Calibration of Sobol indices estimates in case of noisy output

TL;DR

This paper introduces a straightforward noise correction method for Sobol' indices estimation, effectively reducing bias caused by noise in output data, especially for total Sobol' indices, without requiring assumptions on the function or noise distribution.

Contribution

The paper proposes an analytical noise correction technique for Sobol' indices that is simple, assumption-free (beyond stationarity and noise type), and improves unbiasedness in noisy environments.

Findings

The method effectively reduces bias in Sobol' indices estimates.

It increases variance of estimates when noise is present.

The approach is more straightforward than existing methods.

Abstract

This paper presents a simple noise correction method for Sobol' indices estimation. Sobol' indices, especially total Sobol' indices are quite sensitive to the noise in the output and tend to be severly biased (overestimated) if no noise correction is done, which may make their computation meaningless in case of even quite moderate noise levels. Proposed method allows to get approximately unbiased noise free estimation of Sobol' indices at the cost of variance of estimate increase if noise can be represented as a combination of additive and multiplicative stationary noise. %Also we show that it is impossible to do precise noise correction for more complex noise settings. Proposed method is more straightforward than schemes found in the literature and does not introduce any assumptions on the function and noise distribution (except that it assumes noise to be stationary and be a combination of additive and multiplicative). One of the appealing features is that there is actual analytical noise correction expression derived.