This is a very well done presentation - I am genuinely impressed. We could use more of these types of explanations. The more people who understand, the more help we have.
I have always visualized probability and conditional probabilities in terms of Venn diagrams, it is easier to understand stuff this way. I think this is _the_ best way to teach probability to a beginner. What do you think ?!
I am reminded of something I read in Isaac Asimov's book on astronomy, where he talked about his great idea for how to visualize the size of distant objects and how lamentable it was that people don't use his obviously superior method.
I stared at the pages unable to comprehend how he thought the size of a penny held a mile away was easier to visualise than the alternative.
Likewise Eliezer's "Intuitive" explanation of Bayesianity - I've read through it twice (lightly) and it's thoroughly not intuitive. I'd need to study it not just read it.
Presumably there is some distance from my current mental state vector to any with a comfortable grasp of Bayesian probability, and some explanations will take a quick route and some a less direct one. Hence, I think there are different 'best' explanations for different people depending on what they already know, what they want to know and what they want to touch upon along the way.
I'm skeptical that there is one "_the_ best way" to teach probability, or anything else.
I think, for a majority of people, it would be an easier way to study probability. Visualization makes things much more understandable than algebraic formula derivation.
Yea maybe I am bit biased about my opinion because I understood probability easier using visual examples, but people who I have interacted with mostly also understand things easier in the visual form. So I think it maybe _the_ best method to teach probability because it will reach out to a majority of people, ofcourse, there might be people who might understand it better if explained in a different way, but that maybe a minority, so all the different methods can be tried out in school.
One more thing I would like to add is that everyone has a biased opinion of things based on their perception of the world and that's why I think there should be debates. Generalizing from examples and experiences is a natural method developed during evolution.
If a kid touches a hot plate and experiences pain, I think it is perfectly valid that it should generalize that to all other hot plates. :)
I've always been confused about Bayesian probability, until I read that article. I am a heavily visual learner, so the diagrams made a lot of sense to me...I finally get it!!
I think of it as the joint variable event space relative to (or normalized by) the condition variable event space. In a few words what is shown in the article diagrams.
I don't actually remember the formula for Bayes' theorem. I just visualize it as shown in this article, and write down equations from there. For me, anyway, that is actually a more reliable way of working.
I just skimmed the article, having received treatments of Bayes' theorem many times over the course of my almost-finished college career; however, I think this is neat, because making use of visualization/imagery is a good approach to teaching and understanding statistics, which the human brain is (typically) not capable of handling well.
