Oscar Bonilla

I'm sad that every explanation of MCMC uses complicated symbolic explanations. I was trying to explain it once and came up with a fairly intuitive way to visualize it. Probably that is the way it was first discovered, though who knows.

In words, you can visualize it as doing a random walk around the area of a probability graph. Then it just turns into an explanation of why random walks accurately sample from an area, and the various tricks used in MCMC methods to make random walks more efficient.

Relatedly, bayes theorem makes much more sense when you visualize it, e.g. this post: https://oscarbonilla.com/2009/05/visualizing-bayes-theorem/

Good article.

I'm only a bit disappointed that the author seems not to realize that Bayes' theorem is just a simple consequence of probability theory, and should be attractive not because "maybe the brain is Bayesian", but because it is based on sound set-theoretic and analytic principles. If Bayes' theorem is false, so is probability theory, and so is nearly everything we know about probability.

Edit: Here is a good explanation of the theorem that makes it visually clear how only set theory is involved in deriving it: https://oscarbonilla.com/2009/05/visualizing-bayes-theorem/

https://brohrer.github.io/how_bayesian_inference_works.html

https://oscarbonilla.com/2009/05/visualizing-bayes-theorem/

https://plus.maths.org/content/maths-minute-bayes-theorem

http://www.sumsar.net/blog/2017/02/introduction-to-bayesian-data-analysis-part-one/

http://www.yudkowsky.net/rational/bayes