Blog

These posts have evolved from my digital garden¹ into a bit longer form. Their main role is to educate myself and they may be incomplete, written from a very subjective point of view, or contain errors. I’d be grateful for feedback on how to improve them!

On mixtures and admixtures

A quick look at the differences between mixture and admixture models.

Proofs that pi and e are irrational

Two short and well-known proofs of irrationality.

Softmax, mixtures and exponential families

Let’s take a look at a sentence from the variational classification paper.

Beta-Bernoulli distribution

Bernoulli, binomial, beta-binomial… Why don’t we talk about the beta-Bernoulli distribution?

Starting (on finite domains) with Gaussian processes

Gaussian processes are wonderful. Let’s take a look at the machinery behind them in the simplest case: when they are just a multivariate normal distribution.

Setting up a new project repository

From time to time I receive a question on setting up a new project repository. I’m not really qualified to answer this question, but I’ll do my best.

Regression to the mean and biased predictions

We take a closer look at an example where adding some bias can help with making predictions.

From \(t\)-test to “This is what ‘power=0.06’ looks like”

We take a close look at the derivation of the \(t\)-test and reproduce plots used by Andrew Gelman to show implications of low-powered studies.

Strict linear independence of measures

We look at the concept of strict linear independce of measures and see how it is related to identifiability of mixture models.

From kernel regression to the transformer

We’ll go from kernel regression to attention.

Expectation-maximization and Gibbs sampling in quantification

Let’s analyse how to estimate how many cats and dogs can be found in an unlabeled data set.

An almost binomial Markov chain

Everybody knows how to toss a coin. This time we’ll toss it a few times.

The mutual information saga

Behind the scenes of our mutual information research.

Getting started with Bayesian statistics

From time to time I receive a question from students and collaborators how to get started with Bayesian statistics. So here it comes: the list of my favourite resources!

The no free lunch theorem for scientific research

A perfect paper should have novel methodology, solve an important problem, and be correct. In practice, the no free lunch theorem says that at most two of these are possible.

Two distributions on a triangle

Sometimes if you misunderstand something, you can have two interesting distributions, rather than only one.

Histograms or kernel density estimators?

We take a look at summarizing samples with histograms and kernel density estimators.

Matrix determinant from the exterior algebra viewpoint

We look at the ordinary matrix determinant from the exterior algebra point of view.

The Dirichlet process

In an informal fashion we introduce several constructions of the Dirichlet process.

Understanding board games with Monte Carlo simulations

We look at several simple situations occurring in board games and analyse them with Monte Carlo simulations.

Student mentorship: expectations document

I learned from one of my mentors that it’s important to discuss the mutual expectations of the mentorship, be it a PhD thesis or a lab rotation. This document serves as a template, which we can further discuss and adjust.

Footnotes

See this link for a difference. I maintain my digital garden in Obsidian. Please, let me know if you know a good way of integrating Obsidian with Quarto!↩︎