Course Content

The primary motivation for this course is to warm a broader audience to probability theory, as it is central to all scientific fields. Or as E.T. Jaynes - one of the most important researchers on probability theory of the last century - put it: "Probability is the logic of science."

This course equips you with the methods of probability theory and enables you to deal with uncertainties, qualify decisions, assign probabilities and estimate parameters and models. The Bayesian approach provides techniques to update "partial truth".
As a whole, this MOOC delivers the basics that are needed and benefitial for the fields of machine learning and data science.

The course is split into units dealing with discrete and continuous variables with 9 units altogether:

• Unit 1: Bayesics of probability theory
• Unit 2: Discrete probability distributions and samples
• Unit 3: Multivariate distributions - more Bayesics
  
• Unit 4: Combinatorics - The art of counting
  
• Unit 5: Odyssey and stochastic processes
  
• Unit 6: Bayesian deep reasoning
  
• Unit 7: Parameter and model estimation and classification
• Unit 8: Continuous probability distributions and invariance
  
• Unit 9: Bayesian simulation techniques

Course Goals

The ambition of this course is not only to deliver the concepts of probability theory but to promote critical questioning and to sensitize for decision making.
Dozens of paradoxes show how easily the human mind can be misled. Therefore,  the skill to interprete numbers and facts is as important as the ability to make qualified estimations. The course will equip you with the toolbox to draw inference based on uncertain and incomplete information.

Specifically the course will help you to understand how to assign probabilities in a classical and statistical way and more importantly how to use new evidence to update probabilities and solve inverse probability problems (Bayes theorem).

Especially rigorous updating and solving inverse problems are fundamental for machine learning and data science and some examples in the course will show how to estimate parameters and classify data.

Since correct data processing is crucial for knowledge gain by experiments, dealing with outliers and the rigourous drawing of conclusions from sample sets will be topics of this course.

After completing this course you will be enabled to formulate probabilistic statements from (new) data and to use simulations to draw conclusions for stochastic processes.

From a didactical perspective a major goal is to improve discussion culture among participants, to help you to express your ideas and your questions and to foster your engagement.

Previous Knowledge

The first seven modules deal with basic algebra. The content is designed for Bachelor students with a basic mathematical backround. For unit 1 to 7 the sum notation, vector calculus and simple algebraic transformation should be known. The last units about continuous variables require integration techniques.

Course Procedure

Certificate

For actively participating in the course you will receive an automatic confirmation of participation (certificate) which includes your username, the course title, course duration as well as the hours required to complete the course. We want to point out that this certificate merely confirms that the user answered at least 75% of the self-assessment questions correctly.

Licence

This work is licensed under a CC BY 4.0