Nonparametric Bayesian Calibration of Computer Models

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.