Statistics and Probability Theory

Lecturer (assistant)
Number0000004043
TypeLecture
Duration2 SWS
TermSommersemester 2020
Language of instructionEnglish
Position within curriculaSee TUMonline
DatesSee TUMonline

Dates

Admission information

Objectives

After successful completion of this course, students understand and can apply central concepts of statistical and probabilistic modelling and are able to apply those concepts on given data analysis questions. Students can describe, derive and apply models and methods from statistical modelling and machine learning.

Description

The course starts with a refresher of probability theory and statistics for data-analysis, including basic probability principles, random variables, probability distributions, descriptive statistics. It then covers the principles of Statistical inference, including Bayesian inference, Bayesian decision theory, confidence intervals, model selection, as well as canonical models of probabilistic modelling and machine learning, including linear regression and classification approaches. Finally, we include an excursion to modern data-science and big-data anlysis methods, including Bayesian inference and latent varible models (e.g. Laplace approximation, MCMC sampling, variational methods, Gaussian Processes, Deep Probabilistic Models).

Prerequisites

Basic knowledge in linear algebra, calculus, probability theory and programming, e.g. as acquired in 'Fundamentals in Mathematics for Neuroengineering' and 'Fundamentals in Computer Science for Neuroengineering'.

Teaching and learning methods

Basic models and methods in probabilistic modelling are introduced during the lectures. They are transferrred into case-studies during the exercises to introduce examples and to allow students to further investigate while experimenting during group work to provide hands-on experience and introduce skills required in practice with the use of a statistical data-analysis software package (e.g. Python/pandas).

Examination

During a written exam (90 min) students have to develop solutions to given data analysis and modelling problems using methods from statistical modelling and machine learning.

Recommended literature

C.M. Bishop: Pattern Recognition and Machine Learning, Springer; D. Barber: Bayesian Reasoning and Machine Learning, Cambridge University Press.

Links