Fast Bayesian experimental design: Laplace-based importance sampling for the expected information gain

Abstract

In calculating expected information gain in optimal Bayesian experimental design, the computation of the inner loop in the classical double-loop Monte Carlo requires a large number of samples and suffers from underflow if the number of samples is small. These drawbacks can be avoided by using an importance sampling approach. We present a computationally efficient method for optimal Bayesian experimental design that introduces importance sampling based on the Laplace method to the inner loop. We derive the optimal values for the method parameters in which the average computational cost is minimized according to the desired error tolerance. We use three numerical examples to demonstrate the computational efficiency of our method compared with the classical double-loop Monte Carlo, and a more recent single-loop Monte Carlo method that uses the Laplace method as an approximation of the return value of the inner loop. The first example is a scalar problem that is linear in the uncertain parameter. The second example is a nonlinear scalar problem. The third example deals with the optimal sensor placement for an electrical impedance tomography experiment to recover the fiber orientation in laminate composites.

42 pages, 35 figures

Cited by in corpus (27)

• Goal-Oriented Optimal Design of Experiments for Large-Scale Bayesian Linear Inverse Problems
• Bayesian Sequential Optimal Experimental Design for Nonlinear Models Using Policy Gradient Reinforcement Learning
• A note on tools for prediction under uncertainty and identifiability of SIR-like dynamical systems for epidemiology
• Variational Bayesian experimental design for geophysical applications: seismic source location, amplitude versus offset inversion, and estimating CO2 saturations in a subsurface reservoir
• Multilevel Monte Carlo estimation of expected information gains
• Variational Bayesian Approximation of Inverse Problems using Sparse Precision Matrices
• Optimal Bayesian experimental design for subsurface flow problems
• Generalized modes in Bayesian inverse problems
• A fast and scalable computational framework for large-scale and high-dimensional Bayesian optimal experimental design
• Unbiased MLMC stochastic gradient-based optimization of Bayesian experimental designs
• A layered multiple importance sampling scheme for focused optimal Bayesian experimental design
• Variational Bayesian Optimal Experimental Design with Normalizing Flows
• Stability estimates for the expected utility in Bayesian optimal experimental design
• Small-noise approximation for Bayesian optimal experimental design with nuisance uncertainty
• Monte Carlo Integration with adaptive variance selection for improved stochastic Efficient Global Optimization
• Non-asymptotic error estimates for the Laplace approximation in Bayesian inverse problems
• Optimal Design of Validation Experiments for the Prediction of Quantities of Interest
• Neural Message Passing for Objective-Based Uncertainty Quantification and Optimal Experimental Design
• A Multi-fidelity Estimator of the Expected Information Gain for Bayesian Optimal Experimental Design
• Bayesian Experimental Design for Model Discrepancy Calibration: An Auto-Differentiable Ensemble Kalman Inversion Approach
• Goal-Oriented Bayesian Optimal Experimental Design for Nonlinear Models using Markov Chain Monte Carlo
• Optimal Experimental Design for Reliable Learning of History-Dependent Constitutive Laws
• Bayesian Experimental Design for Model Discrepancy Calibration: A Rivalry between Kullback--Leibler Divergence and Wasserstein Distance
• Ensemble-Based Experimental Design for Targeting Data Acquisition to Inform Climate Models
• Efficient Propagation of Uncertainties in Manufacturing Supply Chains: Time Buckets, L-leap and Multilevel Monte Carlo
• An efficient estimation of nested expectations without conditional sampling
• Multimodal Information Gain in Bayesian Design of Experiments