiences for all students. Students with disabilities (including those with psychological conditions, medical conditions and temporary disabilities) can request accommodations for this course by providing an Accommodation Letter issued by Student Disability Services (SDS). Please request accommodations for this course as early as possible to provide time for effective communication and arrangements.
For further information or to start the process of requesting accommodations, please contact Student Disability Services at Engineering for Professionals, ep-disability-svcs@jhu.edu.
Student Conduct Code
The fundamental purpose of the JHU regulation of student conduct is to promote and to protect the health, safety, welfare, property, and rights of all members of the University community as well as to promote the orderly operation of the University and to safeguard its property and facilities. As members of the University community, students accept certain responsibilities which support the educational mission and create an environment in which all students are afforded the same opportunity to succeed academically.
For a full description of the code please visit the following website: https://studentaffairs.jhu.edu/policies-guidelines/student-code/
Classroom Climate
JHU is committed to creating a classroom environment that values the diversity of experiences and perspectives that all students bring. Everyone has the right to be treated with dignity and respect. Fostering an inclusive climate is important. Research and experience show that students who interact with peers who are different from themselves learn new things and experience tangible educational outcomes. At no time in this learning process should someone be singled out or treated unequally on the basis of any seen or unseen part of their identity.
If you have concerns in this course about harassment, discrimination, or any unequal treatment, or if you seek accommodations or resources, please reach out to the course instructor directly. Reporting will never impact your course grade. You may also share concerns with your program chair, the Assistant Dean for Diversity and Inclusion, or the Office of Institutional Equity. In handling reports, people will protect your privacy as much as possible, but faculty and staff are required to officially report information for some cases (e.g. sexual harassment).
Course Auditing
When a student enrolls in an EP course with “audit” status, the student must reach an understanding with the instructor as to what is required to earn the “audit.” If the student does not meet those expectations, the instructor must notify the EP Registration Team [EP-Registration@exchange.johnshopkins.edu] in order for the student to be retroactively dropped or withdrawn from the course (depending on when the "audit" was requested and in accordance with EP registration deadlines). All lecture content will remain accessible to auditing students, but access to all other course material is left to the discretion of the instructor.