The Pennsylvania State University, Spring 2021 Stat 415-001, Hyebin Song
STAT/MATH 415, Section 001: Introduction to Mathematical Statistics
This course serves as an introduction to mathematical statistics, covering the fundamentals of statistical inference. In this course, students will learn the mathematical foundations of statistical inference and how to perform statistical inference procedures to solve practical problems. Topics include, but are not limited to, point estimation, likelihood theory, sufficiency, interval estimation, hypothesis testing, linear models, analysis of variance and Bayesian estimation.
Contact Information
Hyebin Song, Instructor
- Email: hps5320@psu.edu
- Office Hours: Tuesday , Friday 10:00 AM - 11:00 AM, Friday 4:00 - 5:00 PM
Daniel Fariss, Teaching Assistant/ Grader
- Email: dbf5148@psu.edu
Course Information
Link to Syllabus: syllabus
Textbook
The course materials are largely based on Probability and Statistical Inference (10th Edition) by Robert V. Hogg, Elliot Tanis, and Dale Zimmerman.
Lecture Notes
- Probability Review
- Introduction
- Point Estimation
- Interval Estimation
- Hypothesis Testing
- Linear Models
- Analysis of Categorical Data
- Bayesian Estimation
Course Schedule
Please spend at least 1 hour after each lecture reviewing the concepts, looking at the proofs, making sure you can do the class examples by yourself. I strongly encourage you to skim the reading before each class to familiarize yourself with the concepts and statements that will be covered during each lecture.
Here are some studying tips for this class: studying tips
| Column1 | Dates | Topic | Reading | Homework | In-class Quiz |
|---|---|---|---|---|---|
| Week 1 | 1/20 | Course Introduction | |||
| 1/22 | Introduction to Statistical Inference | ||||
| Week 2 | 1/25, 27 | Review on Probability | |||
| 1/29 | Point Estimation (Introduction) | ||||
| Week 3 | 2/1, 3, 5 | Point Estimation (Method of Moments, Maximum Likelihood Estimators) | Section 6.4, 6.6 | #1 (due 2/1) | #1 (2/3) |
| Week 4 | 2/8, 10, 12 | Point Estimation (Properties of Point Estimators, Sufficiency, Rao-Blackwellization) | Section 6.6-6.7 | ||
| Week 5 | 2/15, 17, 19 | Interval Estimation (Introduction to interval estimation, confidence interval for one mean) | Section 7.1-7.2 | #2 (due 2/15) | #2 (2/17) |
| Week 6 | 2/22 | Interval Estimation (confidence interval for two means) | Section 7.3 | ||
| 2/24 | Review | ||||
| 2/26 | Exam 1 | ||||
| Week 7 | 3/1, 3 | Interval Estimation (confidence intervals for two means, proportions) | Section 7.3-7.4 | ||
| 3/5 | Hypothesis Testing (Introduction to hypothesis testing) | Section 8.1 | |||
| Week 8 | 3/8,10,12 | Hypothesis Testing (Introduction to hypothesis testing, duality between CI and tests, test for means) | Section 8.1-8.2, | ||
| Week 9 | 3/15,17,19 | Hypothesis Testing (test for two means, proportions, variances) | Section 8.2-8.4 | #3 (due 3/15) | #3 (due 3/17) |
| Week 10 | 3/22, 24, 26 | Hypothesis Testing (test for variances,statistical power of tests) | Section 8.3, 8.6 | #4 (due 3/22) | #4 (3/24) |
| Week 11 | 3/29 | Review | |||
| 3/31 | Exam 2 | ||||
| 4/2 | Hypothesis Testing (UMP, Neyman-Pearson Lemma) | Section 8.7 | |||
| Week 12 | 4/5 | Hypothesis Testing (LRT) | Section 8.8 | ||
| 4/9 | Linear Models | Section 6.5 | |||
| 4/7 | Wellness Day (No Classes) | ||||
| Week 13 | 4/12,14,16 | Linear Models | Section 7.6,9.6 | #5 (due 4/12) | #5 (4/14) |
| Week 14 | 4/19, 21, 23 | Chi-square tests | Section 9.1-9.2 | ||
| Week 15 | 4/26, 28 | Bayesian Statistics | Section 6.8 | # 6 (due 4/26) | #6 (4/28) |
| 4/30, | Review | ||||
| Week 16 | Final Exam |