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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 ]
The inverse probability problem (in the 18th and 19th centuries) was the problem of estimating a parameter from experimental data in the experimental sciences, especially astronomy and biology. A simple example would be the problem of estimating the position of a star in the sky (at a certain time on a certain date) for purposes of navigation ...
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 ().
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.
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.
RNA folding problem: Is it possible to accurately predict the secondary, tertiary and quaternary structure of a polyribonucleic acid sequence based on its sequence and environment? Protein design : Is it possible to design highly active enzymes de novo for any desired reaction?
Sigmoid curves are also common in statistics as cumulative distribution functions (which go from 0 to 1), such as the integrals of the logistic density, the normal density, and Student's t probability density functions. The logistic sigmoid function is invertible, and its inverse is the logit function.
L-moments are statistical quantities that are derived from probability weighted moments [12] (PWM) which were defined earlier (1979). [8] PWM are used to efficiently estimate the parameters of distributions expressable in inverse form such as the Gumbel , [ 9 ] the Tukey lambda , and the Wakeby distributions.