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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 ]
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.
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.
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 target population.
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 ().
These lists include items which are somehow related to statistics however are not included in this index: List of statisticians; List of important publications in statistics; List of scientific journals in statistics; Topic lists. Outline of statistics; List of probability topics; Glossary of probability and statistics; Glossary of experimental ...
In particular, the bootstrap is useful when there is no analytical form or an asymptotic theory (e.g., an applicable central limit theorem) to help estimate the distribution of the statistics of interest. This is because bootstrap methods can apply to most random quantities, e.g., the ratio of variance and mean.
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 .