March 2024 A continuous multiple hypothesis testing framework for optimal exoplanet detection
Nathan C. Hara, Thibault de Poyferré, Jean-Baptiste Delisle, Marc Hoffmann
Author Affiliations +
Ann. Appl. Stat. 18(1): 749-769 (March 2024). DOI: 10.1214/23-AOAS1810

Abstract

When searching for exoplanets, one wants to count how many planets orbit a given star, and to determine what their characteristics are. If the estimated planet characteristics are too far from those of a planet truly present, this should be considered as a false detection. This setting is a particular instance of a general one: aiming to retrieve parametric components in a dataset corrupted by nuisance signals, with a certain accuracy on their parameters. We exhibit a detection criterion minimizing false and missed detections, either as a function of their relative cost or when the expected number of false detections is bounded. If the components can be separated in a technical sense discussed in detail, the optimal detection criterion is a posterior probability obtained as a by-product of Bayesian evidence calculations. Optimality is guaranteed within a model, and we introduce model criticism methods to ensure that the criterion is robust to model errors. We show on two simulations emulating exoplanet searches that the optimal criterion can significantly outperform other criteria. Finally, we show that our framework offers solutions for the identification of components of mixture models and Bayesian false discovery rate control when hypotheses are not discrete.

Funding Statement

N. C. Hara and J.-B. Delisle acknowledge the financial support of the National Centre for Competence in Research PlanetS of the Swiss National Science Foundation (SNSF).
T. de Poyferré acknowledges support by the NSF under Grant DMS-1928930 while participating in a program hosted by MSRI in Berkeley, CA, during Spring 2021.

Version Information

The current online version of this article, posted on 15 February 2024, supersedes the version posted on 31 January 2024. The changes are as follows: Equation 3 was corrected.

Acknowledgements

N. C. Hara thanks Gwenaël Boué for his insightful remarks, Roberto Trotta for his suggestions, Michaël Crétignier for providing the HD21693 HARPS data, Julien Bect for pointing out resemblances with the label-switching problem, and A. Leleu for his comments on dynamical stability.

Other email address for N. C. Hara: nathan.hara@lam.fr

Citation

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Nathan C. Hara. Thibault de Poyferré. Jean-Baptiste Delisle. Marc Hoffmann. "A continuous multiple hypothesis testing framework for optimal exoplanet detection." Ann. Appl. Stat. 18 (1) 749 - 769, March 2024. https://doi.org/10.1214/23-AOAS1810

Information

Received: 1 March 2022; Revised: 1 June 2023; Published: March 2024
First available in Project Euclid: 31 January 2024

Digital Object Identifier: 10.1214/23-AOAS1810

Keywords: Bayesian , decision theory , Exoplanets , False discovery rate , maximum utility

Rights: Copyright © 2024 Institute of Mathematical Statistics

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Vol.18 • No. 1 • March 2024
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