Advanced Applied Statistics and Multivariate Calculus
AbstractThis course introduces fundamental and advanced concepts in statistics and probability from a data-science perspective. The aim of the course is for the student to be familiarised with probabilistic and statistical methods that are widely used in data analysis.
The aim of the course is to enable the student to work systematically with data sets with several variables which is important in regard to performing statistical analyses in data science. The course builds on the knowledge acquired in courses such as “Applied statistics” and “Machine Learning” and intends to give the student additional tools to identify, and solve statistical problems.
The course will cover the following subjects:
- Probability theory
- Random variables
- Multivariate random variables
- High-dimensional problems
- Convergence of random processes
- Bayesian methods
- Outlier detection and clustering
- The prerequisites required for admission to the course are Linear Algebra and Optimisation or equivalent (vectors and matrices, eigendecomposition, univariate calculus) and Applied Statistics or equivalent (basic probability theory, expectation and variance, univariate distributions, data presentation and visualisation).
- Students must be able to programme. The default language is Python, but other languages are possible.
Intended learning outcomes
After the course, the student should be able to:
- Analyze statistical problems and reason about the most appropriate methods to apply
- Apply and reflect on advanced applied statistical methods and tools for multivariate calculus
- Identify and describe problems that can be solved using multivariate techniques
- Implement basic statistical algorithms and interpret results
- Summarize the results of an analysis in a statistical report
Learning activitiesThe course consists of lectures and seminars ending with a project for the last part of the course. Classes will consist of lectures, seminars, independent programming exercises and discussion sessions.
The default language is Python, but other languages are possible.
For the final project you will specify and work on a relevant project of your choice. In this project you will apply the techniques and algorithms studied during the course on relevant problems. Besides the hours planned for lectures, seminars, tutorial, and exercise, supervision sessions for the projects are planned which complement the theory covered during the lectures and are necessary for meeting the learning objectives of the course. Short lectures will provide theoretical foundations and walk-through examples of relevant data mining algorithms while programming exercises will focus on students discussing, applying, and implementing the central algorithms themselves.
Morris DeGroot and Mark Schervish. Probability and Statistics. Fourth edition. Harlow: Pearson Education, 2014.
Additional readings will be assigned as needed.
Student Activity BudgetEstimated distribution of learning activities for the typical student
- Preparation for lectures and exercises: 20%
- Lectures: 20%
- Exercises: 30%
- Project work, supervision included: 30%
Ordinary examExam type:
D: Submission of written work with following oral, External (7-point scale)
D2G: Submission for groups with following oral exam supplemented by the submission. Shared responsibility for the report.
Group and individual
Mixed exam 1 : Individual and joint student presentation followed by an individual and a group dialogue. The students make a joint presentation followed by a group dialogue. Subsequently the students are having individual examination with presentation and / or dialogue with the supervisor and external examiner while the rest of the group is outside the room.
Z. To be decided
Time and dateOrdinary Exam - submission Thu, 5 Jan 2023, 08:00 - 14:00
Ordinary Exam Mon, 23 Jan 2023, 09:00 - 21:00
Ordinary Exam Tue, 24 Jan 2023, 09:00 - 21:00
Ordinary Exam Wed, 25 Jan 2023, 09:00 - 21:00
Ordinary Exam Thu, 26 Jan 2023, 09:00 - 21:00
Reexam - submission Wed, 22 Feb 2023, 08:00 - 14:00
Reexam Tue, 21 Mar 2023, 12:00 - 18:00