Everything Is Predictable: How Bayesian Statistics Explain Our World by Tom Chivers, 2024
A captivating and user-friendly tour of Bayes's theorem and its global impact on modern life from the acclaimed science writer and author of The Rationalist's Guide to the Galaxy.
Concentration of measures:
Talagrand's "work illustrates the idea that the interplay of many random events can, counter-intuitively, lead to outcomes that are more predictable, and gives estimates for the extent to which the uncertainty is reigned in."
OK I'm obviously doing something wrong so some #fediHelp in #probability would help here. Say I have an automaton whose cells can be in any of three states S1, S2, S3 with probability p1, p2, p3 (p1+p2+p3=1). The probability of a cell c changing from S1 to S2 depends on the neighbors being in state S2. c stays in state S1 if it's not “infected” by any of the neighbors. Say p12(c, n) is the probability of c moving from S1 to S2 if n is S2. What's the total probability of c staying in S1?
Different approach I'm considering: the probability of c being infected by n is k12(c, n) = p1(c)*p2(n)p12(c, n). So the probability of staying S1 is the complement from all neighbors \prod_n(1 - k12(c, n)), but that can't be, as it can be higher than p1(c). Should it be p1(c)\prod_n(1 - k12(c, n))? But then am I not account for p1(c) too many times? I'm obviously missing something, and being out of my element don't even know where to look things up.
Here's a nice puzzle from Tanya Khovanova's blog, who says she saw it on Facebook:
There are 100 cards with integers from 1 to 100. You have three possible scenarios: you pick 18, 19, or 20 cards at random. For each scenario, you need to estimate the probability that the sum of the cards is even. You do not need to do the exact calculation; you just need to say whether the probability is less than, equal to, or more than 1/2.
Vous aimez les oranges 🍊 alors cette question est pour vous.
Étant donné trois points à la surface d'une sphère (exemple une orange), quelle est la probabilité qu'il existe un hémisphère sur lequel ils se trouvent tous ?
⚠️Please boost et commenter en mode content warning.
Nice work by @turion integrating live Bayesian learning into a Functional Reactive Programming app. That's the power of embedded probabilistic programming languages like Monad-Bayes:
'A global team of researchers investigating the statistical and physical nuances of coin tosses worldwide concluded (via Phys.org) that a coin is 50.8% likely to land on the same side it started on, altering one of society’s most traditional assumptions about random decision-making that dates back at least to the Roman Empire.'
In an unplanned exercise in #probability, I let my students of my Field Professionalism/Wilderness First Aid class this semester pick either of two weekends (whichever one works out better for them), and it's exactly 50-50 so far on which one they have picked. #math
In #probability we often use the symbol 'p(.)' to mean some distribution, but e.g p(A) and p(B) are really different distributions since they refer to different events A and B.
What if we got rid of p altogether in writing?
(A, B) : joint of A and B
(A | B) : A conditional on B
etc.