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#bertrand'sparadox#probability#randomsampling

Bertrand's Paradox (with 3blue1brown) - Numberphile

Numberphile

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  • Presented by Grant Sanderson, creator of 3blue1brown

Beginner. No background in the topic needed.

1.4M views4 years ago1 recommendation

Computer scienceMath for programmersAlgorithms

Grant Sanderson of 3blue1brown explains Bertrand's paradox, demonstrating how different methods of defining random chords in a circle yield different probabilities.

Featuring Grant Sanderson, creator of 3blue1brown. Extra footage from this interview: youtu.be/pJyKM-7IgAU 3blue1brown video on the shadow a cube: youtu.be/ltLUadnCyi0 More links & stuff in full description below ↓↓↓ 3blue1brown: youtube.com/channel/UCYO_jab_esuFRV4b17AJtAw Grant on The Numberphile Podcast: youtu.be/A0RH93XvSyU Numberphile is supported by the Mathematical Sciences Research Institute (MSRI): bit.ly/MSRINumberphile We are also supported by Science Sandbox, a Simons Foundation initiative dedicated to engaging everyone with the process of science. simonsfoundation.org/outreach/science-sandbox/ And support from The Akamai Foundation - dedicated to encouraging the next generation of technology innovators and equitable access to STEM education - akamai.com/company/corporate-responsibility/akamai-foundatio… NUMBERPHILE Website: numberphile.com/ Numberphile on Facebook: facebook.com/numberphile Numberphile tweets: twitter.com/numberphile Subscribe: bit.ly/Numberphile_Sub Videos by Brady Haran Patreon: patreon.com/numberphile Numberphile T-Shirts and Merch: teespring.com/stores/numberphile Brady's videos subreddit: reddit.com/r/BradyHaran/ Brady's latest videos across all channels: bradyharanblog.com/ Sign up for (occasional) emails: eepurl.com/YdjL9 Special thanks to our friend Jeff for the accommodation and filming space.

Why it's here

1 person recommends this

What people say. Recommended as an excellent illustration of how intuitive assumptions about randomness can lead to biased results in sampling.

Dave_Rosenthalon Hacker News • Recommends

On “Uniformly Sample Points in a Disk”

So points in a circle is pretty basic, but it does remind me of a nice 3Blue1Brown video ( link to this video ) about random chords of a circle. Some of these 'generate a random sample' situations can be quite non-obvious. edit: The video is about 'Bertrand's Paradox' that another post references.
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zootboyon Hacker News • Mentions

On “Random(Random(Random(Random())))”

In a related vein, there's a Numberphile / 3B1B video about the pitfalls of plotting randomness in a circle: link to this video
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olliejon Hacker News • Mentions

On “How to generate uniformly random points on n-spheres and in n-balls”

…rrect way for a sphere specifically is something like a=rand() b=rand() and the random point is something* like { cos(a) sin(b), sin(b), cos(a) cos(b) }1 I think the best illustration of "reasonable choices of what random values should be used leading to biased results" is Bertrand's paradox which I was introduced to via numberphile/3blue1brown: link to this video and am just glad that nothing I have ever needed random sampling for has ever been important :D 1 please don't use this blindly, I'm really just going off very old recollection, if you need it google random sphere sampling :D…
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u/psharpepin r/compsci • Mentions

On “Computer Scientists Prove Why Bigger Neural Networks Do Better”

Careful here! The concept of a "uniform probability distribution" on a multidimensional manifold (such as the surface of a sphere) isn't uniquely defined - it depends on parameterization: link to this video
2View on Reddit