In statistics, inverse-variance weighting is a method of aggregating two or more random variables to minimize the variance of the weighted average. Each random variable is weighted in inverse proportion to its variance.
Given a sequence of independent observations yi with variances σi2, the inverse-variance weighted average is given by
The inverse-variance weighted average has the least variance among all weighted averages, which can be calculated as
If the variances of the measurements are all equal, then the inverse-variance weighted average becomes the simple average.
Inverse-variance weighting is typically used in statistical meta-analysis to combine the results from independent measurements.
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