Exchangeability
Named by 2 essays across one field — each of them below, with the objects they name alongside it.
A walk that follows its own footsteps
Let a walk step up with probability equal to the share of up-steps it has taken so far, and every count of up-steps after twenty steps is exactly equally likely. The walk leaves along a straight line at a speed chosen by its first few steps, and although it is expected to come back to its start infinitely often, almost every run comes back only a few times.
A restaurant and a shuffled deck
Each new customer sits at a table with chance proportional to the people there, or starts a new one with weight θ. That one rule gives the kinds of species in a catch and the alleles at a gene. At θ = 1 it is exactly the cycles of a shuffled deck, 62.4% of which lie in the longest, and the same shares describe the largest prime factors of a random number.
Named alongside it
The objects these essays reach for when they reach for this one.
Beta distributionExpected valueMartingalePermutationPolya urnPower lawRandom walkRecurrenceSimulation