## New Math Chalk Talk: The Game of Infinity Questions

I have a new math chalk talk up: The Game of Infinity Questions. This is back to establishing the “reasonableness” of Kolmogorov’s Axiom of continuity (in his actual formulation of his axiomatization of probability). Remember, his argument is “it is a bit off to have strong opinions on infinite processes, […]

## abs and relu are not Mercer Kernels

I am sharing some rough notes (in R and Python) here on how while dot(a, b) fulfills “Mercer’s condition” (by definition!, and I’ll just informally call these beasts a “Mercer Kernel”), the seemingly harmless variations abs(dot(a, b)) relu(dot(a, b)) are not Mercer Kernels (relu(x) = max(0, x) = (abs(x) + […]

## New Math Chalk Talk: The Real Numbers

I have a new math chalk talk to share: “The Real Numbers.” Here I go into some of the terrifying true nature of our common model for continuous quantities. (link)

## Some Thoughts on Numbers

Sabine Hossenfelder’s excellent lecture “Is Infinity Real?” has inspired me to talk a bit about numbers. (link)

## Evaluating Probability Models

A video introduction on how to evaluate probability models using the statistical deviance. (link)

## Measure Theoretic Probability Video

I’d like to share a brief orientation video on measure theory based probability. Measure theory is a rigorous axiomatic treatment of probability that defers on interpretation (such as frequentist interpretation, Bayesian interpretation, or even Kolmogorov/Chaitin complexity). (link)

## Tailored Models are Not The Same as Simple Corrections

Let’s take a stab at our first note on a topic that pre-establishing the definitions of probability model homotopy makes much easier to write. In this note we will discuss tailored probability models. There are models deliberately fit to training data that has an outcome prevalence equal to the expected […]

## Upcoming Series: Probability Model Homotopy

I am planning a new example-based series of articles using what I am calling probability model homotopy. This is a notation I am introducing to slow down and make clearer discussing how probability models perform on different populations.