TransWikia.com

Error propagation in an equation without an analytical solution

Cross Validated Asked by slekce on November 14, 2021

Is it possible to formally propagate uncertainties through an equation which does not have an analytical solution? I am an Earth Scientist working on doing a rigorous determination of the age calculated using (U-Th)/He dating, which uses the equation

$$
He = 8*^{238}U(e^{lambda_{238}t}-1)times7*^{235}U(e^{lambda_{235}t}-1)times6*^{232}Th(e^{lambda_{232}t}-1)times^{147}Sm(e^{lambda_{147}t}-1)
$$

We solve for t numerically because the equation cannot be solved for t explicitly. The other variables (e.g., He, 238U, lambda238) are measured or known, each with their own uncertainty. For the sake of argument, let’s say that I know the uncertainty on each value perfectly and all are gaussian. Is there a way to determine the uncertainty in t using "classical error propagation" (e.g., adding in quadrature) without the ability to solve for it explicitly? I know I could build a monte carlo code to figure it out, but I’m wondering if it’s even possible to determine the uncertainty analytically.

Add your own answers!

Ask a Question

Get help from others!

© 2024 TransWikia.com. All rights reserved. Sites we Love: PCI Database, UKBizDB, Menu Kuliner, Sharing RPP