# How to optimize sampling for global sensitivity analysis

What is a good way to sample parameters for performing global sensitivity analysis? Some methods are defined using integrals, some are use Monte Carlo. How do these compare?

• I answered this question for some reason thinking it was on global sensitivity, not local sensitivity for parameter estimation... so I deleted the answer and moved it here, thinking it might be nice to share anyways! – Chris Rackauckas Dec 12 '19 at 15:45
• thanks for doing it. I enjoyed reading it quite a bit! – Anton Menshov Dec 12 '19 at 18:13

What you're looking for goes under the name of quasi-Monte Carlo (QMC) sequences. Quasi Monte Carlo sequences are "more random than random", i.e. they fill high dimensional spaces better than random sequences tend to do, which somewhat matches a more intuitive form of randomness. But more importantly, since they "fill space well" (a property that can be quantified as have a low discrepancy), they tend to be a very good way of sampling to make integrals converge faster. Because of this, quasi Monte Carlo sequences can have faster convergence than Monte Carlo integration methods, moving from $$O(\frac{1}{\sqrt{N}})$$ with random sampling to $$O(\frac{1}{N})$$ for quasi-random sequences with low discrepancy.