Abstract
Optimal experimental design (OED) is of great significance in efficient Bayesian inversion. A popular choice of OED methods is based on maximizing the expected information gain (EIG), where expensive likelihood functions are typically involved. To reduce the computational cost, in this work, a novel double-loop Bayesian Monte Carlo (DLBMC) method is developed to efficiently compute the EIG, and a Bayesian optimization (BO) strategy is proposed to obtain its maximizer only using a small number of samples. For Bayesian Monte Carlo posed on uniform and normal distributions, our analysis provides explicit expressions for the mean estimates and the bounds of their variances. The accuracy and the efficiency of our DLBMC and BO based optimal design are validated and demonstrated with numerical experiments.
Highlights
As acquiring data in experiments is generally computationally demanding and time-consuming, maximizing the informativeness of experimental data is of crucial importance
The contributions of this work are three-fold: first we develop a novel double-loop Bayesian Monte Carlo (DLBMC) to efficiently compute expected information gain (EIG); second we analyze the Bayesian Monte Carlo (BMC) for the normal and the uniform distributions; third we propose Bayesian optimization (BO) to obtain the maximizer of EIG
Bayesian Monte Carlo (DLBMC) estimator is proposed for evaluating the EIG in this work
Summary
As acquiring data in experiments is generally computationally demanding and time-consuming, maximizing the informativeness of experimental data is of crucial importance. In the area of climate science, a complex system with various stochastic inputs is integrated to represent the real climate situation. The locations and the time of putting sensors to collect climate observations are optional. Careful selections of sensor placements are required (see Reference [1] for a detailed discussion). Many works focus on finding experimental data carrying more information, and this topic is usually referred to as optimal experimental design (OED) [2]. We consider the OED problem in the context of the Bayesian inverse problem
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