Beta distribution
Named by 3 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.
What not knowing the coin costs
Kelly's rule stakes the edge, and the edge is the one thing a bettor never has. Estimate it from twenty tosses and stake the estimate, and a lucky start can turn a favourable coin into certain ruin. Learn it toss by toss instead, with Laplace's rule, and the cost of ignorance shrinks to a factor of about the square root of the number of tosses — because a bettor who learns is exactly a bettor who split the money among every fixed fraction at once.
Evidence that can be multiplied
A p-value from one study and a p-value from the next cannot simply be multiplied, and a researcher who decides whether to run the next study by looking at the last one quietly breaks the rule that combines them. An e-value — a number whose average under the null is at most one — can be multiplied, study after study, under any rule for continuing, and never passes twenty to one more than one time in twenty. What it costs is tosses, and what it demands is a decision about which alternatives to be good at finding.
Named alongside it
The objects these essays reach for when they reach for this one.
MartingaleBayes factorBayes' theoremEntropyEstimatorExchangeabilityExpectationLaw of large numbersLikelihoodLogarithmP valuePolya urn