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Emulation and Uncertainty Quantification for Models with Functional Response Using Bayesian Adaptive Splines


When a computer code is used to simulate a complex system, a fundamental task is to assess the uncertainty of the simulator. In the case of computationally expensive simulators, this is often accomplished via a surrogate statistical model, a statistical output emulator. An effective emulator is one that provides good approximations to the computer code output for wide ranges of input values. In addition, an emulator should be able to handle large dimensional simulation output for a relevant number of inputs; it should flexibly capture heterogeneities in the variability of the response surface; it should be fast to evaluate for arbitrary combinations of input parameters; and it should provide an accurate quantification of the emulation uncertainty.

In this work, we develop Bayesian adaptive spline methods for emulation of computer models that output functions. We introduce modifications to traditional Bayesian adaptive spline approaches that allow for fitting large amounts of data and allow for more efficient Markov chain Monte Carlo sampling. We develop a functional approach to sensitivity analysis that can be performed using this emulator. We present a sensitivity analysis of a computer model of the deformation of a protective plate used in pressure driven experiments. This example serves as an illustration of the ability of Bayesian adaptive spline emulators to fulfill all the necessities of computability, flexibility and reliable calculation on relevant measures of sensitivity.

We extend the methods to emulation of an atmospheric dispersion simulator that outputs a plume in space and time based on inputs detailing the characteristics of the release, some of which are categorical. We achieve accurate emulation using Bayesian adaptive splines to model weights on empirical orthogonal functions. We extend the adaptive spline methodology to allow for categorical inputs. We use this emulator as well as appropriately identifiable simulator discrepancy and observational error models to calibrate the simulator using a dataset from an experimental release of particles from the Diablo Canyon Nuclear Power Plant in Central California. Since the release was controlled, these characteristics are known, allowing us to compare our findings to the truth.

We further extend the methods to emulate a computer model that outputs misaligned functional data. We do this by modeling the aligned, or warped, data as well as the warping functions, using separate Bayesian adaptive spline models. We explore inference methods that treat these models jointly and separately, and establish methods to ensure that the warping functions are non-decreasing. These methods are applied to a high-energy-density physics model that outputs a curve representing energy as a function of time.

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