About
I am a PhD student in artificial intelligence at Stanford University. My undergraduate degree is in math, and I like to apply the mathematical framework that I’ve acquired to more applied fields; I think this gives me a unique perspective on them. It also has the advantage of allowing me to more concisely explain the topics in these fields to other mathematically oriented people. That is one of the purposes of this blog.
The other primary purpose is to convince the reader that a field does not have to have a deep underlying theory in order to be academically interesting. In fact, I find artificial intelligence, which has comparatively little theory behind it, to be a fascinating field.
I also find blogs to be a good pedagogical format, and pedagogy, in addition to being inherently rewarding, helps me to organize my own ideas and suggest new directions of research. So this is yet another reason why I keep this blog.
Academically Interesting 
Great post on probability. I know that writing posts like this takes a lot of time and effort, so thanks for doing it. Also, you might want to make a small edit and change your data from (3,5,3) to (3,5,3,3,3,5) in the following equation:
p(2 numbers | (3,5,3)) / p(3 numbers | (3,5,3)) = (1/2)^6 / [9 * (1/3)^6] = 81/64.
Do you have any more good sources on Bayesian modeling? I’ve done a little in the past, but I’m really stuck in a frequentist mindset.
Sorry, your comment got caught by the spam filter initially. Thanks for pointing out the typo, I’ve gone ahead and fixed it in the post.
I personally learned about Bayesian modeling from Josh Tenenbaum’s lecture notes (he’s a cognitive science professor at MIT). The class materials should be here (not sure if the site is publicly accessible): https://stellar.mit.edu/S/course/9/fa09/9.66J/. You could also try the old OCW page for the class: https://ocw.mit.edu/courses/brain-and-cognitive-sciences/9-66j-computational-cognitive-science-fall-2004/.
There are also various articles on Bayesian modeling on https://lesswrong.com/. The website focuses more generally on rationality, so most of the posts will be on other topics; but I found that some of the posts there helped me correct flaws in my understanding.