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Statistical Theory II


2nd term
4 credits
Academic Year:
2022 - 2023
Instruction Method:
Synchronous Online
Auditors Allowed:
Undergrads Allowed:
Grading Restriction:
Letter Grade or Pass/Fail
Course Instructor:
Constantine Frangakis
Frequency Schedule:
One Year Only

Linear algebra; matrix algebra; real analysis; calculus; 140.731


Introduces modern statistical theory; sets principles of inference based on decision theory and likelihood (evidence) theory; derives the likelihood function based on design and model assumptions; derives the complete class theorem between Bayes and admissible estimators; derives minimal sufficient statistics as a necessary and sufficient reduction of data for accurate inference in parametric models; derives the minimal sufficient statistics in exponential families; introduces maximum likelihood and unbiased estimators; defines information and derives the Cramer-Rao variance bounds in parametric models; introduces empirical Bayes (shrinkage) estimators and compares to maximum likelihood in small-sample problems.

Learning Objectives:

Upon successfully completing this course, students will be able to:

  1. Translate the design and estimation goal of a scientific study into a theoretically appropriate statistical framework
  2. Identify appropriate parametric models for the population under study
  3. Calculate the likelihood of the study’s data based on the design and model assumptions
  4. Find the minimal sufficient statistics and the maximum likelihood estimator for the quantity of interest
  5. Find Bayes/empirical Bayes estimators for a loss function and compare small-sample properties to those of the maximum likelihood estimator
Methods of Assessment:

This course is evaluated as follows:

  • 25% Homework
  • 75% Final Exam

Instructor Consent:

Consent required for some students

Consent Note:

Consent required for any students who are not in the Biostatistics PhD program

For consent, contact:

Special Comments:

Please note: This is the virtual section of a course that is also offered onsite. Students will need to commit to the modality for which they register. One 1-hour lab per week (time TBA)