Biostatistics 602: Main Page

Objective

In Winter 2013, Biostatistics 602 aims to provide students with a deep understanding of key concepts of statistical inference. Statistical inference methods instruct us how to use data to address substantive questions. In this course, we will study statistical point and interval estimation, hypothesis testing and basic asymptotic theory. We will primarily focus on classical frequentist’s view of statistical inference, and will briefly touch some basics of Bayesian inference.

Prerequisites

Biostatistics 601 or equivalent knowledge of basic calculus and matrix algebra. In particular, students are expected to have knowledge of the following subjects: random variables, independence, characteristic and moment generating functions, common discrete and continuous distributions, expectations and higher order moments, random sampling. (approximately chapters 1-5.5 of Casella and Berger.)

Textbook

• Statistical Inference, 2nd Edition, by Casella and Berger. (Required)
• Statistical Inference, by Garthwaite, Jolliffe and Jones. (Recommended)
• All of Statistics: A Concise Course in Statistical Inference, by Wasserman (Optional)
• Mathematical Statistics: Basics Ideas and Selected Topics, by Bickel and Doksum. (Optional)

Class Schedule

Classes are scheduled for Tuesday and Thursdays, 1:00 - 3:00pm at USB 2260

Grading

Homework assignments will be given out at approximately every 1.5 weeks. Late submission will not be accepted unless the student obtains permission from the instructor. You are allowed to discuss homework problems with fellow students; however, you must write up the assignment on your own. Plagiarism will not be tolerated.

• Homework: 20%
• Midterm: 35%
• Final: 45%

Topics

We will be primarily focusing on Chapter 6-10 of Casella and Berger. In particular, we will cover the following topics:

Data Reduction (Week 1-4)

• Sufficiency principle (6.2)
  • Sufficient statistics
  • Complete statistics
  • Ancillary statistics
  • The exponential family of distributions
• Likelihood principle (6.3)

Point Estimation (Week 5-10)

• Estimator construction (7.2)
  • Moment estimator
  • Maximum likelihood estimator
  • Bayes estimator, and computational issues
• Evaluation of estimators (7.3)
  • Unbiasedness
  • Sufficiency
• Asymptotic properties (10.1)
  • Consistency
  • Efficiency

Hypothesis Testing (Week 11-13)

• Tests construction (8.2)
  • Null and alternative hypotheses
  • Composite hypotheses
  • Likelihood ratio test
• Evaluation of tests (8.3):
  • Neyman-Pearson lemma
• Asymptotic properties (10.3)

Interval Estimation (Week 14-16)

• Interval construction (9.2)
• Evaluation of intervals (9.3)
• Asymptotic properties (10.4)

Class Notes

• Lecture 1 : Principles of Data Reduction & Sufficient Statistics -- (Handout PDF) (Presentation PDF) (updated 01/12 18:44)
• Lecture 2 : Factorization Theorem -- (Handout PDF) (Presentation PDF) (updated 01/21 16:44)
• Lecture 3 : Minimal Sufficient Statistics -- (Handout PDF) (Presentation PDF) (updated 01/21 16:44)
• Lecture 4 : Ancillary Statistics -- (Handout PDF) (Presentation PDF) (updated 01/23 16:51)
• Lecture 5 : Complete Statistics -- (Handout PDF) (Presentation PDF) (updated 01/28 20:22)
• Lecture 6 : Basu's Theorem -- (Handout PDF) (Presentation PDF) (updated 01/31 00:48)
• Lecture 7 : Exponential Family -- (Handout PDF) (Presentation PDF) (updated 02/04 15:53)
• Lecture 8 : Summary of Data Reduction -- (Handout PDF) (Presentation PDF) (updated 02/04 15:53)
• Lecture 9 : Likelihood Function & Point Estimation -- (Handout PDF) (Presentation PDF) (updated 02/13 17:23)
• Lecture 10 : Maximum Likelihood Estimator -- (Handout PDF) (Presentation PDF) (updated 02/13 17:23)
• Lecture 11 : Evaluation of Point Estimators -- (Handout PDF) (Presentation PDF) (updated 02/28 07:49)
• Lecture 12 : Cramer-Rao Inequality -- (Handout PDF) (Presentation PDF) (updated 02/25 16:40)
• Lecture 13 : Rao-Blackwell Theorem -- (Handout PDF) (Presentation PDF) (updated 02/25 16:40)
• Lecture 14 : Finding the Best Unbiased Estimator -- (Handout PDF) (Presentation PDF) (updated 02/28 00:40)
• Lecture 15 : Bayes Estimator -- (Handout PDF) (Presentation PDF) (updated 03/13 18:28)
• Lecture 16 : Bayes Risk / Consistency -- (Handout PDF) (Presentation PDF) (updated 03/18 01:05)
• Lecture 17 : Asymptotic Evaluation -- (Handout PDF) (Presentation PDF) (updated 03/18 01:05)
• Lecture 18 : Hypothesis Testing -- (Handout PDF) (Presentation PDF) (updated 04/10 14:41)
• Lecture 19 : Likelihood Ratio Tests -- (Handout PDF) (Presentation PDF) (updated 04/10 14:41)
• Lecture 20 : Uniformly Most Powerful Tests -- (Handout PDF) (Presentation PDF) (updated 04/14 17:21)
• Lecture 21 : Asymptotics of LRT / Wald Tests -- (Handout PDF) (Presentation PDF) (updated 04/10 14:41)
• Lecture 22 : p-Values -- (Handout PDF) (Presentation PDF) (updated 04/14 17:21)
• Lecture 23 : Interval Estimation -- (Handout PDF) (Presentation PDF) (updated 04/14 17:21)
• Lecture 24 : E-M Algorithm -- (Handout PDF) (Presentation PDF) (updated 04/14 17:21)
• Lecture 25 : Bayesian Test & Interval-- (Handout PDF) (Presentation PDF) (updated 04/18 01:08)
• Lecture 26 : Review -- (Handout PDF) (Presentation PDF) (updated 04/24 04:26)

Exams & Important Dates

• Midterm : Thursday February 21, 2013, in class
• Final : Thursday April 25, 2013, 4:00-6:00pm
• There will be no class on Thursday April 4th (instructor out of town)

Office Hours

• Monday 4:00PM-5:00PM
• Thursday 4:30PM-5:00PM

Standards of Academic Conduct

• See slides of lecture 01 for details of honor code.
• The following is an extract from the School of Public Health's Student Code of Conduct [1]:

Student academic misconduct includes behavior involving plagiarism, cheating, fabrication, falsification of records or official documents, intentional misuse of equipment or materials, and aiding and abetting the perpetration of such acts. The preparation of reports, papers, and examinations, assigned on an individual basis, must represent each student’s own effort. Reference sources should be indicated clearly. The use of assistance from other students or aids of any kind during a written examination, except when the use of books or notes has been approved by an instructor, is a violation of the standard of academic conduct.

In the context of this course, any work you hand-in should be your own.

Course History

• Min Zhang and Susan Murray taught it in several academic years previously. Most of the class notes here should be credited for them. Hyun Min Kang reorganized class materials into slides.