Yes, you can include prior information on quantities of interest, not just on parameters in your model

Nick Kavanagh writes: I studied economics in college and never heard more than a passing reference to Bayesian stats. I started to encounter Bayesian concepts in the workplace and decided to teach myself on the side. I was hoping to get your advice on a problem that I recently encountered. It has to do with […]

Mickey Mouse, Batman, and conformal mapping

A conformal map between two regions in the plane preserves angles [1]. If two curves meet at a given angle in the domain, their images will meet at the same angle in the range. Two subsets of the plane are conformally equivalent if there is a conformal map between them. The Riemann mapping theorem says […]

Eliminating Tail Calls in Python Using Exceptions

I was working through Kyle Miller‘s excellent note: “Tail call recursion in Python”, and decided to experiment with variations of the techniques. The idea is: one may want to eliminate use of the Python language call-stack in the case of a “tail calls” (a function call where the result is not used by the calling … Continue reading Eliminating Tail Calls in Python Using Exceptions

Hyppocratic oath for maths?

On a free day in Nachi-Taksuura, I came across this call for a professional oath for mathematicians (and computer engineers and scientists in related fields) . By UCL mathematician Hannah Fry. The theme is the same as with Weapons of math destruction, namely that algorithms have a potentially huge impact on everyone’s life and that […]

Star-crossed lovers

A story in The New Yorker quotes the following explanation from Arthur Eddington regarding the speed of light. Suppose that you are in love with a lady on Neptune and that she returns the sentiment. It will be some consolation for the melancholy separation if you can say to yourself at some—possibly prearranged—moment, “She is […]

Coney Island

Inspired by this story (“Good news! Researchers respond to a correction by acknowledging it and not trying to dodge its implications”): Coming down from Psych Science Stopping off at PNAS Out all day datagathering And the craic was good Stopped off at the old lab Early in the morning Drove through Harvard taking pictures And […]

Contributing to open source projects

David Heinemeier Hansson presents a very gracious view of open source software in his keynote address at RailsConf 2019. And by gracious, I mean gracious in the theological sense. He says at one point “If I were a Christian …” implying that he is not, but his philosophy of software echos the Christian idea of […]

Stone-Weierstrass on a disk

A couple weeks ago I wrote about a sort of paradox, that Weierstrass’ approximation theorem could seem to contradict Morera’s theorem. Weierstrass says that the uniform limit of polynomials can be an arbitrary continuous function, and so may have sharp creases. But Morera’s theorem says that the uniform limit of polynomials is analytic and thus […]

Distribution of zip code population

There are three schools of thought regarding power laws: the naive, the enthusiasts, and the skeptics. Of course there are more than three schools of thought, but there are three I want to talk about. The naive haven’t heard of power laws or don’t know much about them. They probably tend to expect things to […]

Landau kernel

The previous post was about the trick Lebesgue used to construct a sequence of polynomials converging to |x| on the interval [-1, 1]. This was the main step in his proof of the Weierstrass approximation theorem. Before that, I wrote a post on Bernstein’s proof that used his eponymous polynomials to prove Weierstrass’ theorem. This […]

Did that “bottomless soup bowl” experiment ever happen?

I’m trying to figure out if Brian “Pizzagate” Wansink’s famous “bottomless soup bowl” experiment really happened. Way back when, everybody thought the experiment was real. After all, it was described in a peer-reviewed journal article. Here’s my friend Seth Roberts in 2006: An experiment in which people eat soup from a bottomless bowl? Classic! Or […]

Lebesgue’s proof of Weierstrass’ theorem

A couple weeks ago I wrote about the Weierstrass approximation theorem, the theorem that says every continuous function on a closed finite interval can be approximated as closely as you like by a polynomial. The post mentioned above uses a proof by Bernstein. And in that post I used the absolute value function as an […]

el lector de cadaveres [book review]

El lector de cadaveres (the corpse reader) by Antonio Garrido (from Valencià) is an historical novel I picked before departing to Japan as the cover reminded me of van Gulik’s Judge Dee which I very enjoyed (until a terrible movie came out!). Although van Gulik apparently took the idea from a 18th-century Chinese detective crime […]