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 […]

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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 […]

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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 […]

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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)

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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.

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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 […]

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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 […]

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I’d like some feedback on a possible article or series. I am thinking about writing and/or recording videos on the measure theoretic foundations of probability. The idea is: empirical probability (probabilities of coin flips, dice rolls, and finite sequences) is fairly well taught and approachable. However, theoretical probability (the type […]

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Here is a fun combinatorial puzzle. I’ve probably seen this used to teach before, but let’s try to define or work this one from memory. I would love to hear more solutions/analyses of this problem. Suppose you have n kettles of soup labeled 0 through n-1. For our problem we […]

Estimated reading time: 14 minutes