On Correlated-noise Analyses Applied To Exoplanet Light Curves

TL;DR

This paper reviews and evaluates three correlated-noise estimators for exoplanet light curves, identifies issues with some methods, and introduces an open-source Bayesian tool for more accurate parameter estimation.

Contribution

It critically assesses existing correlated-noise estimators, corrects wavelet-likelihood equations, and provides a new open-source MCMC tool for exoplanet light-curve analysis.

Findings

Residual-permutation method is unsound for uncertainty estimation.

Time-averaging and wavelet-likelihood methods improve eclipse depth estimates.

Corrections to wavelet-likelihood equations enhance analysis accuracy.

Abstract

Time-correlated noise is a significant source of uncertainty when modeling exoplanet light-curve data. A correct assessment of correlated noise is fundamental to determine the true statistical significance of our findings. Here we review three of the most widely used correlated-noise estimators in the exoplanet field, the time-averaging, residual-permutation, and wavelet-likelihood methods. We argue that the residual-permutation method is unsound in estimating the uncertainty of parameter estimates. We thus recommend to refrain from this method altogether. We characterize the behavior of the time averaging's rms-vs.-bin-size curves at bin sizes similar to the total observation duration, which may lead to underestimated uncertainties. For the wavelet-likelihood method, we note errors in the published equations and provide a list of corrections. We further assess the performance of these techniques by injecting and retrieving eclipse signals into synthetic and real Spitzer light curves, analyzing the results in terms of the relative-accuracy and coverage-fraction statistics. Both the time-averaging and wavelet-likelihood methods significantly improve the estimate of the eclipse depth over a white-noise analysis (a Markov-chain Monte Carlo exploration assuming uncorrelated noise). However, the corrections are not perfect, when retrieving the eclipse depth from Spitzer datasets, these methods covered the true (injected) depth within the 68\% credible region in only $\sim$45--65\% of the trials. Lastly, we present our open-source model-fitting tool, Multi-Core Markov-Chain Monte Carlo ({MC$^3$}). This package uses Bayesian statistics to estimate the best-fitting values and the credible regions for the parameters for a (user-provided) model. {MC$^3$} is a Python/C code, available at https://github.com/pcubillos/MCcubed.