Recommended Literature

All master students are required to have knowledge in three areas:

• Methods of statistical learning and modelling
• Mathematical foundations of statistics
• Statistical software and statistical programming

Content and Literature

Methods of statistical learning and modelling

• Statistical modelling: simple and multiple linear regression, binary and Poisson regression, forecasting, hypothesis testing, model selection
• Inference: point and interval estimators, maximum likelihood and Bayesian estimation, principles of statistical testing, testing based on ML estimators, important tests
• Principles of machine learning: supervised and unsupervised learning, classification, risk minimization, regularization, evaluation, trees, forests, other important methods

Literature

• G. James, D. Witten, T. Hastie, R. Tibshirani. An Introduction to Statistical Learning. MIT Press, 2010.
• 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/ (especially Chapter 1-10)
• Wasserman, L.: All of Statistics. Springer 2004, Chapters 1-11, 13, 14, 20, 21

Mathematical foundations of statistics

• Fundamentals of probability theory: Kolmogorov's axioms, random variables, definition of discrete and continuous distributions, joint and marginal distributions, covariance and correlation, concepts of convergence, laws of large numbers, central limit theorem
• Matrix calculus: determinants, eigenvalues, quadratic form, spectral decomposition, Cholesky decomposition
• Analysis: differentiation, mathematical optimization, integration in R and Rn, Taylor series and Taylor approximation

Literature

• Grimmett, G., Stirzaker D.: Probability and Random Processes. Oxford University Press, 2020, Chapters 1-4 and 7.1-7.4
• Lang, S.: Matrixalgebra. https://www.uibk.ac.at/statistics/personal/lang/publications/matrixalgebra.pdf, Chapters 1–9
• Philip, P.: Calculus II for Statistics Students. https://www.math.lmu.de/~philip/publications/lectureNotes/philipPeter_Calc2_forStatStudents.pdf
• Deisenroth, M.P., Faisal, A.A., Ong, C.S.: Mathematics for Machine Learning. https://mml-book.github.io/book/mml-book.pdf, 2020, Chapters 1-6

Statistical software and statistical programming

• Basics of statistical programming
• Proficiency in a statistical programming language

Literature:

• Wickham, H., Grolemund, G.: R for Data Science. https://r4ds.had.co.nz/index.html
• Bischl, B. et al.: Programming in R - What We Expect You to Know. https://docs.google.com/presentation/d/1ZSHLFrTYhvWWTWBhmc8LOvFfSs5n5iMvuFkHbPwTbbs/edit#slide=id.g13ff11e59a8_0_53