The course is designed to enhance your learning experience.
Each unit is motivated by a story based problem and focussed on providing the skills and techniques to solve it.
Be part of Captain Bayes' crew to sail the ocean of uncertainties and big data and help to succeed in her adventures of probability theory.
Get to know the ideas of your fellow crew comrades Bernoulli, Pascal, Laplace and many more that accompany you during your journey.
The adventures of Captain Bayes are followed by the content videos that deliver the theories and concepts of each unit. To familiarize you with the new learnings, interactive quizzes are integrated in the video to deepen your knowledge practically.
Furthermore listen to Ernesto, the parrot, that will guide you as your learning buddy throughout the course and provide you with learning tips and further material.
At the end of each unit you are ready to help Captain Bayes to solve the raised problems in a self-assessment (5-10 questions).
Hire now, meet Captain Bayes and proof yourself in her tough initial / recruiting task under the following link.
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.
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
========== break of two weeks ==========
- Unit 5: Odyssey and stochastic processes
- Unit 6: Bayesian deep reasoning
========== break of two weeks ==========
- Unit 7: Parameter and model estimation and classification
- Unit 8: Continuous probability distributions and invariance
- Unit 9: Bayesian simulation techniques
There will be a break of two week between unit 4 and 5 due to Easter holidays and another break of two weeks between unit 6 and 7.
Each unit is structured in the following way:
- Adventure of Captain Bayes and her crew:
A short movie introduces the problems and topics of the unit.
- Content video:
The content video delivers the language, knowledge and theorems of each unit and discusses the questions raised by Captain Bayes and her crew.
The video is garnished with small questions, that shall help you to readily apply the discussed concepts.
- Interactive simulations:
To deepen the comprehension, interactive simulations (pluto notebooks running Julia) are provided for you, that also allow you to adopt the code if you are interested in and like to experiment with it.
The forum shall be the place for you to discuss questions with the other participants.
We try to moderate your discussions and support you with answers to your questions if possible.
- The quiz:
The quiz marks the end of each unit and helps you to proof your obtained skills. You will be rewarded with a badge which acts as a microcredential (see https://info.badgr.com/) and can be downloaded as image. Your email address and the course details will be hashed in the meta-data of that image and can be verified using https://badgecheck.io/
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.
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.
Furthermore a badge (microcredential) is created for you (see https://info.badgr.com/) and can be downloaded as image. Your email address and the course details will be hashed in the meta-data of that image and can be verified using https://badgecheck.io/