- August 16, 2019
# How to show that a Markov chain converges quickly

Markov chains appear everywhere: they are used as a computational tool within Bayesian statistics, and a theoretical tool in other areas such as optimal control and reinforcement learning. Conditions under which a general Markov chain $X_t$ eventually converges to a stationary distribution $\pi$ are well-studied, and can largely be considered classical results. These are, informally, as follows.

- June 8, 2019
# Some macros for making TeX source more readable

The TeX typesetting system is a lovely bit of software: one can easily use it to typeset production-grade documents such as mathematical papers. However, typesetting complex equations can be tedious, learning to use TeX well can involve memorizing a large number of macros, and it can be difficult to understand the meaning of an equation from looking purely at its source. TeX can be made more readable by utilizing packages and introducing macros to simplify code.

- September 15, 2018
# Building this website

Lots of people, both in the academic and software communities, have personal websites. Building one with today’s frameworks is easier than perhaps at any point in history, yet many people still have websites consisting of an index file inside of a folder hosted by some outdated service. In this post, I describe how this website is built, showcasing software used to make all aspects of developing and maintaining a blog intuitive and easy.

- March 23, 2018
# How to use R packages such as ggplot in Julia

Julia is a wonderful programming language. It’s modern with good functional programming support, and unlike R and Python - both slow - Julia is fast. Writing packages is straightforward, and high performance can be obtained without bindings to a lower-level language. Unfortunately, its plotting frameworks are, at least in my view, not as good as the ggplot package in R. Fortunately, Julia’s interoperability with other programming languages is outstanding. In this post, I illustrate how to make ggplot work near-seamlessly with Julia using the RCall package.

- February 9, 2018
# What does it really mean to be Bayesian?

In my previous posts, I introduced Bayesian models and argued that they are meaningful. I claimed that studying them is worthwhile because the probabilistic interpretation of learning that they offered can be more intuitive than other interpretations. I showcased an example illustrating what a Bayesian model looks like. I did not, however, say what a Bayesian model actually is – at least not in a sufficiently general setting to encompass models people regularly use. I’m going to discuss that in this post, and then showcase some surprising behavior in infinite-dimensional settings where the general approach is necessary. The subject matter here can be highly technical, but will be discussed at an intuitive level meant to explain what is going on.