Exploring Bayes' Rule in 5 Levels of Complexity

Bayes' Rule lets us update probabilities (and our beliefs!) based on new evidence. Let's explore Bayes' Rule in 5 levels, starting with medical testing and trial evidence, and ending with an exploration of the power of Bayesian statistics.

This video was sponsored by Brilliant.

00:00 Introduction
00:38 Level 1 - Medical Testing
03:11 Level 2 - Trial Evidence
05:36 Level 3 - Proving Bayes' Rule
07:00 Sponsored Message
08:35 Level 4 - Continuous Case
11:13 Level 5 - Bayesian Statistics

[keipfar]

This is one of the cleanest explanations of Bayes rule I have ever seen.

[j-rey-]

I studied math in college, and I can say, without a doubt, that probability is the most counterintuitive branch of math I have personally experienced, and maybe the most counterintuitive in general. It is no surprise that the average person doesn't understand it at all.

[diribigal]

My secret is that I've never understood the difference between being a Frequentist and being a Bayesian. When I read a description of what *either* group believes, I just think "yeah, that sounds reasonable".

[avaraportti]

Conditional probability is both the hardest and the most important concept in probability

[davidcollins]

I've taught statistics at University. This is a great educational video.

[jasperdavdson]

So glad the algorithm let me come and learn something from you again before I take statistics

[karraguer]

Very cool. Examples related to information theory and communications are also very clear.

[RSLT]

Wow, this a fantastic video on bayes' rule ❤

[TRex-fubt]

My favorite application of Bayes is running the inference engine in reverse. That is, fitting a model and using it to simulate new data.

[j-rey-]

I wanted to bring up this video again that I would love your perspective on. Numberphile did a cool video about 1 + 2 + 3 + ... = -1/12 that makes it seem like it has practical applications, and isn't just a mathematical curiosity. Some of their steps are pretty dubious in my opinion, namely the part where they introduce a cos(n/N) just after the 10 minute mark, so you may be able to shed some light on it. The video is called "Does -1/12 Protect Us From Infinity? - Numberphile"

[valentinussofa]

I love math. Thanks to YouTube algorithm. Finally, I found this precious learning channel.

[raileite]

Amazing video, reminded me of important concepts while also deepening my knowledge, in a fast, direct and practical way.
Congratulations on the continuous sponsor from Brilliant.

[intrepiddt]

What a great explanation! Thank you for creating such content.

[SuryaBudimansyah]

Statistics is my main weakness of mathematics, so I'll just leave a like

[hdrevolution]

You're one of the most intelligent YouTubers I've ever seen

[gustavoalejandromorletavil]

Polymer distributions wpuld be my favorito application of Bayes' theorem

[HloBruh]

So I was messing with complex numbers and Euler's formula and I came across this:
e^2πi = e^(πi)2 = cos(2π) + isin(2π) = 1 + i(0) = 1
So e^2πi = 1 so 2π1 = ln(1) but ln(1) = 0 so 2πi = 0 BUT HOW???