The text below is taken verbatim from Dablander & Bury (2022), which was published here. Bury et al. (2021) present a powerful approach to anticipating tipping points based on deep learning that not only substantially outperforms traditional early warning indicators, but also classifies the type of bifurcation that may lie ahead. Their work... Read more 10 May 2022 - 3 minute read
Climate change always felt like a distant, almost surreal threat to me. I learned about it in high school over ten years ago and thought: “This sounds pretty bad … But surely the people in power — the adults in the room — will manage to fix this and we can all just move on.” And so I grumbled on in the comfort and ignorance of my own life,... Read more 21 Jan 2022 - 39 minute read
The unusually stable climate of the past 10,000 years has enabled agriculture and civilization. And without further intervention, at least another 10,000 years of stability would have ensued. Yet starting in the 1950s, in what has been dubbed The Great Acceleration, humans dramatically grew their population and their economies, becoming a ... Read more 06 Jan 2022 - 4 minute read
Simulations are integral to many scientific disciplines and inquiries. I was therefore delighted when Mike Lees asked me to organize — together with Eric Dignum, Alex Gabel, Christian Spieker, Anna Keuchenius, and Vitor Vasconcelos — the Simulation-based Science colloquium for the summer semester 2021. The colloquium is usually hosted at the Ins... Read more 18 Jul 2021 - 14 minute read
If you think of Dogecoin — the cryptocurrency based on a meme — you can’t help but also think of Elon Musk. That guy loves the doge, and every time he tweets about it, the price goes up. While we all know that correlation is not causation, we might still be able to quantify the causal effect of Elon Musk’s tweets on the price of Dogecoin. Soun... Read more 07 Feb 2021 - 11 minute read
Dynamical systems theory provides a unifying framework for studying how systems as disparate as the climate and the behaviour of humans change over time. In this blog post, I provide an introduction to some of its core concepts. Since the study of dynamical systems is vast, I will barely scratch the surface, focusing on low-dimensional systems t... Read more 17 Dec 2020 - 38 minute read
This blog post was originally published on July $22^{\text{th}}$ 2020, but was updated on August $9^{\text{th}}$ 2020 to compare the risks of partying in Amsterdam, Barcelona, and London using the most recent coronavirus case numbers. There is no doubt that, every now and then, one ought to celebrate life. This usually involves people coming to... Read more 22 Jul 2020 - 31 minute read
This blog post first appeared on the Science versus Corona blog. It introduces this Shiny app. The novel coronavirus has a firm grip on nearly all countries across the world, and there is large heterogeneity in how countries have responded to the threat. Some countries, such as Brazil and the United States, have fared exceptionally poorly. Oth... Read more 19 Jun 2020 - 8 minute read
The COVID-19 pandemic will end only when a sufficient number of people have become immune, thus preventing future outbreaks. Principally, so-called exit strategies differ on whether immunity is achieved through natural infections, or whether it is achieved through a vaccine. Countries across the world are scrambling to find an adequate exit stra... Read more 11 Jun 2020 - 12 minute read
Last summer, I wrote about love affairs and linear differential equations. While the topic is cheerful, linear differential equations are severely limited in the types of behaviour they can model. In this blog post, which I spent writing in self-quarantine to prevent further spread of SARS-CoV-2 — take that, cheerfulness — I introduce nonlinear ... Read more 22 Mar 2020 - 41 minute read
Writing blog posts has been one of the most rewarding experiences for me over the last year. Some posts turned out quite long, others I could keep more concise. Irrespective of length, however, I have managed to publish one post every month, and you can infer the occassional frenzy that ensued from the distribution of the dates the posts appeare... Read more 27 Dec 2019 - 13 minute read
An extended version of this blog post is available from here. Causal inference goes beyond prediction by modeling the outcome of interventions and formalizing counterfactual reasoning. In this blog post, I provide an introduction to the graphical approach to causal inference in the tradition of Sewell Wright, Judea Pearl, and others. We first ... Read more 30 Nov 2019 - 40 minute read
Bayesian inference using Markov chain Monte Carlo methods can be notoriously slow. In this blog post, we reframe Bayesian inference as an optimization problem using variational inference, markedly speeding up computation. We derive the variational objective function, implement coordinate ascent mean-field variational inference for a simp... Read more 30 Oct 2019 - 26 minute read
If you are reading this, you are probably a Ravenclaw. Or a Hufflepuff. Certainly not a Slytherin … but maybe a Gryffindor? In this blog post, we let three subjective Bayesians predict the outcome of ten coin flips. We will derive prior predictions, evaluate their accuracy, and see how fortune favours the bold. We will also discover a neat tric... Read more 28 Sep 2019 - 17 minute read
Differential equations are a powerful tool for modeling how systems change over time, but they can be a little hard to get into. Love, on the other hand, is humanity’s perennial topic; some even claim it is all you need. In this blog post — inspired by Strogatz (1988, 2015) — I will introduce linear differential equations as a means to study the... Read more 29 Aug 2019 - 36 minute read
Leonardo Bonacci, better known as Fibonacci, has influenced our lives profoundly. At the beginning of the $13^{th}$ century, he introduced the Hindu-Arabic numeral system to Europe. Instead of the Roman numbers, where I stands for one, V for five, X for ten, and so on, the Hindu-Arabic numeral system uses position to index magnitude. This leads ... Read more 28 Jul 2019 - 19 minute read
The number of storks and the number of human babies delivered are positively correlated (Matthews, 2000). This is a classic example of a spurious correlation which has a causal explanation: a third variable, say economic development, is likely to cause both an increase in storks and an increase in the number of human babies, hence the correlatio... Read more 29 Jun 2019 - 10 minute read
Practice makes better. And faster. But what exactly is the relation between practice and reaction time? In this blog post, we will focus on two contenders: the power law and exponential function. We will implement these models in Stan and extend them to account for learning plateaus and the fact that, with increased practice, not only th... Read more 30 May 2019 - 34 minute read
Regularization is the process of adding information to an estimation problem so as to avoid extreme estimates. Put differently, it safeguards against foolishness. Both Bayesian and frequentist methods can incorporate prior information which leads to regularized estimates, but they do so in different ways. In this blog post, I illustrate these tw... Read more 15 Apr 2019 - 20 minute read
“Which variables are important?” is a key question in science and statistics. In this blog post, I focus on linear models and discuss a Bayesian solution to this problem using spike-and-slab priors and the Gibbs sampler, a computational method to sample from a joint distribution using only conditional distributions. Variable selection is a beas... Read more 31 Mar 2019 - 60 minute read
In a previous blog post, we looked at the history of least squares, how Gauss justified it using the Gaussian distribution, and how Laplace justified the Gaussian distribution using the central limit theorem. The Gaussian distribution has a number of special properties which distinguish it from other distributions and which make it easy to wor... Read more 28 Feb 2019 - 20 minute read
Judea Pearl said that much of machine learning is just curve fitting1 — but it is quite impressive how far you can get with that, isn’t it? In this blog post, we will look at the mother of all curve fitting problems: fitting a straight line to a number of points. In doing so, we will engage in some statistical detective work and discover the met... Read more 11 Jan 2019 - 22 minute read
The blog post reviews and summarizes the book “Ten Great Ideas about Chance” by Diaconis and Skyrms. A much shorter version of this review has been published in Significance, see here. In ten short chapters, Persi Diaconis and Brian Skyrms provide a bird’s eye perspective on probability theory and its connection to other disciplines. The book... Read more 11 Jan 2019 - 15 minute read