11–20 of 21 posts
Got a lot of respect for Andrew Gelman, but it's too bad he didn't cite Persi Diaconis: http://statweb.stanford.edu/~susan/papers/headswithJ.pdf
The Gelman-Nolan paper is from 2002; the Diaconis et al. paper is from 2007, and cites Gelman-Nolan. Gelman and Nolan are pretty smart, but they don't have a time machine.
It's already biased towards the face that is facing up to start. With practice or by accident, you can toss it so that it wobbles but doesn't actually flip over. A casual observer cannot tell the difference. Explained in http://www.amazon.com/Heads-Or-Tails-Gary-Kosnitzky/dp/B00FM...
TODO: Build a robot with precise enough control that it can flip a coin (properly flipping, not just wobbling) and then catch it in a desired state (either heads or tails) with substantial accuracy.
It's already biased towards the face that is facing up to start. With practice or by accident, you can toss it so that it wobbles but doesn't actually flip over. A casual observer cannot tell the difference. Explained in http://www.amazon.com/Heads-Or-Tails-Gary-Kosnitzky/dp/B00FM...
TODO: Build a robot with precise enough control that it can flip a coin (properly flipping, not just wobbling) and then catch it in a desired state (either heads or tails) with substantial accuracy.
More to the paper, I liked the point about using unexpected results to drive student engagement. In one of the early episodes of Very Bad Wizards, they described some aspects of teaching as like a magic show. I think it's a good analogy.
( The post got truncated by a bad character in my blockquote paste (sorry!). It should be legible now (and include two figures). )
Got a lot of respect for Andrew Gelman, but it's too bad he didn't cite Persi Diaconis: http://statweb.stanford.edu/~susan/papers/headswithJ.pdf
Earlier quoted context omitted.
The Gelman-Nolan paper is from 2002; the Diaconis et al. paper is from 2007, and cites Gelman-Nolan. Gelman and Nolan are pretty smart, but they don't have a time machine.
Indeed Diaconis et al. cites Gelman-Nolan.
"In light of all the variations, it is natural to ask if inhomogeneity in the mass distribution of the coin can change the outcome. [Lindley, 1981] followed by [Gelman & Nolan, 2002] give informal arguments suggesting that inhomogeneity doesn’t matter for flipped coins caught in the hand. Jaynes reports that 100 flips of a jar lid showed no evidence of bias. We had coins made with lead on one side and balsa wood on the other. Again no bias showed up. All of this changes drastically if inhomogenious coins are spun on the table (they tend to land heavy side up). As explained above, some of this bias persists for coins flipped onto a table or floor."
You have to love Persi Diaconis. Having coins made up with lead on one side and balsa wood on the other.
That's why cypherpunks each bring their own coin and XOR the heads. Or flip a biased coin twice. If you get HH or TT, discard and start over. If you get HT or TH, take the first flip of the pair. More to the paper, I liked the point about using unexpected results to drive student engagement. In one of the early episodes of Very Bad Wizards, they described some aspects of teaching as like a magic show. I think it's a…
> That's why cypherpunks each bring their own coin and XOR the heads
I'm not sure what part of the article you are referring to here, but this is more about the XOR being decorrelated from either of the inputs than about anything to do with the efficacy/existence of a biased coin, right?
It's already biased towards the face that is facing up to start. With practice or by accident, you can toss it so that it wobbles but doesn't actually flip over. A casual observer cannot tell the difference. Explained in http://www.amazon.com/Heads-Or-Tails-Gary-Kosnitzky/dp/B00FM...
TODO: Build a robot with precise enough control that it can flip a coin (properly flipping, not just wobbling) and then catch it in a desired state (either heads or tails) with substantial accuracy.
http://www.npr.org/templates/story/story.php?storyId=1697475