Information for those interested in the Master's Program

Master's program

In the Master's program Statistics and Data Science, the basic scientific concepts and methods of statistics are deepened and expanded as a basis for responsible data analysis. Due to its strong research-oriented focus, the completed degree program enables students to further develop and redesign suitable statistical methods even in very complex application situations. During their studies, students further choose to deepen their understanding with respect to one of five focus areas: Machine Learning, Biostatistics, Social Science and Data Science, Econometrics or Methodology and Modeling.

Additional information for enrolled students

If you want to learn more about the concrete lectures and specialization possibilities, you can visit the page with Information for enrolled students in the current available master's program (here you can find also the study regulations and the module catalogue)

Application

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

Enrollment

Student Counseling

For individual questions about the Master's program please reach out to Lea Höhler. master.consultancy@stat.uni-muenchen.de