Course syllabus
MVE155 / MSG200 Statistical inference (7.5 hp) 2024
Course is offered by the department of Mathematical Sciences
Exams
The June 5 exam with the solutions is here.
The March 12 exam is here, and with solutions here.
Teacher
Lectures: Tony Johansson
Exercises: Tony Johansson
Course purpose
"Statistical Inference" is a second course in mathematical statistics suitable for students with different backgrounds. A main prerequisite is an introductory course in probability and statistics. The course gives a deeper understanding of some traditional topics in mathematical statistics such as methods based on likelihood, aspects of experimental design, non-parametric testing, analysis of variance, introduction to Bayesian inference, chi-squared tests, multiple regression.
Sample exam & Distribution tables
A sample exam is here.
For the final exam, tables of distribution values will be provided for you. The tables can be found here. Do not bring this document with you to the exam.
Topics not included this year
I move through topics at a slower pace than previous lecturers in this course, and have decided to scrap some topics. These are:
- Bayesian hypothesis tests (the basics of Bayesian statistics are still covered)
- McNemar's test
- 2-way ANOVA and Friedman's test
Lecture notes
Please note that these notes may contain mistakes. The correspondence between lectures and notes is not one-to-one (the main difference is some examples are tweaked).
- Chapter 1, Probability
- Chapter 2, Sample Mean and Variance
- Chapter 3, Method of Moments and Maximum Likelihood Estimates
Supplemental material
Under this header I will post any supplemental material that I write. Please let me know if you find any errors.
- The distribution of the T statistic. Not mandatory, but recommended for those who wish to see proper definitions and proofs.
Preliminary schedule
The linked notes are from last year, when the course was taught by Aila Särkkä. This year's content will be similar but not identical.
|
Mon 15/1, 13:15-15:00, Vasa B |
Lecture: Introduction; Parametric models (notes, Chapter 1) |
Chapter 1 |
|
Tue 16/1, 13.15-15.00, KC |
Lecture: Parametric models | Chapter 1 |
|
Wed 17/1, 13.15-15.00, HC3 |
Exercises | Chapter 1 |
|
Fri 19/1, 13.15-15.00, KA |
Lecture: Random sampling (notes, Chapter 2) |
Chapter 2 |
| Mon 22/1, 13.15-15.00, KC | Exercises | Chapter 2 |
| Tue 23/1, 13.15-15.00, KC |
Lecture: Random sampling |
Chapter 2 |
| Wed 24/1, 13.15-15.00, KA | Exercises (R code: Problem 7, Problem 10) | Chapter 2 |
| Fri 26/1, 13.15-15.00, KA | Lecture: Parameter estimation (notes, Chapter 3) | Chapter 3 |
| Mon 29/1, 13.15-15.00, KA | Exercises | Chapter 3 |
| Tue 30/1, 13.15-15.00, KC |
Lecture: Hypothesis testing (notes, Chapter 4) |
Chapter 4 |
| Wed 31/1, 13.15-15.00, KA | Exercises | Chapter 4 |
| Fri 2/2, 13.15-15.00, KA | Lecture: Hypothesis testing | Chapter 4 |
| Mon 5/2, 13.15-15.00, Pascal | Exercises | Chapter 4 |
| Fri 9/2, 13.15-15.00, KB | Lecture: Bayesian inference (notes, Chapter 5) | Chapter 5 |
| Mon 12/2, 13.15-15.00, Pascal |
Exercises |
Chapter 5 |
| Tue 13/2, 13.15-15.00, Pascal | Lecture: Summarising data (notes, Chapter 6) |
Chapter 6 |
| Wed 14/2, 13.15-15.00, Pascal | Exercises (R code) | Chapter 6 |
| Fri 16/2, 13.15-15.00, KA | Lecture: Summarising data, Comparing two samples (notes, Chapter 7) | Chapter 7 |
| Mon 19/2, 13.15-15.00, Pascal | Exercises | Chapter 7 |
| Tue 20/2, 13.15-15.00, Pascal | Lecture: Comparing two samples, Analysis of variance (notes, Chapter 8) | Chapter 8 |
| Wed 21/2, 13.15-15.00, Pascal | Exercises | Chapter 8 |
| Fri 23/2, 13.15-15.00, KA |
Lecture: Analysis of variance |
Chapter 8 |
| Mon 26/2, 13.15-15.00, Pascal | Exercises | Chapter 8 |
| Tue 27/2, 13.15-15.00, Pascal |
Lecture: Categorical data analysis (notes, Chapter 9) |
Chapter 9 |
| Wed 28/2, 13.15-15.00, Pascal |
Exercises |
Chapter 9 |
| Fri 1/3, 13.15-15.00, KA | Lecture: Multiple regression (notes, Chapter 10) | Chapter 9 |
| Mon 4/3, 13.15-15.00, Pascal |
Exercises |
Chapter 9 |
| Tue 5/3, 13.15-15.00, Pascal | Lecture: Multiple regression | Chapter 10 |
| Wed 6/3, 13.15-15.00, Pascal | Exercises | Chapter 10 |
| Fri 8/3, 13.15-15.00, KA |
Questions and answers session |
Chapters 1-10 |
| Tue 12/3, 14:00-18:00 | Exam (register before 25.02.2024) |
Course literature
The course is build around the compendium - click and download. The compendium may undergo minor updates during the course.
Recommended additional textbook: Mathematical statistics and data analysis, 3rd edition (2nd edition is also OK), by John Rice (Cremona).
Learning objectives and syllabus
Learning objectives:
- summarize multiple sample data in a meaningful and informative way,
- recognize several basic types of statistical problems corresponding to various sampling designs,
- estimate relevant parameters and perform appropriate statistical tests for multiple sample data sets.
Link to the syllabus on Studieportalen: Study plan
Examination form
The grading of the course is based on a written examination. Preparing for the final exam, check Section 12.1 of the Compendium to see the list of the topics that may be addressed by the final exam questions.
You are allowed to use a Chalmers allowed calculator and your own course summary (four A4 pages) during the final exam. Importantly, this summary should not be produced by copying and pasting of different parts of the compendium.
Several old exams with solutions are given in the module "Old exams". Aila's old exams of the course Experimental design: Exam 1 and solutions, Exam 2.
Maximal number of points for the final exam is 30. Passing limits
- Chalmers students: 12 points for '3', 18 points for '4', 24 points for '5'
- GU students: 12 points for 'G', 20 points for 'VG'