Course syllabus adopted 2026-02-19 by Head of Programme (or corresponding).
Overview
- Swedish nameMatematisk statistik med maskininlärning
- CodeMVE785
- Credits7.5 Credits
- OwnerTKMSK
- Education cycleFirst-cycle
- Main field of studyMathematics
- DepartmentMATHEMATICAL SCIENCES
- GradingTH - Pass with distinction (5), Pass with credit (4), Pass (3), Fail
Course round 1
- Teaching language English
- Application code 44126
- Open for exchange studentsNo
Credit distribution
Module | Sp1 | Sp2 | Sp3 | Sp4 | Summer | Not Sp | Examination dates |
|---|---|---|---|---|---|---|---|
| 0126 Project 2.5 c Grading: UG | 2.5 c | ||||||
| 0226 Examination 5 c Grading: TH | 5 c |
In programmes
Examiner
- Stefan Lemurell
- Associate Professor, Algebra and Geometry, Mathematical Sciences
Eligibility
General entry requirements for bachelor's level (first cycle)Applicants enrolled in a programme at Chalmers where the course is included in the study programme are exempted from fulfilling the requirements
Specific entry requirements
The same as for the programme that owns the courseApplicants enrolled in a programme at Chalmers where the course is included in the study programme are exempted from fulfilling the requirements
Course specific prerequisites
Basic courses in mathematical analysis, linear algebra and programming.Aim
This course introduces fundamental methods of descriptive statistics, probability, random variables, statistical inference, and multivariate modelling with an applied strand in modern data analysis and introductory machine learning. Students learn how to explore data, quantify uncertainty, construct and interpret statistical models, and evaluate predictive performance using principled methods (train/test splits, cross-validation, and resampling). Group projects run throughout the course and culminate in a presentation and reproducible analysis report.Learning outcomes (after completion of the course the student should be able to)
1. **Describe and summarise data** using appropriate graphical and numerical tools, recognising outliers, skewness, and sampling variability.2. **Apply probability concepts** to analyse uncertainty and interpret model assumptions. Work with random variables (discrete and continuous), compute probabilities, expectations, and variances, and interpret distributional models.
3. **Construct confidence intervals and perform hypothesis tests**, including interpreting p-values, errors, and practical significance.
4. **Build and evaluate statistical and predictive models**, from simple to more advanced regression models, using appropriate error metrics and principled validation procedures. Quantify uncertainty of model performance using resampling methods and cross-validation.
5. **Communicate results** in a clear, reproducible, and professionally structured form, including limitations and assumptions.
Content
**Probability**- Probability measure, events, basic combinatorics.
- Random variables, expectation and variance.
- Main distributions: Binomial, Poisson, Exponential, Normal.
- Central Limit Theorem and Poisson Theorem and their applications.
**Statistics:
- Descriptive statistics.
- Sample mean and variance.
- Estimates: point and interval, sampling.
- Hypothesis testing: one and two-sample tests.
- Regression and correlation, multiple regression.
**Machine Learning**
* data quality; baselines and correct evaluation setup (train/test, leakage awareness).
* classification metrics and probabilistic classification
* bootstrap uncertainty for metrics; cross-validation for model selection.
* small neural networks as a predictive model
Organisation
The teaching of the course is organised around the following components: lectures on the theory, computer lab work in the web-based Virtual Learning Environment (VLE) and practical work in small group projects.Literature
The main source is the VLE Study Guide, which is available for browsing and download as a whole or in parts from within the VLE.
For ML part: Google's Machine Learning Crash Course https://developers.google.com/machine-learning/crash-course
Douglas C. Montgomery and George C. Runger. Applied Statistics and Probability for Engineers. 4th ed., Wiley, 2006.
Examination including compulsory elements
To pass the course, students must achieve at least 40% in the examination and complete the group project.The final course grade is determined by the result of the examination. During the course, students will have the opportunity to take in-course tests. Students who pass these tests may be exempt from the final examination. Further details, including the test format and exact dates, are published on the course webpage.
Students who do not pass the examination in June, or who have not completed the project requirements, must take a re-sit examination in August or January and/or complete any outstanding project work individually, in order to pass the course.
If there are special reasons, the course examiner may assess individual students using alternative methods to those described above, for example, where a student has an approved decision from Chalmers regarding disability study support.
The course examiner may assess individual students in other ways than what is stated above if there are special reasons for doing so, for example if a student has a decision from Chalmers about disability study support.