Quantiles can represent key operational and business metrics, but the computational challenges associated with inference has hampered their adoption in online experimentation. In a new paper, I present a two-sample difference-in-quantile hypothesis test and confidence interval based on a likelihood-...

Transformer has a mathematical bug that has been overlooked for 6+ years. I propose fixing its outliers with two new devices, Softmax One and QuietAttention: Attention Is Off By One

A paper from Spotify on quantile estimation has been making the rounds. I take a stab at their critical conjecture, and uncover a few Formulas for Bootstrapping Sample Medians.

A/B tests run faster with CUPED. Here I explain the underlying math, and use it to invent an even better variance-reduction technique for online experiments: You Can’t Spell CUPED Without Frisch-Waugh-Lovell

An essay that bids farewell to x87, a computing architecture too long for this world: The Floppy Disk of Floating Point

I’ve updated Formulas for Bayesian A/B Testing to include a new equation for analyzing four-pronged (A/B/C/D) tests.

What rolls down stairs and counts unique items imprecisely? HyperLogLog. Also SlowerLogLog

A Lost Lady, a Willa Cather novel which entered the public domain this year, is a gentle study in decline on the former frontier. Read my Preface to A Lost Lady

Brave New World reacquainted political philosophy with the prurient, after a two thousand year hiatus. Read my Preface to Brave New World

The Time Machine is my favorite science fiction novella. What makes it special? Read my Preface to The Time Machine

Frankenstein turned two hundred last year. Why is it still relevant? My very own Preface to Frankenstein

How much is the EveryDay Bonus from American Express worth? A probabilistic investigation: The Amex EveryDay Bonus: A Stochastic Valuation Model

I’m learning Swift. Some minor grievances I have with the language: Things That Bother Me About Swift

In honor of the upcoming Festivus, I am sharing some Mac-related grievances: Things That Bother Me About macOS

I spent a few weeks with Perl 6. Here’s what I think: A Review of Perl 6

The Perl 6 virtual machine is a promising piece of technology: Why I’m Learning Perl 6

Identifying and quantifying dead ends, the bane of all adventure game players: Adventure Games and Eigenvalues

Reflections on the Microsoft Surface Studio and Apple’s inevitable giant iPad: Big Tablets Are Coming

Making C more flexible, with the help of x86_64 calling conventions: Type Punning Functions in C

A systems-y look at HTML template rendering: Elixir RAM and the Template of Doom

Nintendo keeps trying to fix Splatoon’s ranking system. They won’t succeed without a solid understanding of linear algebra. Read more: Splatoon’s Ranking System Is Still Broken

Cut your A/B sample sizes in half, using this one weird trick: Simple Sequential A/B Testing

I’ve added several new formulas to “A Formula for A/B Testing” (now known as Formulas for Bayesian A/B Testing). In addition to including the count data formula on the page, I have extended both formulas to work with three-pronged tests, that is, A/B/C tests.

Evaluating Splatoon’s Ranking System — Using probability theory to uncover a subtle bug in Splatoon.

Inferring Tweet Quality From Retweets — Modeling tweets, retweets, and the passage of time.

Ranking News Items With Upvotes — A formula for social news websites.

Deriving the Reddit Formula — What can expected-utility theory tell us about Reddit’s “hot” formula?

A Taste of Rust — I tried Rust, and it was better than eating a bucket of nails.

Four Days of Go — If you see the Go gopher, tell him I would like my pajamas back.