Flippin’ Fun!
Bayes
Stan
Python
I wrote an answer to a question about sequences of coin flips a couple days back that I was quite chuffed with. In short, the question asked for statistical ways to determine if a sequence of coin flips was from an unbiased coin or a human trying to appear random. The resulting model turned into a fun game on twitter centered around determining if people who follow me could simulate a sequence of coin flips that looked random (without using a real RNG, or some funny workaround. I have a lot of faith in my twitter followers…maybe too much).
Hacking Sklearn To Do The Optimism Corrected Bootstrap
Statistics
Machine Learning
Python
Scikit-Learn
Its late, I can’t sleep, so I’m writing a blog post about the optimism corrected bootstrap.
On Interpretations of Confidence Intervals
Statistics
The 95% in 95% confidence interval refers not to the probability that any one interval contains the estimand, but rather to the long term relative frequency of the estimator containing the estimand in an infinite sequence of replicated experiments under ideal conditions.
Gradient Descent with ODEs
Python
Machine Learning
Statistics
Gradient descent usually isn’t used to fit Ordinary Differential Equations (ODEs) to data (at least, that isn’t how the Applied Mathematics departments to which I have been a part have done it). Nevertheless, that doesn’t mean that it can’t be done. For some of my recent GSoC work, I’ve been investigating how to compute gradients of solutions to ODEs without access to the solution’s analytical form. In this blog post, I describe how these gradients can be computed and how they can be used to fit ODEs to synchronous data with gradient descent.
Coins and Factors
Python
Riddler
I love Fivethirtyeight’s Riddler column. Usually, I can solve the problem with computation, but on some rare occasions I can do some interesting math to get the solution without having to code. Here is the first puzzle I ever solved. It is a simple puzzle, yet it has an elegant computational and analytic solution. Let’s take a look.
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