Course syllabus
MVE155 / MSG200 Statistical inference (7.5 hp)
Course is offered by the department of Mathematical Sciences
Teachers
Lectures: Aila Särkkä (aila@chalmers.se)
Exercises/Lectures: Adrien Malacan (malacan@chalmers.se)
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. There is also a small project included in the course where the theory learned during the course will be applied.
Preliminary schedule
The notes below will be updated during the course.
|
Tue 20/1, 13:15-15:00 |
Chapter 1 | |
|
Tue 20/1, 15:15-17:00 |
Exercises: Introduction to R (ExerciseSheetR.pdf) |
|
|
Thu 22/1, 13:15-15:00 |
Lecture: Parametric models | Chapter 1 |
|
Fri 23/1, 13:15-15:00 |
Chapter 2 |
|
| Tue 27/1, 13:15-15:00 | Lecture: Random sampling | Chapter 2 |
| Tue 27/1, 15:15-17:00 | Exercises | Chapter 1 (problems 1, 2, 3, 4, 5, 7) |
| Thu 29/1, 13:15-15:00 | Chapter 3 | |
| Fri 30/1, 13:15-15:00 | Exercises | Chapter 2 (problems 2, 3, 4, 9, 10) |
| Tue 3/2, 13:15-15:15 | Lecture (Adrien): Hypothesis testing (slides) | Chapter 4 |
| Tue 3/2, 15:15-17:15 | Exercises | Chapter 3 (problems 4, 6, 8) |
| Thu 5/2, 13:15-15:00 |
Lecture (Adrien): Hypothesis testing |
Chapter 4 |
| Fri, 6/2 13:15-15:00 | Chapter 5 | |
| Tue 10/2, 13:15-15:00 |
Lecture (Adrien): Bayesian inference |
Chapter 5 |
| Tue 10/2, 15:15-17:00 |
Exercises |
Chapter 4 (problems 2, 3, 7, 13) |
| Thu 12/2, 13:15-15:00 | Lecture: Summarising data (slides) | Chapter 6 |
| Fri 13/2, 13:15-15:00 |
Exercises |
Chapter 5 (problems 1, 3, 4, 8, 9) |
| Thu 19/2, 13:15-15:00 |
Lecture: Summarising data |
Chapter 6 |
| Fri 20/2, 13:15-15:00 | Lecture: Comparing two samples (slides, notes) |
Chapter 7 |
| Tue 24/2, 13:15-15:00 |
Lecture: Comparing two samples |
Chapter 7 |
| Tue 24/2, 15:15-17:00 | Exercises |
Chapter 6 (Problems 4,5,8 and 10) |
| Thu 26/2, 13:15-15:00 | Lecture: Analysis of variance (slides, notes) | Chapter 8 |
| Fri 27/2, 13:15-15:00 |
Exercises |
Chapter 7 (Problems 4,5,9) |
| Tue 3/3, 13:15-15:00 | Lecture: Analysis of variance (examples of ANOVA data) | Chapter 8 |
| Tue 3/3, 15:15-17:00 |
Exercises |
Chapter 8 (Problems 1,2,6,8) |
| Thu 5/3, 13:15-15:00 | Chapter 9 | |
| Fri 6/3, 13:15-15:00 | Lecture (Adrien): Multiple regression (slides) | Chapter 10 |
| Tue 10/3, 13:15-15:00 |
Exercises |
Chapter 9 (Problems 1,7,10,11,14) |
| Tue 10/3, 15:15-17:00 | Lecture (Adrien): Multiple regression | Chapter 10 |
| Thu 12/3, 13:15-15:00 | Exercises | Chapter 10 (problems 2,5,7,10 + R output) |
| Fri 13/3, 13:15-15:00 | Guest lecture by Magnus Pettersson, Statistikkonsulterna Väst AB | |
| Fri 20/3, 14:00-18:00 | Exam |
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 at Chalmers.
Use of AI tools
During your studies, you are free to use AI tools to support your learning. During the exam, the use of any kind of AI tools is not allowed.
Examination form
The grading of the course is based on a written examination and a compulsory project.
Project
The purpose of the project is that in groups of 3 -4 people, you plan a study and collect data that will be analyzed using statistical methods you have learned in the course and R. The projects are presented orally in the end of the course. You can come up with a project related to your main field of study or choose something that you find interesting in general and that sounds fun. To give you some ideas, one may be interested in studying e.g.
- Relationship between shoe size and height
- Whether the amount of coffee we drink varies in age
- Whether trams/busses run according to their schedule.
- If the quantity of water that one drinks in a day is normally distributed, etc.
A minimum requirement for the project is that you generate data, i.e., collect your own real-world data (surveys, measurements or observations), describe the data using appropriate measures and plots, and perform at least two statistical tests. Any statistical method covered in the course (regression, t-test, ANOVA, chi square tests,…) can be used. It may not always be possible to guarantee significant results, but you should at least have a research hypothesis that could possibly be true.
Before you start your project, please, check your project idea with Aila (aila@chalmers.se) or Adrien (malacan@chalmers.se), preferably by February 13th.
Examination of the project will be based on a 15–20 minutes presentation followed by a short discussion of around 10 minutes. The presentation should include:
- Description of the research question and data
- Your null and research hypotheses
- Description of the experimental design and the statistical methods used
- Presentation of the results of your analysis
- A final discussion, where you discuss the assumptions, you have made to perform the analyses and whether they are held, as well as the limitations of your study.
The presentations will be held in March. There will be 90-minute slots, in each of which 3 groups are presenting their work. During the presentation we expect every member of the group to speak at least once and to participate in the discussion. You should attend all presentations in your slot. The grade for the presentation is pass/fail. Bonus points (at most 2) are awarded for clear communication, good reasoning and active participation during the discussion.
Have fun preparing the project!
Exam
You are allowed to use a Chalmers allowed calculator and your own course summary of four A4 pages (two A4 double sided or four A4 single sided). Tables of distribution values will be provided for you.
Several old exams with solutions are given in the module "Old exams".
Maximal number of points for the final exam is 30. Passing limits (including the bonus points) are
- Chalmers students: 12 points for '3', 18 points for '4', 24 points for '5'
- GU students: 12 points for 'G', 20 points for 'VG'