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Why simple quadrature is just as good as Monte Carlo
Name
1908.00947.pdf
Description
Accepted version
Size
511.97 KB
Format
Adobe PDF
Checksum (MD5)
beacc18f910da32407d08d7c918100ec
Author(s)
Vanslette, Kevin
Al Alsheikh, Abdullatif
Youcef-Toumi, Kamal
Date Issued
2020
Journal
Monte Carlo Methods and Applications
Publisher
Walter de Gruyter GmbH
Version
Author's final manuscript
Abstract
© 2020 Walter de Gruyter GmbH, Berlin/Boston. We motive and calculate Newton-Cotes quadrature integration variance and compare it directly with Monte Carlo (MC) integration variance. We find an equivalence between deterministic quadrature sampling and random MC sampling by noting that MC random sampling is statistically indistinguishable from a method that uses deterministic sampling on a randomly shuffled (permuted) function. We use this statistical equivalence to regularize the form of permissible Bayesian quadrature integration priors such that they are guaranteed to be objectively comparable with MC. This leads to the proof that simple quadrature methods have expected variances that are less than or equal to their corresponding theoretical MC integration variances. Separately, using Bayesian probability theory, we find that the theoretical standard deviations of the unbiased errors of simple Newton-Cotes composite quadrature integrations improve over their worst case errors by an extra dimension independent factor α N - 12. This dimension independent factor is validated in our simulations.
Terms of Use
Creative Commons Attribution-Noncommercial-Share Alike
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DOI of Published Version
10.1515/mcma-2020-2055
