Forskjell mellom versjoner av «Propagation of uncertainties for a function of observables»

Revisjonen fra 14. mai 2011 kl. 08:33

We want to estimate the uncertainty of a function [math]f[/math] of a set of [math]n[/math] observables [math]\vec{x}[/math] with associated uncertainties [math]\sigma_i[/math]. We assume that the observables [math]\vec{x}[/math] are sampled from normal distributions which are narrow relative to the form of the function and approximate the function with its Taylor-series expansion, keeping only the lowest-order derivatives [math]f(\vec{x}+\vec{\delta_x}) = f(\vec{x}) + {df(\vec{x}) \over d{\vec{x}}}\cdot \vec{\delta_x} + h.o.[/math].

The uncertainty in [math]f[/math] is estimated as the square root of its mean variance [math]\sqrt{\sigma^2_f}[/math] where [math]\sigma^2_f=\lt (f-\lt f\gt )^2\gt .[/math]