The quick proof of Bayes’ theorem

Hi David, happy new year to you too! Thanks for the kind words, I hope you enjoy the follow on probability content soon to come...

3blue1brown

Happy New Year - love your videos and think you're making math more accessible and interesting. I have appreciated new ways of seeing things thanks to your videos

Thanks so much!

3blue1brown

Love your imagination! I want to support you so that you keep making great videos. You're changing math education, which I believe is so badly needed. Cheers!

The thought is that it’s useful to have seen for if we get to a topic like maximum likelihood estimation.

3blue1brown

Excellent as always. I do have a small suggestion, however. You introduce the term 'likelihood' but do not use it subsequently. It is an example of statisticians taking a perfectly normal English word and using it in a totally different technical sense (likelihood of what, exactly?). Do you need to introduce the term at all? Or if you must, should you say a bit more about it. Some statisticians use the term 'data model' in place of 'likelihood'.

Oh, yes, all that probability things looks just like The Monty Hall Paradox. I don't know how is it possible to feel such a things, like probability math, they are so counterintuitive.

1D_Inc

Maybe it's me, but for me this one is not as clear as it could be. I think it's the following people often do not realize. If we consider the discrete case, p(a) and p(b) are 1-dim vectors. However, p(a|b) and p(b|a) are matrices. So is p(a,b). The multiplication of the vector p(a) and the matrix p(b|a) gives the matrix p(a,b). Or, the other way around if we divide p(a,b) by the vector p(a) we get p(b|a). You can visualize this by doing a sweep. If you color p(a) with different shades of red depending on the probabilities in the vector, you can make it - I think - very clear. Color p(b) with different shades of blue. Most importantly, color p(a,b) as well. It has information on top of the information in p(a) and p(b). That's something else people do not often realize. The joint distribution has information about the interplay between a and b, not about a and b itself.

The geometric illustrations really help me, especially when the two variables are not independent.

white beard geek

I found the visual proof in the first minute much less clear than the original video. Maybe it was too fast... but it didn't connect the geometry of the boxes to the formula as well IMO. The part about independence was nice and a worthy foot note on its own.

Gabe

This is how I learned Bayes's Theorem - Memorize a Formula and hope to know when to use it. I never knew when to use it. I'm so glad Grant's taken this approach.

Very nice footnote!

Gregor Shapiro