Application for the Master Statistics and Data Science

Master Statistics and Data Science

The application for the Master Statistics and Data Science program is possible via the following links (portal opens on March 15th for Winter Semester/September 15th for Summer Semester):

• For students without LMU user ID
• For students with LMU user ID

Time line

Applicants who neither have German citizenship nor are considered as "Bildungsinländer" must additionally submit an application for admission to studies to the LMU International Office. Acceptance from the international office does not imply acceptance to the program. 

Requirements

The following are considered prerequisites for prospective master's students.

Statistical Modelling: Linear and generalized linear regression, interpretation of additive models; regularization (Ridge, Lasso); model selection (AIC, BIC); principal component analysis

Statistical Inference: point and interval estimators; maximum likelihood including asymptotic statements, likelihood inference in GLMs; priors and posteriors including predictive posterior; principles of statistical testing, testing based on ML estimators, important tests, multiple testing

Principles of Machine Learning: Risk minimization; classification, regression in machine learning context, LDA, QDA, naive Bayes, KNN; evaluation, resampling, standard performance metrics, ROC analysis; decision trees, fundamentals of neural networks; fundamentals of hyperparameter tuning

Fundamentals of probability theory: Kolmogorov's axioms; random variables, moments; definition of discrete and continuous distributions, joint and marginal distributions, definition and properties of conditional expectations, covariance and correlation; concepts of convergence, laws of large numbers, central limit theorem

Linear algebra: abstract vector spaces, basis systems; linear functions, kernel, range, invertibility; inner products, orthogonality, projections; eigenvalues, eigenvectors, spectral decomposition; quadratic forms, SVD, Cholesky decomposition

Analysis: convergence, sequences, series; continuity, differentiability; convexity, open and closed sets; differentiation in R^d, integration in R^d; Taylor series and Taylor approximation; basics of nonlinear optimization problems

Statistical software and statistical programming: Proficiency in a statistical programming language (R or python); programming paradigms (functional/OOP/imperative); control flow, vectorization, iteration; functions & data types; basic algorithms; error handling & debugging; version control; data visualization; Familiarity with a standard ML toolkit in R or Python and some applied ML experience

The following sources cover most of the knowledge above:

• Held, L, Sabanés Bové, D.: Likelihood and Bayesian Inference. Springer 2020, Chapters 1-7.
• Fahrmeir, L., Kneib, Th., Lang, S., Marx, B.D.: Regression. Springer 2021, Chapters 1-4
• Bischl, B. et al.: Introduction to Machine Learning (I2ML). https://slds-lmu.github.io/i2ml/ The first 10 chapters of I2ML cover the BSc part.
• Anton, H., & Rorres, C. (2013). Elementary linear algebra: applications version. John Wiley & Sons.
• Peter Philip (2024). Calculus I and Calculus II for Statistics students. Lecture Notes, LMU Munich.
• Grimmett, G. and Stirzaker, D.: Probability and Random Processes. Oxford University Press, 2001, Chapters 1-4 and 7

Selection process

This is a non-binding outline. Only the text of the „Satzung über das Eignungsverfahren für den Masterstudiengang Statistics and Data Science an der Ludwig-Maximilians-Universität München“ is valid.

Basic requirements

• Bachelor's degree (180 ECTS) in Statistics or Data Science as a major, minor, or focus.
• At least 150 ECTS (equal to 5 semesters) must be proven by the time of application, final degree can be submitted later.
• English proficiency B2 (or English degree).

Selection Process – First stage

The application will be assessd by grade in the previous studies (up to 5 points) and knowledge in three areas:

• Methods of statistical learning and modeling (up to 6 points): statistical inference, statistical modelling, and  machine learning
• Mathematical foundations of statistics (up to 5 points): probability theory, linear algebra, analysis
• Statistical software and statistical programming (up to 4 points)

Applicants without the necessary prerequisites can (for example) apply for the Bachelor Statistics and Data Science to acquire missing knowledge.

Test

• If you are eligible for the second stage, we will send you a written test. 
• You have two weeks to upload the solutions. 
• If the test is passed, you will be invited to an selection interview.

Selection interview

• The interview will take 15 minutes
• Knowledge in the three areas will be discussed

Enrollment

Enrollment in the Master's programs at the Institute of Statistics is only possible if you are directly admitted by the selection comitee.

• General information on enrollment

Contact

If you have questions regarding the application process, please contact Lea Höhler (master.consultancy@stat.uni-muenchen.de).