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This paper develops a frequentist solution to the functional calibration problem, where the value of a calibration parameter in a computer model is allowed to vary with the value of control variables in the physical system. The need of functional calibration is motivated by engineering applications where using a constant calibration parameter results in a significant mismatch between outputs from the computer model and the physical experiment. Reproducing kernel Hilbert spaces (RKHS) are used to model the optimal calibration function, defined as the functional relationship between the calibration parameter and control variables that gives the best prediction. This optimal calibration function is estimated through penalized least squares with an RKHS-norm penalty and using physical data. An uncertainty quantification procedure is also developed for such estimates. Theoretical guarantees of the proposed method are provided in terms of prediction consistency and consistency of estimating the optimal calibration function. The proposed method is tested using both real and synthetic data and exhibits more robust performance in prediction and uncertainty quantification than the existing parametric functional calibration method and a state-of-art Bayesian method.
Weighted log-rank tests are arguably the most widely used tests by practitioners for the two-sample problem in the context of right-censored data. Many approaches have been considered to make weighted log-rank tests more robust against a broader fami
The goal of nonparametric regression is to recover an underlying regression function from noisy observations, under the assumption that the regression function belongs to a pre-specified infinite dimensional function space. In the online setting, whe
The geometry of spaces with indefinite inner product, known also as Krein spaces, is a basic tool for developing Operator Theory therein. In the present paper we establish a link between this geometry and the algebraic theory of *-semigroups. It goes
Let a labeled dataset be given with scattered samples and consider the hypothesis of the ground-truth belonging to the reproducing kernel Hilbert space (RKHS) of a known positive-definite kernel. It is known that out-of-sample bounds can be establish
Large renewable energy projects, such as large offshore wind farms, are critical to achieving low-emission targets set by governments. Stochastic computer models allow us to explore future scenarios to aid decision making whilst considering the most