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This work frames the problem of black-box safety validation as a Bayesian optimization problem and introduces a method that iteratively fits a probabilistic surrogate model to efficiently predict failures. The algorithm is designed to search for failures, compute the most-likely failure, and estimate the failure probability over an operating domain using importance sampling. We introduce three acquisition functions that aim to reduce uncertainty by covering the design space, optimize the analytically derived failure boundaries, and sample the predicted failure regions. Results show this Bayesian safety validation approach provides a more accurate estimate of failure probability with orders of magnitude fewer samples and performs well across various safety validation metrics. We demonstrate this approach on three test problems, a stochastic decision-making system, and a neural-network-based runway detection system. This work is open-sourced ( https:\/\/github.com\/sisl\/BayesianSafetyValidation.jl )\u00a0and is currently being used to supplement the FAA certification process of the machine learning components for an autonomous cargo aircraft. <\/jats:p>","DOI":"10.2514\/1.i011395","type":"journal-article","created":{"date-parts":[[2024,5,28]],"date-time":"2024-05-28T17:52:59Z","timestamp":1716918779000},"page":"533-546","update-policy":"https:\/\/doi.org\/10.2514\/aiaa_crossmarkpolicy","source":"Crossref","is-referenced-by-count":7,"title":["Bayesian Safety Validation for Failure Probability Estimation of Black-Box Systems"],"prefix":"10.2514","volume":"21","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-2403-454X","authenticated-orcid":false,"given":"Robert J.","family":"Moss","sequence":"first","affiliation":[{"name":"Stanford University"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Mykel J.","family":"Kochenderfer","sequence":"additional","affiliation":[{"name":"Stanford University"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Maxime","family":"Gariel","sequence":"additional","affiliation":[{"name":"Xwing"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Arthur","family":"Dubois","sequence":"additional","affiliation":[{"name":"Xwing"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1387","reference":[{"issue":"1","key":"r3","first-page":"17","volume":"19","author":"Kochenderfer M. 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