Approximating Gaussian Process Emulators with Linear Inequality Constraints and Noisy Observations via MC and MCMC
This addresses the challenge of creating more realistic Gaussian process emulators with constraints for real-world applications where data are noisy, though it appears to be an incremental improvement over existing constrained GP methods.
The paper tackles the problem of approximating Gaussian process emulators with linear inequality constraints when observations are noisy, introducing a noise term to relax interpolation conditions and developing corresponding approximation methods. The results show improved performance of Monte Carlo and Markov Chain Monte Carlo samplers with noisy observations, and more flexible, realistic implementations in 2D and 5D coastal flooding applications.
Adding inequality constraints (e.g. boundedness, monotonicity, convexity) into Gaussian processes (GPs) can lead to more realistic stochastic emulators. Due to the truncated Gaussianity of the posterior, its distribution has to be approximated. In this work, we consider Monte Carlo (MC) and Markov Chain Monte Carlo (MCMC) methods. However, strictly interpolating the observations may entail expensive computations due to highly restrictive sample spaces. Furthermore, having (constrained) GP emulators when data are actually noisy is also of interest for real-world implementations. Hence, we introduce a noise term for the relaxation of the interpolation conditions, and we develop the corresponding approximation of GP emulators under linear inequality constraints. We show with various toy examples that the performance of MC and MCMC samplers improves when considering noisy observations. Finally, on 2D and 5D coastal flooding applications, we show that more flexible and realistic GP implementations can be obtained by considering noise effects and by enforcing the (linear) inequality constraints.