{"ID":2865512,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2509.22597","arxiv_id":"2509.22597","title":"Nonparametric Bayesian Calibration of Computer Models","abstract":"Calibration of computer models is a key step in making inferences, predictions, and decisions for complex science and engineering systems. We formulate and analyze a nonparametric Bayesian methodology for computer model calibration. This paper presents a number of key results including; establishment of a unique nonparametric Bayesian posterior corresponding to a chosen prior with an explicit formula for the corresponding conditional density; a maximum entropy property of the posterior corresponding to the uniform prior; the almost everywhere continuity of the density of the nonparametric posterior; and a comprehensive convergence and asymptotic analysis of an estimator based on a form of importance sampling. We illustrate the problem and results using several examples, including a simple experiment.","short_abstract":"Calibration of computer models is a key step in making inferences, predictions, and decisions for complex science and engineering systems. We formulate and analyze a nonparametric Bayesian methodology for computer model calibration. This paper presents a number of key results including; establishment of a unique nonpar...","url_abs":"https://arxiv.org/abs/2509.22597","url_pdf":"https://arxiv.org/pdf/2509.22597v3","authors":"[\"Haiyi Shi\",\"Lei Yang\",\"Jiarui Chi\",\"Troy Butler\",\"Haonan Wang\",\"Derek Bingham\",\"Don Estep\"]","published":"2025-09-26T17:17:14Z","proceeding":"stat.ME","tasks":"[\"stat.ME\",\"math.ST\",\"stat.CO\"]","methods":"[]","has_code":false}