**Please note: This course will be taught in hybrid mode. Hybrid delivery of courses will include synchronous live sessions during which on campus and online students will be taught simultaneously. **

Susumu Shikano is Professor of Political Methodology. He is doing research on spatial models of politics and diverse topics in political behaviour. Before going to Konstanz, he was professor ad interim at the University of Potsdam (2008) and assistant professor at the University of Mannheim (2001-2008). He received a Dr. Phil (2001) and Venia Legendi (2007) for political science from the University of Mannheim.

Empirical researchers working with statistical models are owing a lot to probability theory, however, often without noticing it. Being informed about probability theory has at least two advantages: 1) Use of statistical softwares and interpretation of their outputs become better-grounded; 2) It becomes easier to learn more advanced techniques such as machine learning. In this course, we first discuss the basics of probability theory, which include: set theory; the three axioms of probability theory; rules in probability calculation; discrete and continuous random variables; joint, marginal and conditional densities; the Gaussian distribution; limit theorem; random process. After discussing the above topics, the course continues with how probability theory contributes to different types of social science research. More specifically, maximum likelihood estimation, Bayesian inference, MCMC and Bayesian networks will be discussed. All these abstract topics will be accompanied with some concrete samples for better understanding, whereby simple R codes for some calculation and/or visualization will be used.

**Course Objectives**

Students will gain a solid understanding of probability theory in the first week by learning the basics concepts and rules of probability theory. Based on that, students will learn in the second week how probability theory is used to make inferences in different contexts. More specifically, the course will introduce maximum likelihood, Bayesian inference, Markov Chain Monte Carlo techniques and Bayesian networks in their very basic forms. More extensive discussion will be provided by the other corresponding advanced courses in the ESS program.

**Course Prerequisites**

A solid understanding of descriptive statistics and a basic understanding of regression analysis is of great advantage. This course is not an introduction to R but assumes that students are familiar with basic R programming.

**Required text**

We shall be using the following textbook: Joe Blitzstein and Jessica Hwang *Introduction to Probability*, 2nd Edition. A free version is available online free version available online at https://projects.iq.harvard.edu/stat110

**Background knowledge required:**

**Mathematics:**

Calculus = elementary

Linear Regression = elementary

**Statistics:**

OLS = elementary

Maximum likelihood = elementary

**Computing Background:**

R = elementary