TLDR
📺 What’s happening with videos?
Recent: The algorithm that (eventually) revolutionized statistics: A video on the Metropolis Algorithm and my submission to the Summer of Math Exposition contest. Last year was bootstrap, this year is Metropolis, and I have a pretty good idea what I want to do next year (another famous algorithm).
Upcoming: An explainer for the chi-squared test
📰 What is this issue about?
How I approach learning for both videos and research
🧐 What am I enjoying right now?
Book — I’m still preparing for JSM (Joint Statistical Meeting) in August. I’m reading some clinical trial textbooks to get ready for on-site interviews. I’m going through Adaptive Design Methods in Clinical Trials by Chow and Chang to buff up my adaptive trial knowledge.
Thing — Melting to the recent heat wave. Buying an ice making machine was a godsend.
📦 Other stuff
I wrote guided solutions to problems to Andrew Gelman’s Bayesian Data Analysis. It’s for advanced self-learners teaching themselves Bayesian statistics
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In this issue…
I wanted to discuss the recent process I went through to finish my submission to the Summer of Math Exposition competition (SoME, community edition).
I like to use the competition as a way to challenge myself. Normally, I try to choose a topic that I don’t already have a solid grasp of. Last year, I chose the bootstrap and that was WAY above my comfort level. But, I did my best to explain everything that I had learned during my research and learning process. It definitely wasn’t perfect, but it was very intellectually gratifying.
This year I went with Markov Chains and the Metropolis algorithm. I’ve never learned about either, but I was aware that they were immensely important to statistics. So it was a great candidate to tackle for the competition.
A recipe for fast learning
Since I try to stick to a biweekly upload schedule, I only had two weeks to learn about the algorithm, see how it works and try to convert that into a video. It’s not a comfy timeframe, but it was workable.
What’s different with a competition video compared to a regular video of mine nowadays is that I need to do a lot of research and reading to develop the script. This takes up a lot of time, and it’s in my best interest to do it fast.
So how do you quickly pick up a topic you don’t know much about?
Find the “Cliffnotes” ASAP
One mistake I used to make was to start directly with the source material; in this case, the original manuscript for the Metropolis algorithm. One advantage of looking at the source paper is that you can understand the problems and perspectives that the authors were concerned about when they made the paper. This can help you understand where the authors are coming from.
But, a downside is that you may have no idea how this problem is relatable to a wider audience. What was tougher with the Metropolis paper was that it was written for a physics audience. I can see some of the equations and see some statistical analogues, but it’s not always clear to me.
It’s still possible to learn from the original paper, it just might be slow. A faster thing you can do is to find another paper that reviews or gives a historical perspective on the thing you’re learning about. In history jargon, this would be a “secondhand source”. In my case, a review article by Chib and Greenberg reviewing the algorithm was a godsend. They gave me the context I needed in language I could understand.
Maybe it might feel a little cheap to read someone else’s analysis and perspective on a groundbreaking algorithm. It’s okay. 99% things under the sun are not new, but most people haven’t seen what’s there, so you might as well try to put it in your own words. You will learn a lot faster from trying to do that anyways.
Another “Cliffnotes” you can use in a general research context are textbooks or review articles. They should be the first thing you look for when you’re diving into a new area. The authors have already done all the heavy lifting of picking out the main papers and idea. Maybe not the most innovative stuff, but enough to canvas.
Stress test a personal metaphor
A good way to stress test your understanding is to develop an ongoing metaphor for whatever topic you’re trying to learn. For me, I developed a metaphor using travel and spending time in a new city. Markov Chains deal with “states” and distributions of these states, so it made sense to me.
But in learning the Metropolis algorithm, I regularly needed to tune the metaphor to fit it better. The target distribution became “how a local spends all of their time”, something no one would know about if you asked them. But Metropolis compares the current state to the possible next, which lends itself well to comparing preferences.
It won’t be perfect, but that continual challenge is good for forcing you to try to encode that knowledge. I couldn’t figure out a great way to explain that complicated acceptance probability that appears in the Metropolis algorithm.
I debated including the algorithm in the video or not, but in the end, I opted to keep it. It helped me understand the algorithm better. It might piss some people off who don’t get it or hate the obfuscation of technical details, but if it helped you, there’s a good chance it can help someone.
Be comfortable with shotgun learning
In undergraduate classes, and even graduate classes to some extent, a professor largely dictates what you learn. Most of the relevant information and exercises are included.
But this nice framing is mostly absent in Ph.D learning. A textbook or review article can get you far, but they will only go so far as their publish date. From there, you’ll face a scattershot set of research articles, programming tutorials and nice blog posts when you’re learning. There’s no guiding principle in all these different sources, other than the fact that they all have the same topic.
This is very uncomfortable at first. It’s very easy to bemoan that “no one taught me that we needed this”, but when it comes to research or personal projects, you have to learn it. You’re going to develop a Frankenstein-like collection of knowledge, and it’s going to feel disconnected.
But no one can ever predict what your current progress is in learning a topic, so it
The solution to this is to develop a keen sense of when you don’t understand something. It’s that feeling when you’re reading technical notation or complicated prose and you feel your eyes glaze over until you see something you do understand.
Once you start feeling this, you can start asking yourself why it doesn’t make sense. You want to get at the root cause of your confusion as fast as possible so that you can write a better Google query.
With a bunch of disparate sources, you can try to figure out where they refer to the same idea, so you can compare and contrast them. Similar notation can help with this.
Morale of the story
Learning is done in making the connections between all the relevant concepts that make up a topic. The things I’ve listed are different tactics for speeding up the development of these connections. They helped me make the Metropolis video, and I hope they’ll help you with whatever you’re learning.
Thanks for reading, see you when the next video comes out.
Christian