[no_identd]

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:

https://econ.ucsb.edu/~doug/240a/Coin%20Flip.htm

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".

[jointpdf]

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.

[nyc111]

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.

[jackpirate]

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:

https://www.stat.columbia.edu/~gelman/research/published/dic...

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:

https://izbicki.me/blog/how-to-create-an-unfair-coin-and-pro...

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

https://izbicki.me/blog/how-to-cheat-at-settlers-of-catan-by...

[no_identd]

>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.

[olooney]

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

What metaphor for a Bernoulli trial do you prefer?

[hackermailman]

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...

[theoh]

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

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

https://math.uchicago.edu/~shmuel/Network-course-readings/MC...

[hopler]

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