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Square root biased sampling is a sampling method proposed by William H. Press, a computer scientist and computational biologist, for use in airport screenings. It is the mathematically optimal compromise between simple random sampling and strong profiling that most quickly finds a rare malfeasor, given fixed screening resources.
A method analogous to piece-wise linear approximation but using only arithmetic instead of algebraic equations, uses the multiplication tables in reverse: the square root of a number between 1 and 100 is between 1 and 10, so if we know 25 is a perfect square (5 × 5), and 36 is a perfect square (6 × 6), then the square root of a number greater than or equal to 25 but less than 36, begins with ...
Since the square root is a strictly concave function, it follows from Jensen's inequality that the square root of the sample variance is an underestimate. The use of n − 1 instead of n in the formula for the sample variance is known as Bessel's correction , which corrects the bias in the estimation of the population variance, and some, but ...
The standard deviations will then be the square roots of the respective variances. Since the square root introduces bias, the terminology "uncorrected" and "corrected" is preferred for the standard deviation estimators: s n is the uncorrected sample standard deviation (i.e., without Bessel's correction)
Square roots and other roots: Integer square root; Methods of computing square roots; nth root algorithm; hypot — the function (x 2 + y 2) 1/2; Alpha max plus beta min algorithm — approximates hypot(x,y) Fast inverse square root — calculates 1 / √ x using details of the IEEE floating-point system
For example, in cluster sampling we can use a two stage sampling in which we sample each cluster (which may be of different sizes) with equal probability, and then sample from each cluster at the second stage using SRS with a fixed proportion (e.g. sample half of the cluster, the whole cluster, etc.).
These n h must conform to the rule that n 1 + n 2 + ... + n H = n (i.e., that the total sample size is given by the sum of the sub-sample sizes). Selecting these n h optimally can be done in various ways, using (for example) Neyman's optimal allocation. There are many reasons to use stratified sampling: [7] to decrease variances of sample ...
If y n < f(0), then the initial estimate x 1 was too high. Given this, use a root-finding algorithm (such as the bisection method) to find the value x 1 which produces y n−1 as close to f(0) as possible. Alternatively, look for the value which makes the area of the topmost layer, x n−1 (f(0) − y n−1), as close to the desired value A as