Evaluating Gaussian process metamodels and sequential designs for noisy level set estimation

Abstract We consider the problem of learning level set for which a noisy black-box function exceeds given threshold. To efficiently reconstruct set, we investigate Gaussian process (GP) metamodels. Our focus is on strongly stochastic simulators, in particular with heavy-tailed simulation noise and low signal-to-noise ratio. guard against misspecification, assess performance three variants: (i) GPs Student- t observations; (ii) processes (TPs); (iii) classification modeling sign response. In conjunction these metamodels, analyze several acquisition functions guiding sequential experimental designs, extending existing stepwise uncertainty reduction criteria to contour-finding context. This also motivates our development (approximate) updating formulas compute such functions. schemes are benchmarked by using variety synthetic experiments 1–6 dimensions. an application estimation determining optimal exercise policy Bermudan options finance.