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.
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 […]
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 […]
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 […]
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 […]
We are sharing a chalk talk rehearsal on applied probability. We use basic notions of probability theory to work through the estimation of sample size needed to reliably estimate event rates. This expands basic calculations, and then moves to the ideas of: Sample size and power for rare events. Please […]
In Gelman and Nolan’s paper “You Can Load a Die, But You Can’t Bias a Coin” The American Statistician, November 2002, Vol. 56, No. 4 it is argued you can’t easily produce a coin that is biased when flipped (and caught). A number of variations that can be easily biased […]
Two of the most common methods of statistical inference are frequentism and Bayesianism (see Bayesian and Frequentist Approaches: Ask the Right Question for some good discussion). In both cases we are attempting to perform reliable inference of unknown quantities from related observations. And in both cases inference is made possible […]
Elon Musk’s writing about a Tesla battery fire reminded me of some of the math related to trying to estimate the rate of a rare event from a single occurrence of the event (plus many non-event occurrences). In this article we work through some of the ideas.
It occurred to us recently that we don’t have any articles about Bayesian approaches to statistics here. I’m not going to get into the “Bayesian versus Frequentist” war; in my opinion, which style of approach to use is less about philosophy, and more about figuring out the best way to […]