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It has become commonplace to use complex computer models to predict outcomes in regions where data does not exist. Typically these models need to be calibrated and validated using some experimental data, which often consists of multiple correlated outcomes. In addition, some of the model parameters may be categorical in nature, such as a pointer variable to alternate models (or submodels) for some of the physics of the system. Here we present a general approach for calibration in such situations where an emulator of the computationally demanding models and a discrepancy term from the model to reality are represented within a Bayesian Smoothing Spline (BSS) ANOVA framework. The BSS-ANOVA framework has several advantages over the traditional Gaussian Process, including ease of handling categorical inputs and correlated outputs, and improved computational efficiency. Finally this framework is then applied to the problem that motivated its design; a calibration of a computational fluid dynamics model of a bubbling fluidized which is used as an absorber in a CO2 capture system.
This work relates the framework of model-based clustering for spatial functional data where the data are surfaces. We first introduce a Bayesian spatial spline regression model with mixed-effects (BSSR) for modeling spatial function data. The BSSR mo
We propose a methodology for filtering, smoothing and assessing parameter and filtering uncertainty in score-driven models. Our technique is based on a general representation of the Kalman filter and smoother recursions for linear Gaussian models in
This paper develops a Bayesian network-based method for the calibration of multi-physics models, integrating various sources of uncertainty with information from computational models and experimental data. We adopt the Kennedy and OHagan (KOH) framew
Several results on constrained spline smoothing are obtained. In particular, we establish a general result, showing how one can constructively smooth any monotone or convex piecewise polynomial function (ppf) (or any $q$-monotone ppf, $qgeq 3$, with
Functional data, with basic observational units being functions (e.g., curves, surfaces) varying over a continuum, are frequently encountered in various applications. While many statistical tools have been developed for functional data analysis, the