This module develops the theoretical foundations of methods used in statistical practice. The module rigorously introduces basic concepts of probability from a mathematical perspective. It aims to equip the students with a basic knowledge in probability which will reveal the interplay between probability theory and fundamental areas of mathematics, will allow students to formulate general real or abstract problems in a probabilistic model and will unravel the fundamentals which statistical methods are built on. In more detail the module will be developed around the concepts of probability distributions, random variables, independence, sums of random variables, limit laws and their application (Central Limit Theorem and laws of large numbers), and structures that depend on the present to study the future evolution of stochastic phenomena (Markov chains). The module also covers key topics in estimation and statistical inference, including method of moments and maximum likelihood.

Term(s) offered: Autumn/Spring/Summer term module; 20 [10 ECTS credits]
Credit: 1.5
General Education: I B