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Title: Coverage aspects of Gaussian processes with an application to particle Physics Authors:  Debdeep Pati - Texas A&M University (United States) [presenting]
Anirban Bhattacharya - Texas A and M University (United States)
Yun Yang - Florida State University (United States)
Abstract: Gaussian process (GP) regression is a powerful interpolation technique due to its flexibility in capturing non-linearity. We provide a general framework for understanding the frequentist coverage of point-wise and simultaneous Bayesian credible sets in GP regression. Identifying both the mean and covariance function of the posterior distribution of the Gaussian process as regularized M-estimators, we show that the sampling distribution of the posterior mean function and the centered posterior distribution can be respectively approximated by two population level GPs. Our results show that inference based on GP regression tends to be conservative; when the prior is under-smoothed, the resulting credible intervals and bands have minimax-optimal sizes, with their frequentist coverage converging to a non-degenerate value between their nominal level and one. We demonstrate the validity of our theoretical results through numerical examples and an application to the famous proton radius puzzle.