# Posts

### A Quasiperiodic Counterexample

The problem Consider a function $$f: [0, 1] \to \mathbb{R}$$ that is continuous with $$f(0) = f(1)$$. It is possible to prove that for …

### A Function Golf Challenge

“Code golf” is the practice of trying to solve a specific problem or implement a specific algorithm in the smallest possible number of …

### The Perfect Math Library Doesn't Exi-

Introduction Many mathematicians have a rough mental list of “desert island” books - a small set of books they would choose if stranded …

### Bootstrapping LOWESS

In chapter 1 of their 2016 book Computer Age Statistical Inference, Bradley Efron and Trevor Hastie use as an example a study of kidney …

### Bayesian Estimation of Multinomial Parameter Ratios

Consider a multinomial distribution with $$c$$ categories and associated probabilities $$\pi_i$$, where $$i = 1,...,c$$. It is often …

### Simpson’s Paradox: A Tale of Two Carpenters

Once upon a time, in a small town, there were two carpenters: Bob and Tom. Bob was an honest, hardworking carpenter with a good …

### The Power of Simulation

I’m reading a book that deals with the history of probability theory (Classic Problems of Probability by Prakash Gorroochurn). It is …

### Average Logarithms and the Geometric Mean

I recently came across a surprising connection between the geometric mean and logarithms. At least, it was surprising to me, but isn’t …