What If We Find Nothing? Bayesian Analysis Of The Statistical Information Of Null Results In Future Exoplanet Habitability And Biosignature Surveys

Future telescopes will survey temperate, terrestrial exoplanets to estimate the frequency of habitable (η_Hab) or inhabited (η_Life) planets.

This study aims to determine the minimum number of planets (N) required to draw statistically significant conclusions, particularly in the case of a null result (i.e., no detections).

Using a Bayesian framework, we analyzed surveys of up to N=100 planets to infer the frequency of a binary observable feature (η_obs) after null results. Posterior best fits and upper limits were derived for various survey sizes and compared with predicted yields from missions like the Large Interferometer for Exoplanets (LIFE) and the Habitable Worlds Observatory (HWO).

Our findings indicate that N=20−50 “perfect” observations (100% confidence in detecting or excluding the feature) yield conclusions relatively independent of priors. To achieve 99.9% upper limits of η_obs≤0.2/0.1, approximately N≃40/80 observations are needed. For “imperfect” observations, uncertainties in interpretation and sample biases become limiting factors.

We show that LIFE and HWO aim for sufficiently large survey sizes to provide statistically meaningful estimates of habitable environments and life prevalence under these assumptions. However, robust conclusions require careful sample selection and high-confidence detection or exclusion of features in each observation.

Daniel Angerhausen, Amedeo Balbi, Andjelka B. Kovačević, Emily O. Garvin, Sascha P. Quanz

Subjects: Earth and Planetary Astrophysics (astro-ph.EP); Instrumentation and Methods for Astrophysics (astro-ph.IM)
Cite as: arXiv:2504.06779 [astro-ph.EP] (or arXiv:2504.06779v1 [astro-ph.EP] for this version)
https://doi.org/10.48550/arXiv.2504.06779
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Related DOI:
https://doi.org/10.3847/1538-3881/adb96d
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Submission history
From: Daniel Angerhausen
[v1] Wed, 9 Apr 2025 11:02:19 UTC (1,902 KB)
https://arxiv.org/abs/2504.06779
Astrobiology,