## How often do the L1 and L2 norms agree?

Turns out that I am still on a recreational mathematics run. Here is one I have been working on, arising from trying to explain norms and data science. Barry Rowlingson and John Mount asked the following question. Generate vectors v1 and v2 in Rn with each coordinate generated IID normal […]

## Just For Fun: Computing the Probability of Winning a Tournament

Taking a break from weekend’s Elden Ring gaming to work out the probability of winning a tournament. The article can be found here: Some Math Inspired by Losing in Elden Ring. It is a variation on a “persuasion by calculation of examples” style I am working on.

## Upcoming Talk on Probability Models

Nina Zumel and John Mount will be speaking at the online University of San Francisco Seminar Series in Data Science! How and why to use probability models to outperform decision rules Friday April 30, 2021 12:30pm – 2pm Pacific Time See here for full details and to RSVP In this […]

## When Profitable Betting Systems are not Possible

I felt a bit guilty explaining a Kelly/Thorp style card betting system without discussing why these ideas don’t work on fair coin games. So I have “writeup for engineers” on the martingale theory of such games. This has example code, so one could try to come up with a betting […]

## Kelly Thorp Betting

I demonstrate a Kelly/Thorp betting system for the simple card game of guessing if the next card from a standard deck is red or black. I have a video of the play here. And a derivation of the betting strategy in R is here. A derivation of the proof you […]

## 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)

## New Free Video Lecture: Estimating the Odds with Bayes’ Law

I am excited to share my new free video lecture: Estimating the Odds with Bayes’ Law. (link)

## 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.

## Kolmogorov’s Axioms of Probability: Even Smarter Than You Have Been Told

Introduction I’d like to talk about the Kolmogorov Axioms of Probability as another example of revisionist history in mathematics (another example here). What is commonly quoted as the Kolmogorov Axioms of Probability is, in my opinion, a less insightful formulation than what is found in the 1956 English translation of […]

## A Gruesome Example of Bayes’ Law

Here is an incredibly clear, but unfortunately gruesome, example of a variation of Bayes’ Law. A good teachable point. Consider the recent CDC article “Community and Close Contact Exposures Associated with COVID-19 Among Symptomatic Adults ≥18 Years in 11 Outpatient Health Care Facilities.” It states: Adults with positive SARS-CoV-2 test […]