The multinomial distribution models counts across multiple categories after a fixed number of independent trials. In validation work, it appears when bootstrap resampling repeatedly draws a sample of length N with replacement. section 7.4
That direct approach can become impractical: each of 10,000–100,000 bootstrap iterations may require multinomial sampling over thousands or millions of observations, repeated N times. Reviewing observations independently enables a faster alternative: binomial(n, 1/n), closely approximated by Poisson(1) when N is large. section 7.4
Bootstrap confidence bounds
To estimate uncertainty for recall, repeatedly resample the original dataset and calculate the metric. The resulting distribution supports a lower confidence bound, such as a 99% bound; replacing multinomial sampling with independent Poisson(1) sampling can make the process 100–1,000 times faster. section 7.4
