A Bayesian gambling problem

First, let me start off with what this post is not. It is not a thorough discussion into the arguments between Frequentists and Bayesians. With that said, I’ll provide a resource at the end in order to highlight the differences between these two views and give you a reason to care about Bayesian statistics. I delved into this subject myself not too long ago using a course on Coursera that I highly recommend, and this is my attempt to introduce and summarize some of the fundamental ideas.

The Bayesian model is an important paradigm that should be part of an introductory statistics course, yet when I took my university’s equivalent of “Stats 101,” we didn’t even make it to good ol’ NHST (null hypothesis significance testing). Furthermore, a quick Google search doesn’t seem to reveal a lot of “friendly” guides akin to Khan Academy for basic statistics and Paul’s Online Math Notes for calculus. There are some posts, slideshows, and long pdf textbooks that are pretty good, but I find myself glazing through blocks of formality, convincing fooling myself that I understand the concepts, and then losing interest like a kid in high school just waiting for the bell to ring. Ideally, this post will encapsulate the main ideas in a more captivating way.

Finding the perfect cup of coffee with gradient descent (part 1)

In middle school, there was a rather popular website kids went to called Cool Math Games (don’t worry, it’s not terribly sketchy). Anyway, I forget the specific details, but I do recall having a bit of “independent time” to work on educational-related things, and one student assured our teacher that the site was indeed, educational. When she found out that learning consisted of Bloons Tower Defense and other nonsense, well…let’s just say that was the end of that. Don’t get the wrong impression; despite this incident, my 6th grade teacher an amazing educator and inspiring individual. Also, Cool Math Games did have some information on mathematics such as an article on counting I tried skimming over at the time. I gave up upon encountering \(n \choose k\), kind of like how I recently struggled through an entire day trying to understand tensors.

The Photoelectric Effect

A while back, I created a small demo on Khan Academy. Since I’ve decided to use this blog to post educational material (and other things that I have yet to decide on), I figured that I may as well take the time to share and flesh out a mini lesson plan. Of course, after I found a way to embed Processing.js, I realized that the default angle mode is in radians while Khan Academy defaults to degrees. As a result, the CodePen snippet below has some hacky-looking modifications from the original, but it’s mostly identical. Either way, this is a good reminder to 1.) use radians from now on, and 2.) work on factoring out more constant variables so that I don’t have to go on a programmer’s version of hide-and-go seek. With that mental note out of the way, onto the lab!