Unbiased estimator
Named by 2 essays across 2 fields — each of them below, with the objects they name alongside it.
Too many orders to list
The rule is an average over every order the players could have arrived in. At seven players that is five thousand orders and at twenty it is more than there are seconds in the age of the universe — so the average is sampled, and the error falls at a rate that can be measured.
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.
SamplingVarianceAlternating seriesApproximationConvergence rateEstimatorEstimator biasIntractabilityMonte CarloPermutationPoisson approximationPower series