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Inverse probability weighting is a statistical technique for estimating quantities related to a population other than the one from which the data was collected. Study designs with a disparate sampling population and population of target inference (target population) are common in application. [1]
In statistics, the Horvitz–Thompson estimator, named after Daniel G. Horvitz and Donovan J. Thompson, [1] is a method for estimating the total [2] and mean of a pseudo-population in a stratified sample by applying inverse probability weighting to account for the difference in the sampling distribution between the collected data and the a target population.
Given the data, one must estimate the true position (probably by averaging). This problem would now be considered one of inferential statistics. The terms "direct probability" and "inverse probability" were in use until the middle part of the 20th century, when the terms "likelihood function" and "posterior distribution" became prevalent.
For normally distributed random variables inverse-variance weighted averages can also be derived as the maximum likelihood estimate for the true value. Furthermore, from a Bayesian perspective the posterior distribution for the true value given normally distributed observations and a flat prior is a normal distribution with the inverse-variance weighted average as a mean and variance ().
inverse-variance weighting, also known as analytic weights, [24] is when each element is assigned a weight that is the inverse of its (known) variance. [ 25 ] [ 9 ] : 187 When all elements have the same expectancy, using such weights for calculating weighted averages has the least variance among all weighted averages.
Inverse transform sampling (also known as inversion sampling, the inverse probability integral transform, the inverse transformation method, or the Smirnov transform) is a basic method for pseudo-random number sampling, i.e., for generating sample numbers at random from any probability distribution given its cumulative distribution function.
In probability theory and statistics, an inverse distribution is the distribution of the reciprocal of a random variable. Inverse distributions arise in particular in the Bayesian context of prior distributions and posterior distributions for scale parameters .
Inverse Distance Weighting as a sum of all weighting functions for each sample point. Each function has the value of one of the samples at its sample point and zero at every other sample point. Inverse distance weighting ( IDW ) is a type of deterministic method for multivariate interpolation with a known scattered set of points.