140.732.41
Statistical Theory II
 Location:
 Internet
 Term:
 2nd term
 Department:
 Biostatistics
 Credits:
 4 credits
 Academic Year:
 2022  2023
 Instruction Method:
 Synchronous Online
 Class Times:

 M W, 10:30  11:50am
 Auditors Allowed:
 No
 Undergrads Allowed:
 No
 Grading Restriction:
 Letter Grade or Pass/Fail
 Course Instructor:
 Contact:
 Constantine Frangakis
 Resources:
 Prerequisite:
Linear algebra; matrix algebra; real analysis; calculus; 140.731
 Description:

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 CramerRao variance bounds in parametric models; introduces empirical Bayes (shrinkage) estimators and compares to maximum likelihood in smallsample problems.
 Learning Objectives:

Upon successfully completing this course, students will be able to:
 Translate the design and estimation goal of a scientific study into a theoretically appropriate statistical framework
 Identify appropriate parametric models for the population under study
 Calculate the likelihood of the study’s data based on the design and model assumptions
 Find the minimal sufficient statistics and the maximum likelihood estimator for the quantity of interest
 Find Bayes/empirical Bayes estimators for a loss function and compare smallsample 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/online section of a course that is also offered inperson. Students will need to commit to the modality for which they register. One 1hour lab per week (time TBA).