“Mathematics knows no races or geographical boundaries; for mathematics, the cultural world is one country.”
David Hilbert
Latest posts

The subtleties of computing quantiles  June 21, 2020
Computing quantiles is a good way to summarize the distribution of a numerical dataset. But confusingly there are nearly a dozen different definitions of quantile that can all claim to be correct, and in all cases it is difficult to actually compute quantiles for very large datasets. I will explain why there are so many definitions, and compare a couple of different strategies for doing computations at scale.

Working with Python Project Directories  March 05, 2020
This short post contains some tips and tricks for dealing with complicated Python project directories in an organized way.

Jensen's Inequality and Statistics  September 01, 2019
Jensen's inequality is a beautiful little workhorse lemma from convex geometry. I have stumbled into it an number of times recently as I have been reading and writing about statistics and information theory, so I decided to split it off into its own blog post. After introducing the inequality (and proving that it holds), I will give a few snappy applications to basic statistics, including the classical inequality between arithmetic, geometric, and harmonic means as well as a basic inequality relating the mean, median, and standard deviation.

The RadonNikodym Theorem  May 27, 2019
The RadonNikodym theorem is a workhorse result in measure theory, with numerous applications to probability dynamics (such as the existence of conditional expectations and the existence of KLdivergence). I will give a simple proof using Hilbert spaces.

Gibbs' Inequality  May 27, 2019
It is a fairly standard fact that relative entropy (KLdivergence) is positive definite, but I was unsatisfied with the proofs of this fact that I saw when I glanced through the literature. In this post I will provide a complete proof which works on a general probability space.