A Bayesian Framework for Exoplanet Direct Detection and Non-Detection

TL;DR

This paper introduces a Bayesian framework for analyzing high contrast imaging data in exoplanet detection, emphasizing the advantages of Bayesian upper limits over traditional frequentist methods for more accurate hypothesis testing.

Contribution

It develops a Bayesian approach for exoplanet detection and non-detection analysis, including model comparison and data combination strategies, improving interpretability and constraint power.

Findings

Bayesian upper limits are more interpretable than frequentist thresholds.

Model comparison can constrain the nature of detected point sources.

Bayesian methods enhance the analysis of combined radial velocity and imaging data.

Abstract

Rigorously quantifying the information in high contrast imaging data is important for informing follow-up strategies to confirm the substellar nature of a point source, constraining theoretical models of planet-disk interactions, and deriving planet occurrence rates. However, within the exoplanet direct imaging community, non-detections have almost exclusively been defined using a frequentist detection threshold (i.e. contrast curve) and associated completeness. This can lead to conceptual inconsistencies when included in a Bayesian framework. A Bayesian upper limit is such that the true value of a parameter lies below this limit with a certain probability. The associated probability is the integral of the posterior distribution with the upper limit as the upper bound. In summary, a frequentist upper limit is a statement about the detectability of planets while a Bayesian upper limit is a statement about the probability of a parameter to lie in an interval given the data. The latter is therefore better suited for rejecting hypotheses or theoretical models based on their predictions. In this work we emphasize that Bayesian statistics and upper limits are more easily interpreted and typically more constraining than the frequentist approach. We illustrate the use of Bayesian analysis in two different cases: 1) with a known planet location where we also propose to use model comparison to constrain the astrophysical nature of the point source and 2) gap-carving planets in TW Hya. To finish, we also mention the problem of combining radial velocity and direct imaging observations.