TY - JOUR

T1 - A Bayesian Framework for Exoplanet Direct Detection and Non-detection

AU - Ruffio, Jean Baptiste

AU - Mawet, Dimitri

AU - Czekala, Ian

AU - Macintosh, Bruce

AU - De Rosa, Robert J.

AU - Ruane, Garreth

AU - Bottom, Michael

AU - Pueyo, Laurent

AU - Wang, Jason J.

AU - Hirsch, Lea

AU - Zhu, Zhaohuan

AU - Nielsen, Eric L.

N1 - Funding Information:
This research was supported by grants from NSF, including AST-1411868 (J.-B.R., B.M.) and AST-1518332 (R.J.D.R.). Support was provided by grants from NASA, including NNX14AJ80G (B.M., J.-B.R.), NNX15AD95G (R.J.D.R.) and NNX15AC89G (R.J.D.R.). This work benefited from NASAs Nexus for Exoplanet System Science (NExSS) research coordination network sponsored by NASAs Science Mission Directorate. Facility: Keck:II(NIRC2).

PY - 2018/11

Y1 - 2018/11

N2 - 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.

AB - 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.

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U2 - 10.3847/1538-3881/aade95

DO - 10.3847/1538-3881/aade95

M3 - Article

AN - SCOPUS:85056692258

VL - 156

JO - Astronomical Journal

JF - Astronomical Journal

SN - 0004-6256

IS - 5

M1 - 196

ER -