Instructor: Dr. Surajit Ray
Department of Mathematics and Statistics
MCS 222, 111 Cummington Street, Boston, MA 02215
Phone: (617) 353-5209, Fax: (617) 353-8100
Class Time: Tue,Thu 12:30-2:00 PM
Class Room: MCS B31
Office Hours: TBD

Blackboard Login ( BU Students)

Course Description:
This is the second course in the MA781-782 sequence. This sequence is designed to provide a solid foundation in mathematical statistics. In MA782, we will build on the material we covered in MA781, and will introduce fundamental approaches to hypothesis testing procedures, including likelihood ratio based techniques and optimal classification based on Neyman-Pearson Lemma. We will also discuss computational approaches to hypothesis testing, and develop Bayesian approaches for hypothesis testing.

The prerequisite for this course is MA781, and the course assumes strong background in elementary probability theory (MA581 or equivalent).



Homework will be assigned regularly during the course and a due date will be announced. No late homework will be accepted. To receive full credit for your solutions of the homework problems, all work must be shown.

There will be one midterm and one find. All exams are required. Each test will be based on a combination of in-class and take-home exams. A research project and in-class presentation will constitute a part of the final exam. Exact dates of the exams will be announced later.

Grade Distribution:
Homework: 30%, MIDTERM: 35%, FINAL: 35%

Week-by-Week Syllabus:

Week Topic
1 Introduction to Hypothesis Testing
2 Constructing Tests: Likelihood Ratio Tests (LRT)
3 Examples of LRT- Univariate and Multivariate
4 Likelihood ratio tests in the presence of nuisance parameters
5 Construction of tests using asymptotic distribution of LRT
6 Optimal Tests- Risk Function, Decision Rule
7 Neyman Pearson Lemma
8 Uniformly Most Powerful Tests, Examples of Monotone likelihood ratio
9 Karlin-Rubin Theorem, Uniformly Most Powerful Unbiased Tests
10 Confidence Interval Procedure for hypothesis tests
11Bootstrap based hypothesis tests and Confidence Interval Procedures, Permutation Tests.
12 Bootstrap based inference in regression
13 Bayesian Hypothesis Testing
14 Review

Please Note:
You are responsible for knowing, and abiding by, the provisions of the GRS Academic Conduct Code, which is posted at
Violations of the code are punishable by sanctions including expulsion from the University.