Summer of Math Exposition

It would have been nice to see the video addressing the example with the traffic intersection again at the end. Other than that, the video is well structured. However, I think it would have been better to submit a video that is its own video and not a second part to another video.

A nice adaptation of the Sun Rise Problem, something I found quite difficult to follow when I came across it recently in a book of mine. Well done!

if i could suggest anything it would be to take more breaks in the narration motivation >5/10 clarity >5/10 novelty 5/10 memorability 5/10

I liked the examples that really helped me to better understand the mathematics in a "simpler" way. The animations also really helped.

Motivation: Very good. I was a bit nervous at first that the motivation would lie solely on the "cutesy" baby example, but was pleased to see you gave a nod to more realistic applications. Clarity: Exceptional. Animations added to the narrative, which was already quite cleanly laid out. My only complaint is that in the symbolic notation for the posterior (e.g. at 6:58), I had some difficulty because I didn't realize that this was representing an entire distribution rather than the probability of a particular event— that's what I "expect" P(A | p_i) to mean. But this was clarified quickly as you got into the visuals soon afterward. Novelty: I can't really speak to this because I've not seen an analysis of this sunrise problem, at least not carefully enough to notice where this explanation was different. Nevertheless, I thought it worked quite well, and particularly appreciated the analysis of sample size and prior effects. Memorability: This gave me probably the best understanding I've seen so far about how the vocab words (posterior, etc.) fit into the components of Bayes' Theorem.

Your visualizations are excellent and do a good job of demonstrating the concepts, and your choice of discretizing the statistics involved was an excellent choice for promoting understanding. My major issue is that your target audience for this video series (including part 1) seems to me to be people who already understand Bayesian stats, if only at a surface level. I think something that contributes negatively towards that impression is that we didn't really build up towards our answer over the course of the video - we simply asked the question corresponding to the *next* step at every point, as opposed to working backwards from the end to justify the method. When it comes to following through lines like this, the old adage about essay writing comes to mind: "Show them what you're gonna tell them, then tell them, then remind them what you just told them." Right now we're missing that "Show" part except in this nebulous way of "oh we'll be using Bayes, which can answer questions like this one". Interjecting the example of a traffic intersection when teeing up the rest of the video is probably more hurtful than helpful, considering that you don't revisit it in the future as an example with different priors. One other thing I feel like I should recommend is that the "trivial" example should likely be the second "test your understanding" example; it felt weird seeing you calculate the probability for p=1 (where the number of observations makes absolutely no difference) and challenge with p=0.9 (where the number of observations makes an obvious difference). Overall, your visualizations are beautiful, but I fear that some of the lesson structure will bounce off a more general audience especially in terms of memorability and clarity.

interesting