MaxEnt power spectrum estimation using the Fourier transform for irregularly sampled data applied to a record of stellar luminosity

TL;DR

This paper develops a maximum entropy spectral estimation method using Fourier transforms tailored for irregularly sampled data with gaps, such as stellar luminosity records, to produce more reliable power spectra.

Contribution

It introduces a novel maximum entropy approach that avoids arbitrary factors and handles data with known or bounded variance, improving spectral analysis of imperfect data.

Findings

The method produces spectra with less spurious structure.

Application to stellar luminosity data demonstrates effectiveness.

Avoids overfitting by using entropic regularization.

Abstract

The principle of maximum entropy is applied to the spectral analysis of a data signal with general variance matrix and containing gaps in the record. The role of the entropic regularizer is to prevent one from overestimating structure in the spectrum when faced with imperfect data. Several arguments are presented suggesting that the arbitrary prefactor should not be introduced to the entropy term. The introduction of that factor is not required when a continuous Poisson distribution is used for the amplitude coefficients. We compare the formalism for when the variance of the data is known explicitly to that for when the variance is known only to lie in some finite range. The result of including the entropic measure factor is to suggest a spectrum consistent with the variance of the data which has less structure than that given by the forward transform. An application of the methodology to example data is demonstrated.