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, […]

Estimated reading time: 1 minute

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) + […]

Estimated reading time: 2 minutes

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)

Estimated reading time: 20 seconds

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)

Estimated reading time: 25 seconds

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 […]

Estimated reading time: 4 minutes

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.

Estimated reading time: 8 minutes