Testing MCMC code, part 1: unit tests

This post is taken from a tutorial I am writing with David Duvenaud.

Overview

When you write a nontrivial piece of software, how often do you get it completely correct on the first try?  When you implement a machine learning algorithm, how thorough are your tests?  If your answers are “rarely” and “not very,” stop and think about the implications.

There’s a large literature on testing the convergence of optimization algorithms and MCMC samplers, but I want to talk about a more basic problem here: how to test if your code correctly implements the mathematical specification of an algorithm. Continue reading “Testing MCMC code, part 1: unit tests”

The Central Limit Theorem

[latexpage]The proof and intuition presented here come from this excellent writeup by Yuval Filmus, which in turn draws upon ideas in this book by Fumio Hiai and Denes Petz. Suppose that we have a sequence of real-valued random variables

\begin{equation}

X_1, X_2, \ldots .

\end{equation}

Define the random variable

\begin{equation}

A_N = \frac{X_1 + \cdots + X_N}{\sqrt{N}}

\end{equation}

to be a scaled sum of the first $N$ variables in the sequence. Now, we would like to make interesting statements about the sequence

\begin{equation}

A_1, A_2, \ldots .

\end{equation} Continue reading “The Central Limit Theorem”

JIT compilation in MATLAB

A few years ago MATLAB introduced a Just-In-Time (JIT) accelerator under the hood. Because the JIT acceleration runs behind the scenes, it is easy to miss (in fact, MathWorks seems to intentionally hide it so that users do not change their coding style, probably because the JIT accelerator is changed regularly). I just wanted to briefly mention what a JIT accelerator is and what it does in MATLAB. Continue reading “JIT compilation in MATLAB”