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Concept
Inverse-variance weighting
Summary
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, i.e. proportional to its precision.
Given a sequence of independent observations yi with variances σi2, the inverse-variance weighted average is given by
: \hat{y} = \frac{\sum_i y_i / \sigma_i^2}{\sum_i 1/\sigma_i^2} .
The inverse-variance weighted average has the least variance among all weighted averages, which can be calculated as
: Var(\hat{y}) = \frac{1}{\sum_i 1/\sigma_i^2} .
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 or sensor fusion to combine the results from independent measurements.
Context
Suppose an experimenter wishes to measure the value of a quantity, say the acc
Official source
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