Posterior consistency for Gaussian process approximations of Bayesian posterior distributions
Copyright policy )Posterior consistency for Gaussian process approximations of Bayesian posterior distributions
We study the use of Gaussian process emulators to approximate the parameter-to-observation map or the negative log-likelihood in Bayesian inverse problems. We prove error bounds on the Hellinger distance between the true posterior distribution and various approximations based on the Gaussian process emulator. Our analysis includes approximations based on the mean of the predictive process, as well as approximations based on the full Gaussian process emulator. Our results show that the Hellinger distance between the true posterior and its approximations can be bounded by moments of the error in the emulator. Numerical results confirm our theoretical findings.
Bayesian approach, inverse problem, Bayesian approach, surrogate model, Gaussian process regression, posterior consistency, Gaussian processes, Numerical solution to inverse problems in abstract spaces, posterior consistency, Numerical Analysis (math.NA), 510, Numerical interpolation, Numerical integration, FOS: Mathematics, inverse problem, Nonparametric regression and quantile regression, Mathematics - Numerical Analysis, surrogate model, Gaussian process regression
Bayesian approach, inverse problem, Bayesian approach, surrogate model, Gaussian process regression, posterior consistency, Gaussian processes, Numerical solution to inverse problems in abstract spaces, posterior consistency, Numerical Analysis (math.NA), 510, Numerical interpolation, Numerical integration, FOS: Mathematics, inverse problem, Nonparametric regression and quantile regression, Mathematics - Numerical Analysis, surrogate model, Gaussian process regression
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