COVID-19: The Incredible Shrinking Boost of the Booster Shot


With COVID-19 after the vaccination is before the vaccination. Now that most people in the developed countries have been vaccinated the question arises of how much boost is in the booster shot. We are here to help you understand the real power (or lack thereof) of the booster, so read on!
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Solving Einstein’s Puzzle with Constraint Programming


The following puzzle is a well-known meme in social networks. It is said to have been invented by young Einstein and back in the days I was ambitious enough to solve it by hand (you should try too!).

Yet, even simpler is to use Constraint Programming (CP). An excellent choice for doing that is MiniZinc, a free and open-source constraint modelling language. And the best thing is that you can control it by R! If you want to see how, read on!
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The Most Dangerous Equation, or Why Small is Not Beautiful!


Over one billion dollars have been spent in the US to split up big schools into smaller ones because small schools regularly show up in rankings as top performers.

In this post, I will show you why that money was wasted because of a widespread (but not so well known) statistical artifact, so read on!
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Is the Stock Market Efficient? Let your ZIP Compression Tool give an Answer!


One of the most fiercely fought debates in quantitative finance is whether the stock market (or financial markets in general) is (are) efficient, i.e. whether you can find patterns in them that can be profitably used.

If you want to learn about an ingenious method (that is already present in anyone’s computer) to approach that question, read on!
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The Pólya Urn Model: A simple Simulation of “The Rich get Richer”


What is the “opposite” of sampling without replacement? In a classical urn model sampling without replacement means that you don’t replace the ball that you have drawn. Therefore the probability of drawing that colour becomes smaller. How about the opposite, i.e. that the probability becomes bigger? Then you have a so-called Pólya urn model!

Many real-world processes have this self-reinforcing property, e.g. leading to the distribution of wealth or the number of followers on social media. If you want to learn how to simulate such a process with R and encounter some surprising results, read on!
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New Bundesliga Forecasting Tool: Can Underdog Herta Berlin beat Bayern Munich?


The Bundesliga is Germany’s primary football league. It is one of the most important football leagues in the world, broadcast on television in over 200 countries.

If you want to get your hands on a tool to forecast the result of any game (and perform some more statistical analyses), read on!
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The “Youth Bulge” of Afghanistan: The Hidden Force behind Political Instability


In view of the current dramatic events in Afghanistan many wonder why the extensive international efforts to bring some stability to the country have failed so miserably.

In this post, we will present and analytically examine a fascinating theory that seems to be able to explain political (in-)stability almost mono-causally, so read on!
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Learning Path for “Data Science with R” – Part I


Over the course of the last two and a half years, I have written over one hundred posts for my blog “Learning Machines” on the topics of data science, i.e. statistics, artificial intelligence, machine learning, and deep learning.

I use many of those in my university classes and in this post, I will give you the first part of a learning path for the knowledge that has accumulated on this blog over the years to become a well-rounded data scientist, so read on!
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The Small Data Rule: Infer the Big Picture from only Five Values!


Everybody is talking about big data but the real skill lies in the art of inferring useful information from only a handful of values!

If you want to learn how to determine the range of the typical value of a dataset (i.e. the median) with just five values and why this works, read on!
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Euler Coding Challenge: Build Maths’ Most Beautiful Formula in R


In this post, we will first give some intuition for and then demonstrate what is often called the most beautiful formula in mathematics, Euler’s identity, in R – first numerically with base R and then also symbolically, so read on!
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