Investigating the Influence of Asymmetric Errors on Retrievals of Exoplanet Transmission Spectra

TL;DR

This paper evaluates the impact of asymmetric error bars on exoplanet transmission spectrum retrievals, finding that current Gaussian assumptions are generally safe but may introduce bias with higher asymmetries.

Contribution

It compares symmetric and asymmetric likelihoods in retrievals, highlighting the conditions under which asymmetry affects parameter estimation.

Findings

Minimal impact of asymmetry at 77% observed in JWST data

Potential bias with asymmetry levels exceeding 80%

Shape mismatch in likelihood can lead to incorrect parameters

Abstract

In studies of exoplanet atmospheres using transmission spectroscopy, Bayesian retrievals are the most popular form of analysis. In these procedures it is common to adopt a Gaussian likelihood. However, this implicitly assumes that the upper and lower error bars on the spectral points are equal. With recent observations from the James Webb Space Telescope (JWST) offering higher quality of data, it is worth revisiting this assumption to understand the impact that an asymmetry between the error bars may have on retrieved parameters. In this study, we challenge the approximation by comparing retrievals using a symmetric, Gaussian likelihood, and an asymmetric, split normal likelihood. We find that the influence of this assumption is minimal at the scales of asymmetry observed in JWST observations of WASP-39 b (with a maximum asymmetry of 77%) but we show that it would become critical with greater levels of asymmetry (e.g. an average asymmetry of 80%). Furthermore, we stress the importance of the shape of the asymmetric distribution and the difficulty in fitting this distribution from three summary statistics (the median and an upper and lower bound on the transit depth). An asymmetric likelihood sampler will incorrectly predict parameters if the shape of the likelihood does not match that of the underlying noise distribution even when the levels of asymmetry are equal in both. Overall, we find that it is safe to use the Gaussian likelihood assumption for current datasets but it is worth considering the potential bias if greater asymmetries are observed.