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140.732.71
Statistical Theory II

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Course Status
Cancelled

Course Status

Cancelled

Location

Internet

Term

2nd Term

Department

Biostatistics

Credit(s)

4

Academic Year

2022 - 2023

Instruction Method

Synchronous Online

Auditors Allowed

No

Available to Undergraduate

No

Grading Restriction

Letter Grade or Pass/Fail

Course Instructor(s)

Contact Name

Frequency Schedule

One Year Only

Resources

Prerequisite

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:
- 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 small-sample properties to those of the maximum likelihood estimator

Methods of Assessment

This course is evaluated as follows:

- 25% Homework
- 75% Final Exam

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)