Summer of Math Exposition

A very clear and original approach to the Bayes’ Theorem. I think I will use the example of this video for my lessons.

The treasure hunt example provides good motivation for the topic. The explanation is mostly clear, although the Bayes Theorem formula appears very suddenly, and isn’t explained. There is some novelty in the choice of the example, but otherwise the video doesn’t stand out. The example is also quite memorable, and the reasoning behind the probabilities should be easy to remember. The conclusion about medical tests is rather memorable too.

Nice video for introducing Bayes theorem. I believe most of the parts were clear. The only part I found confusing is why we can stop early when we find junk… I mean, since we found it already - isn’t it the same as finding gold? Do you count the time we spend picking it up? That part wasn’t clear to me.

The video is memorable and has a good motivation [finding gold = getting rich :-)]. The novelty is the weakest point, I believe. There are many toy examples like this out there.

I like the topic of this video, but I don’t think it was all that effective overall. I’m still not quite sure what the main point is supposed to be. I feel like if I were an instructor I would be able to produce a better lesson, and for the video to be useful I should feel that I could NOT do better.

I enjoyed the putting data in context

Ironically, the examples’ confounding variables make the explanation more confusing. No numerical examples were given for the time spent on detected junk versus gold coins, and it was not explained why the follow-up test to separate out the people with the disease can’t be used on the whole population to begin with since it’s so much more accurate. Other explanations of Bayes’ Theorem describe it as updating knowledge through multiple tests rather than determining an initial success rate; in these examples, if your friend followed behind you with the other metal detector and scanned your findings before you started digging, or if someone takes the medical test twice and gets a positive result both times. The most helpful part of this exposition is the beginning, where the success rate is calculated and fewer false positives (detector B) is shown to yield better results over more true positives in this example.

Overall an alright video, but unfortunately, unless I’m missing something, I don’t think you came to the correct conclusion given the metaphor you were building. You had me for most of the problem, but it broke down for me when you said “we can quickly discard the non-gold false-positives”.

I thought the entire reason we were deciding between the two metal detectors was because we only have a day on the island? Because of this limited amount of time, I assumed the actual problem was having to maximize the amount of time we are digging for gold rather than junk, so we maximize the chances the detector detects gold. If it’s trivial to discard the false positives, then the choice is obvious between the two. We might as well have a metal detector with 100% true and false positive rates.

It’s because of this that the medicine analogy doesn’t quite fit either. I see what you were trying to do with Bayes acting as a sort of seive, that’s an interesting way of looking at it that I’ve never seen before that seems useful, but the connection to the main problem just doesn’t quite work.

Initial Thoughts

Great job! I really enjoyed the video, and thought it was a great example for showing how true positives and false positives compare.

What was Great

Your explanation was very simple and easy to understand, which I thought was great, especially for the high-school/undergraduate audience you have listed. The visuals you used with the squares to show the probabilities made the math much easier to see. I also really enjoyed the follow up equations showing the correct beeps over the total beeps. That put the theorem in intuitive terms, making it feel like common sense.

Ideas for Improvement

One thing that I think could have made the video better is a transition from the intuitive explanation to an explanation of the formula for Bayes’ Theorem that you showed. It’s been a while since I’ve done any statistics, so I had to pause the video and digest the notation for a minute to make sure I understood what it was saying. Taking a little time to show how the notation in the formula translates back into the intuitive formula you showed visually or vice versa would be helpful.

Concluding Thoughts

Overall, I was impressed with your video, both with the useful content and the fun example you used to explain it. I know I would’ve appreciated this video if it were there when I was a high schooler first learning about statistics. Thanks for putting it out there!

Nice but the narrative is has large gap between words

Nice video. I’d try to edit some of the pauses in the audio to be shorter, they get a bit awkward. Also I’m not sure if this is the example because detector A will beep way more often so you can dig stuff up at a faster rate. This is very pedantic but it would’ve been good to say “you can only dig x times due to wildlife conservation laws” or something silly like that.

A clear explanation of Bayes’ theorem with a fun example. I think the “amazing” point, that “the highly sensitive 99% detector is mathematically worst!” isn’t explicit enough. Maybe playing around with the numbers to make the gap between detectors bigger. The false positives are explored but I think the video could delve deeper into false negatives and the “lost” gold.

I liked the concept of finding gold and junk in terms of reframing the probability in terms of the context here. Maybe metal detector might not be the best case here because it should always detect certain metals, and another framing of the problem could be more intuitive. It might also help to show why this is independent of how the data is distributed on how one is better then the other on how this really shows Bayes’ theorem, and what is the importance of it, as it isn’t clear what Bayes’ theorem would immediately apply here to someone who has not seen it.