Blending spatial modeling and probabilistic bisection
Sergio Rodríguez · Winter Simulation Conference · 2016
Probabilistic Bisection Algorithms (PBA) pinpoint an unknown quantity by applying Bayesian updating to knowledge acquired from noisy oracle replies. We consider the generalized PBA setting (G-PBA) where the statistical distribution of the oracle is unknown and location-dependent, so that model inference and knowledge updating must be performed simultaneously. To this end, we propose to blend spatial modeling of oracle properties (namely regressing batched oracle responses on sampling locations) with the existing PBA information-directed sampling. The resulting sampling strategies account for the trade-off between inferring the latent oracle distribution versus reducing the uncertainty about the unknown point to be learned. We demonstrate that spatial modeling improves the original G-PBA schemes by applying our approach to root-finding of monotone noisy responses.