A posteriori noise estimation in variable data sets

TL;DR

This paper introduces a method for estimating measurement noise in variable data sets by analyzing weighted sums, applicable to diverse data types like spectra and light curves, with guidelines for practical use.

Contribution

It presents a novel a posteriori noise estimation procedure based on weighted sums, extending the DER_SNR algorithm for broader applications.

Findings

Effective in synthetic data, spectra, and light curves

Provides practical guidelines for diverse data sets

Demonstrates reliable noise estimation with well-sampled data

Abstract

Most physical data sets contain a stochastic contribution produced by measurement noise or other random sources along with the signal. Usually, neither the signal nor the noise are accurately known prior to the measurement so that both have to be estimated a posteriori. We have studied a procedure to estimate the standard deviation of the stochastic contribution assuming normality and independence, requiring a sufficiently well-sampled data set to yield reliable results. This procedure is based on estimating the standard deviation in a sample of weighted sums of arbitrarily sampled data points and is identical to the so-called DER_SNR algorithm for specific parameter settings. To demonstrate the applicability of our procedure, we present applications to synthetic data, high-resolution spectra, and a large sample of space-based light curves and, finally, give guidelines to apply the procedure in situation not explicitly considered here to promote its adoption in data analysis.