Propagation of uncertainty

Summary

Propagation of uncertainty computes how the uncertainties of input quantities carry over to a quantity computed from them. Inputs are modelled as random variables with known means, variances and covariances. For a smooth function one usually linearizes it at the means. The output covariance is then $J \Sigma J^{T}$, where $J$ is the Jacobian matrix and $\Sigma$ the input covariance matrix. It is the standard tool for error bars in experimental science; for guaranteed bounds one uses interval arithmetic instead.