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Gaussian Process Based Expected Information Gain Computation for Bayesian Optimal Design.

Zhihang Xu1,2,3, Qifeng Liao1

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Summary
This summary is machine-generated.

This study introduces a novel double-loop Bayesian Monte Carlo (DLBMC) method and Bayesian optimization (BO) for efficient optimal experimental design (OED). These methods reduce computational costs for maximizing expected information gain (EIG) using fewer samples.

Keywords:
Bayesian Monte CarloBayesian optimal experimental designBayesian optimization

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Area of Science:

  • Computational Mathematics
  • Statistical Inference
  • Experimental Design

Background:

  • Optimal experimental design (OED) is crucial for efficient Bayesian inversion.
  • Maximizing expected information gain (EIG) is a common OED approach but involves computationally expensive likelihood functions.

Purpose of the Study:

  • To develop a computationally efficient method for calculating EIG.
  • To propose a Bayesian optimization (BO) strategy for finding the OED maximizer with minimal samples.

Main Methods:

  • A novel double-loop Bayesian Monte Carlo (DLBMC) method is developed to compute EIG.
  • A Bayesian optimization (BO) strategy is employed to identify the optimal experimental design parameters.

Main Results:

  • The DLBMC method efficiently computes EIG, significantly reducing computational cost.
  • The BO strategy effectively finds the EIG maximizer using a small number of samples.
  • Explicit expressions for mean estimates and variance bounds are derived for Bayesian Monte Carlo on uniform and normal distributions.

Conclusions:

  • The developed DLBMC and BO-based OED methods offer a computationally efficient and accurate approach for Bayesian inversion.
  • Numerical experiments validate the effectiveness and efficiency of the proposed methods.