140.732.41
Statistical Theory II

Location
Internet
Term
2nd Term
Department
Biostatistics
Credit(s)
4
Academic Year
2023 - 2024
Instruction Method
Synchronous Online
Class Time(s)
M, W, 10:30 - 11:50am
Auditors Allowed
No
Available to Undergraduate
No
Grading Restriction
Letter Grade or Pass/Fail
Course Instructor(s)
Constantine Frangakis
Contact Name
Constantine Frangakis
Frequency Schedule
Every Year
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 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. Examine foundational concepts of statistical inference (units, population, design and sample, estimator and variance, sufficiency, information, Bayes and maximum likelihood estimator)
  2. Translate the design and estimation goal of a scientific study into a theoretically appropriate statistical problem
  3. Identify appropriate parametric models for the population under study
  4. Calculate the likelihood of the study’s data based on the design and model assumptions
  5. Find the minimal sufficient statistics and the maximum likelihood estimator for the quantity of interest
  6. 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
Consent Contact
cfranga1@jhu.edu
Special Comments

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