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Seeing Theory: A visual introduction to probability and statistics (2017) (brown.edu)
526 points by jicks 4 months ago | hide | past | web | favorite | 18 comments

Glad to see this once more.

Some Hacker News Discussions of this:

1. https://news.ycombinator.com/item?id=13735714

2. https://news.ycombinator.com/item?id=13760353

I wish they'd cover the sample space/parameter space distinction "harder", as it seems key to the numerous philosophical divides in the foundations of statistics & probability theory, and it seems like a very good candidate for colorful & animated visualization.

Also, note that the classic coin flipping example used there right in the beginning serves as an extremely bad & misleading analogy, see here for why:


I wish we'd stop using it in Stats & Physics 101, or at least add huge disclaimers to it, something like "Coins don't actually behave this way, not even mathematically idealized ones".

Coin flipping is a canonical example that has historical, theoretical, and practical relevance--it's definitely a bit much to call it "extremely bad & misleading". Mathematically idealized coins do behave in this way, because you have the freedom to define the probability of the events however you like (so long as you do not violate the axioms of probability).

Also, there are lots of (abstract) mathematical nuances to explore around coin flipping once you get into stochastic processes (there are special aspects of Bernoulli RVs with p=0.5).

Besides, sometimes an imperfect example is a better one--it can stimulate thought and discussion about how well concepts--like modeling a coin flip with a random variable--map to the real world.

The chance part of the coin flipping comes from the inability of the human hand to adjust the speed of flipping exactly the same everytime. Is this correct? A coin flipped by a robot should land the same side always.

Your ucsb link describes an unfair coin flipping protocol, and not the fair protocol commonly used in practice. In particular, it provides a "strategy" at the end to generate an unfair toss (which requires, e.g., that you be both the flipper and the chooser). Other studies, such as the famous You can load a die, bit you can't bias a coin investigate fair flipping protocols and argue that you cannot, in fact, bias a coin:


I have some blog posts on developing biased coins and dice, and the results show that any coin with a measurable bias is quite obviously not fair:


whereas you can undetectably bias dice at home with just a bit of water:


>Your ucsb link describes an unfair coin flipping protocol, and not the fair protocol commonly used in practice.

It ALSO does describe this, yes. However, the way you phrased your comment makes it seem like that contradicts what I said whereas it doesn't seem to, as the post I linked also outlines innate issues with fair coin flip protocols:

>Let's assume the coin is fabricated perfectly, down to the last vigintillionth of a yoctometer. And, since it's possible to train one's thumb to flip a coin such that it comes up heads or tails a huge percentage of the time, let's assume the person flipping the coin isn't a magician or a prestidigitator. In other words, let's assume both a perfect coin and an honest toss, such as the kind you might make with a friend to decide who pays for lunch.


>In that case there's an absolute right and wrong answer to the age-old question...


> Heads or tails?


>...because the two outcomes of a typical coin flip are not equally likely.


>The 50-50 proposition is actually more of a 51-49 proposition, if not worse. The sacred coin flip exhibits (at minimum) a whopping 1% bias, and possibly much more. 1% may not sound like a lot, but it's more than the typical casino edge in a game of blackjack or slots.

The comments there then further discuss this.

I saw Persi Diaconis lecture on coin flips and shuffling cards once. Very interesting guy.

What metaphor for a Bernoulli trial do you prefer?

Lecture 16 in this Discrete Probability pdf[1] covers how Diaconis and his students decrypted some prison ciphertext brought to them

[1] http://www.cs.cmu.edu/~odonnell/papers/probability-and-compu...

I found the original account by Diaconis, with more detail:

"The Markov Chain Monte Carlo Revolution" (it's the first example in the paper)


In other news, physics textbooks are all wrong because infinite sheets and spherical cows don't exist.

I looked up the Victor Powell visualization they cite and it's quite a bit more in-depth then the version they have:


But seriously, all of these interactive visualizations are amazing. I wish they had this kind of stuff when I was an undergrad. I remember trying to plot the beta distribution for different alpha and beta parameters in MATLAB trying to get an intuition for it; just dragging the sliders around on the prior and watching it update as each data point comes in is a million times more accessible.

Sometimes a good analogy can take the place of a visualization [1], albeit I did imagine a distribution getting more concentrated.

[1] http://varianceexplained.org/statistics/beta_distribution_an...

Great visualizations. Really liked the practical examples it had for every topic. Only problem I felt was, that there wasn't an underlying explanation why one thing followed another. And without understanding the problems you are solving, you can't really appreciate the hundreds of years worth of mathematical progress leading to these innovations.

Slightly off topic, but beautiful site. I love sites that change and update the content in a floating manner as you scroll... NYT website has had articles like this for the past few years..

Does anyone know of packages or libraries that can help you do this? Or do I just need to hack my own JavaScript?

"Scrollytelling" is the term you're looking for - The Pudding did a solid walkthrough of a few libraries [1], and I've found scrollama [2] to be a solid bare-bones library. This talk [3] is a few years old, but it's a good one for seeing some different approaches scrollytelling can take.

[1] https://pudding.cool/process/how-to-implement-scrollytelling...

[2] https://github.com/russellgoldenberg/scrollama

[3] http://vallandingham.me/scroll_talk/examples/

Thanks for this. That's exactly what I was looking for.

Scrollytelling is a terrible name! But at least theres a term for it.

Reminded me of https://ncase.me/trust/

Love to see people trying to make topics in math and cs more accessible to a wider audience

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