Estimator bias
Named by 4 essays across one field — each of them below, with the objects they name alongside it.
Getting pi by dropping needles on the floor
Throw a needle at a lined floor enough times, count how often it crosses a line, and pi falls out. There is no circle anywhere in the experiment.
The error that does not care how many dimensions
A grid gets rapidly better in one dimension and hopelessly worse in twenty. Random points get better at the same slow rate whatever the dimension, which is why a method that is bad everywhere ends up being the only one that works.
Sampling where the answer lives
Monte Carlo error cannot be made to fall faster than the square root, so the only thing left to attack is the constant in front of it. Drawing points where the integrand is large, and dividing by how often they were drawn, leaves the answer alone and can shrink the noise many times over.
How many new kinds the next sample will show
Count how many kinds were seen once, twice, three times. Good and Toulmin's alternating sum f₁t − f₂t² + f₃t³ − … then predicts, with no bias at all, how many new kinds a further sample t times as large will reveal. It works perfectly up to t = 1 and is worthless just beyond: past that point the kinds seen most often are multiplied by t to a high power, and the spread of the estimate passes 10⁴⁰ by t = 1.5. Truncating the sum at a random point rescues it, and each fourfold increase in the first sample buys about half a unit more of future.
Named alongside it
The objects these essays reach for when they reach for this one.
SamplingConvergence rateMonte CarloVarianceIndependenceIntegralAlternating seriesBuffon's needleCentral limit theoremConvergenceCurse of dimensionalityEstimator