Summer of Math Exposition

I liked the video a lot. I had experience with MH algorithms before I watched the video. The derivation of the acceptance probability from the detailed balance equation was something that I hadn't seen before and was excellent. I found the analogy of asking people in Portland what they should do very confusing though. I also thought that your honest example of how hard you found it was good. The MH algorithm is such an all-purpose tool that it can be heard to use in any specific case. Are you sure that you ran a long enough burn in? You often need to throw away a huge number of iterations at the start to see that you've reached the stationary distribution. And you can also apply thinning, where you only keep every nth observation if you want your sample to have low autocorrelation. I think that you could have mentioned that it was such an all purpose tool. But also I didn't find the examples that compelling. As I said, I found the Portland one confusing, and it was unclear how the results from the hierarchical Bayesian model was more useful than a simpler analysis. In my own experience the advantage of the analysis is that, if you can get the sampler working, you can estimate any quantity about any distribution. My own field is change point detection, where we find sudden changes in the parameters of time series. Using MH we can ask questions like "what's the posterior distribution of the number of changes?" or "what's the posterior probability that there was a change point in this interval?", which you can't obtain from a simpler analysis.

A great hook to the video, followed by great explanations and analogies. Good job!

Rating as "Better than most" I watch a lot of math videos but in saying that I'm not particularly interested in statistics. This one though was very interesting. I liked the way you gave the history of the algorithm. The video was well paced, had good examples and was nicely explained. An engaging narrator. I would like to watch more from you - hey maybe you could convert me to like statistics.

This is an interesting topic. I think the example was unfortunate because it didn’t work.

The video provides an in-depth dive into the the topic for the the general public of math videos, myself included. Statistics is not one my general interests it the filed of mathematics, although I am fascinated when presented with an interesting statistical fact or piece of math. The video has a clear goal - to explain the Metropolis algorithm. As I saw this requires some background in the field and you made an effort to present the needed concepts. Here comes the part where I felt a bit lost. There is a lot that needs to be learned, but time is a constraint. I could follow your explanations of the core ideas and they were visually explained in a nice way. The examples with Portland were a good and fun stepping stone. The problem for me came in regards to the bigger picture. I failed to connect the dots and follow you as you reached your final goal. One thing I think can help is to simplify the the core concepts that are required. Of course this should not make the original concept simplified to the point it becomes unrecognizable. A good example for me is 3Blue1Brown's videos on the Fourier series and analysis. The idea is the same but the without the complicated parts that only get in the way thus making Fourier series more reachable. I saw that in the end of your video that you have made more videos about statistics. As a person not in the field I am looking forward to seeing more videos that show what professional statistics looks like in detail. I am open to discussion and learning more! Wishing success, Chavdar Nenov

Good motivation. Love the historical comment. Very creative explanation for Metropolis-Hastings. High-quality video.

Overall, I thought the video was well-animated, but it wasn't clear to me in the middle of the video why we needed separate distributions g and alpha. Also, I got lost at the end of the video when you started talking about the specific example.

I really liked the simple contexts you used to explore the complex ideas, like activities in Portland or the Like/view ratio. Fantastic.

The theoretical explanation was good but the implementation was a little scattered.