Fast Bayesian estimation of prediction uncertainty in analysis of a computer experiment

Bela Nagy, Jason Loeppky, and William Welch (presenter)
University of British Columbia

In analysis of the input-output relationship of a complex computer code, a Gaussian process (random function, kriging) model is commonly used for as a surrogate to predict the code output. For mathematical and computational simplicity, the variance formula often used ignores uncertainty from estimating the covariance parameters of the statistical model. This extra uncertainty can be nontrivial for small sample sizes (relative to the dimensionality of the input variables). A Bayesian MCMC analysis potentially accounts for these other sources of prediction uncertainty, but is computationally demanding and can require user sophistication. We propose a Fast Bayesian Implementation (FBI) which is simple mathematically and computationally, and can be used as a "black box". Simulations suggest it provides a reliable assessment of prediction error.

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