The standout post from that sequence. The standard statement of the CLT says that the input distributions must be identically distributed, but it turns out that requirement can be bent pretty far without issues.

Also from that sequence: proving that the form of the Bayesian posterior suggests that Bayesian calculations will often converge to a Gaussian. I think this is the same thing the Bernstein-von Mises theorem is about, though I didn't know that when I wrote it.

Collected links to my research & math posts.

A sequence on interpreting the central limit theorem in terms of convolutions.

The standout post from that sequence. The standard statement of the CLT says that the input distributions must be identically distributed, but it turns out that requirement can be bent pretty far without issues.

Also from that sequence: proving that the form of the Bayesian posterior suggests that Bayesian calculations will often converge to a Gaussian. I think this is the same thing the Bernstein-von Mises theorem is about, though I didn't know that when I wrote it.

A simple post describing the basics of when and how to use the Beta distribution, meant for Data Scientists and analysts who haven't heard of the Beta.

A speculative post about interpreting the mean, mode, and median in terms of how much information each uses from the underlying distribution.

Activated Charcoal for Hangover Prevention: a heavily researched essay about why activated charcoal might help prevent hangovers.

A short analysis about a toy game. Has some nice graphs.

Describing a few types of measures from Measure Theory.

A post thinking about how to interpret uncalibrated predictions from a classifier. I wrote this before knowing about Platt/Isotonic/Spline calibration; any of those would solve the issues raised in the post.

A post exploring a wider definition of priors, and finding hints of them in frequentist practice.

Adding to an argument Jaynes made in Probability Theory: The Logic of Science, about Occam's Razor and the geometry of probability-space.

Thoughts on a different way to present True Positive Rate / FPR / TPR / TNR.